2 Marker Question

Simplified Physics: 2 Marks Questions

Class 11

Chapter–1: Units and Measurements

Topic 1: Need for Measurement and SI Units

• Define a fundamental SI unit and give two examples. (CBSE 2020)
  A fundamental SI unit is a basic unit of measurement in the International System of Units (SI) that cannot be derived from other units. Examples include the meter (m) for length and the kilogram (kg) for mass.

Topic 2: Significant Figures

• How many significant figures are in 0.007050? (CBSE 2021)
  The number 0.007050 has 4 significant figures. The zeros before 7 are not significant, but the zeros between 7 and 5 are significant.

Topic 3: Dimensions and Dimensional Analysis

• Write the dimensional formula of force. (CBSE 2018)
  The dimensional formula of force is [M L T⁻²], where M is mass, L is length, and T is time.

Topic 4: Uncertainty in Measurements

• Define absolute uncertainty with an example. (CBSE 2022)
  Absolute uncertainty is the margin of error associated with a measurement. For example, if a length is measured as 5.0 ± 0.1 cm, the absolute uncertainty is 0.1 cm.

Chapter–2: Motion in a Straight Line

Topic 1: Motion and Velocity

• What is the difference between average velocity and instantaneous velocity? (CBSE 2019)
  Average velocity is the total displacement divided by total time, while instantaneous velocity is the velocity at a specific instant, determined by the slope of the position-time graph at that point.

Topic 2: Uniformly Accelerated Motion

• Derive the relation v = u + at. (CBSE 2020)
  The relation v = u + at is derived from the definition of acceleration (a = Δv/Δt), where v is final velocity, u is initial velocity, a is acceleration, and t is time, leading to v = u + at.

Chapter–3: Motion in a Plane

Topic 1: Vector Addition

• Define the addition of vectors and give an example. (CBSE 2021)
  Vector addition is the process of combining two or more vectors to find their resultant. Example: If vector A = 3i + 4j and vector B = 2i + 5j, the resultant is (3+2)i + (4+5)j = 5i + 9j.

Topic 2: Projectile Motion

• What is the maximum height in projectile motion? (CBSE 2017)
  The maximum height in projectile motion is given by h = (u² sin²θ)/(2g), where u is initial velocity, θ is the angle of projection, and g is acceleration due to gravity.

Chapter–4: Laws of Motion

Topic 1: Newton's Laws

• State Newton's first law of motion. (CBSE 2018)
  Newton's first law of motion states that an object at rest stays at rest, and an object in motion stays in motion with a constant velocity, unless acted upon by a net external force.

Topic 2: Conservation of Momentum

• State the law of conservation of linear momentum. (CBSE 2019)
  The law of conservation of linear momentum states that the total momentum of a closed system remains constant if no external forces act on it.

Chapter–5: Work, Energy and Power

Topic 1: Work and Energy

• Define work done by a constant force. (CBSE 2020)
  Work done by a constant force is the product of the force, the displacement, and the cosine of the angle between them, given by W = F d cosθ.

Topic 2: Potential Energy

• What is potential energy of a spring? (CBSE 2021)
  The potential energy of a spring is given by PE = (1/2)kx², where k is the spring constant and x is the displacement from the equilibrium position.

Chapter–6: System of Particles and Rotational Motion

Topic 1: Centre of Mass

• Define the centre of mass of a two-particle system. (CBSE 2019)
  The centre of mass of a two-particle system is the point where the total mass of the system can be considered to be concentrated, calculated as (m₁x₁ + m₂x₂)/(m₁ + m₂).

Topic 2: Moment of Inertia

• What is moment of inertia? (CBSE 2020)
  Moment of inertia is a measure of an object's resistance to angular acceleration, given by I = Σmr², where m is mass and r is the perpendicular distance from the axis of rotation.

Chapter–7: Gravitation

Topic 1: Universal Law of Gravitation

• State Kepler's second law of planetary motion. (CBSE 2021)
  Kepler's second law states that a line joining a planet to the Sun sweeps out equal areas in equal intervals of time.

Topic 2: Gravitational Potential

• Define gravitational potential energy. (CBSE 2018)
  Gravitational potential energy is the energy possessed by an object due to its position in a gravitational field, given by PE = mgh, where m is mass, g is acceleration due to gravity, and h is height.

Chapter–8: Mechanical Properties of Solids

Topic 1: Elasticity

• State Hooke's law. (CBSE 2019)
  Hooke's law states that the force required to extend or compress a spring is directly proportional to the displacement, expressed as F = -kx.

Chapter–9: Mechanical Properties of Fluids

Topic 1: Pressure

• State Pascal's law. (CBSE 2020)
  Pascal's law states that the pressure applied to an enclosed fluid is transmitted uniformly in all directions.

Chapter–10: Thermal Properties of Matter

Topic 1: Thermal Expansion

• What is anomalous expansion of water? (CBSE 2021)
  Anomalous expansion of water is the unusual property where water expands when cooled from 4°C to 0°C, unlike most substances.

Chapter–11: Thermodynamics

Topic 1: Laws of Thermodynamics

• State the first law of thermodynamics. (CBSE 2022)
  The first law of thermodynamics states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system, ΔU = Q - W.

Topic 2: Thermodynamic Processes

• Define an isothermal process. (CBSE 2019)
  An isothermal process is a thermodynamic process in which the temperature of the system remains constant during the change.

Chapter–12: Kinetic Theory

Topic 1: Kinetic Interpretation

• What is the kinetic interpretation of temperature? (CBSE 2020)
  The kinetic interpretation of temperature states that the temperature of a gas is proportional to the average kinetic energy of its molecules.

Topic 2: Mean Free Path

• Define mean free path. (CBSE 2021)
  Mean free path is the average distance traveled by a molecule between successive collisions in a gas.

Chapter–13: Oscillations

Topic 1: Simple Harmonic Motion

• Define simple harmonic motion. (CBSE 2018)
  Simple harmonic motion is a type of periodic motion where the restoring force is directly proportional to the displacement and acts in the opposite direction.

Topic 2: Energy in SHM

• What is the total energy of a particle in SHM? (CBSE 2019)
  The total energy of a particle in simple harmonic motion is constant and given by E = (1/2)mω²A², where m is mass, ω is angular frequency, and A is amplitude.

Chapter–14: Waves

Topic 1: Wave Motion

• What is the difference between transverse and longitudinal waves? (CBSE 2020)
  Transverse waves have oscillations perpendicular to the direction of wave propagation, while longitudinal waves have oscillations parallel to the direction of wave propagation.

Topic 2: Wave Speed

• Derive the formula for the speed of a wave. (CBSE 2021)
  The speed of a wave is given by v = fλ, where f is the frequency and λ is the wavelength, derived from the relationship between wave properties.

Class 12

Chapter–1: Electric Charges and Fields

Topic 1: Electric Charges

• 1. What are the types of electric charges? (CBSE 2019)
  The types of electric charges are positive and negative, with like charges repelling and unlike charges attracting each other.
• 2. Define the SI unit of electric charge. (CBSE 2018)
  The SI unit of electric charge is the coulomb (C), defined as the charge transported by a constant current of one ampere in one second.
• 3. What is the charge on an electron? (CBSE 2020)
  The charge on an electron is approximately -1.6 × 10⁻¹⁹ coulombs.
• 4. Explain the term quantization of charge. (CBSE 2017)
  Quantization of charge means that electric charge exists in discrete amounts, which are integral multiples of the elementary charge, i.e., 1.6 × 10⁻¹⁹ C.
• 5. State the law of conservation of electric charge. (CBSE 2016)
  The law of conservation of electric charge states that the total electric charge in an isolated system remains constant; it can neither be created nor destroyed.
• 6. Differentiate between conductors and insulators with respect to electric charges. (CBSE 2019)
  Conductors allow electric charges to flow freely (e.g., copper, silver), while insulators resist the flow of electric charges (e.g., glass, rubber).
• 7. State Coulomb’s law in electrostatics. (CBSE 2015)
  Coulomb’s law states that the force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them, expressed as F = k |q₁q₂|/r², where k is Coulomb’s constant.
• 8. Define electric field. (CBSE 2021)
  An electric field is a region around a charged object where another charge experiences a force due to the presence of the charged object.
• 9. What is the SI unit of electric field strength? (CBSE 2018)
  The SI unit of electric field strength is newton per coulomb (N/C) or volt per meter (V/m).
• 10. What is the principle of superposition in electrostatics? (CBSE 2017)
  The principle of superposition states that the net electric force on a charge due to multiple charges is the vector sum of the forces exerted by each charge individually.

Topic 2: Coulomb's Law

• 1. State Coulomb's law. (CBSE 2020)
  Coulomb's law states that the force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them, expressed as F = k |q₁q₂|/r², where k is Coulomb's constant.
• 2. What is the value of Coulomb’s constant in SI units? (CBSE 2019)
  The value of Coulomb’s constant (k) in SI units is approximately 8.99 × 10⁹ N·m²/C².
• 3. How does the force between two charges change if the distance between them is doubled? (CBSE 2018)
  According to Coulomb’s law, if the distance between two charges is doubled, the force becomes one-fourth of its original value, as the force is inversely proportional to the square of the distance.
• 4. What is the nature of the force between two positive charges? (CBSE 2017)
  The force between two positive charges is repulsive, as like charges repel each other according to Coulomb’s law.
• 5. How does the force between two charges change if the medium between them changes from air to water? (CBSE 2021)
  The force between two charges decreases in a medium like water because the force is inversely proportional to the permittivity of the medium, and water has a higher permittivity than air.
• 6. What is the mathematical expression for Coulomb’s law in vector form? (CBSE 2016)
  The vector form of Coulomb’s law is given by F = k (q₁q₂/r²) * r̂, where F is the force, k is Coulomb’s constant, q₁ and q₂ are the charges, r is the distance between them, and r̂ is the unit vector in the direction of the force.
• 7. What happens to the force between two charges if the magnitude of both charges is doubled? (CBSE 2019)
  If the magnitude of both charges is doubled, the force between them becomes four times the original force, as the force is directly proportional to the product of the charges.
• 8. Define the permittivity of free space. (CBSE 2015)
  The permittivity of free space (ε₀) is a physical constant that describes the ability of a vacuum to permit electric field lines, with a value of approximately 8.85 × 10⁻¹² C²/N·m².
• 9. Why is Coulomb’s law applicable only to point charges? (CBSE 2020)
  Coulomb’s law is applicable to point charges because it assumes charges are concentrated at a single point with no spatial extent, ensuring the inverse-square law holds accurately.
• 10. What is the significance of the negative sign in Coulomb’s law for unlike charges? (CBSE 2018)
  The negative sign in Coulomb’s law for unlike charges indicates an attractive force, as the force acts in the opposite direction to the displacement vector between the charges.

Topic 3: Electric Field

• 1. Define electric field intensity. (CBSE 2021)
  Electric field intensity at a point is the force experienced by a unit positive charge placed at that point, given by E = F/q.
• 2. What is the SI unit of electric field intensity? (CBSE 2019)
  The SI unit of electric field intensity is newton per coulomb (N/C) or volt per meter (V/m).
• 3. What is an electric field line? (CBSE 2018)
  An electric field line is an imaginary line or curve drawn such that the tangent at any point gives the direction of the electric field at that point.
• 4. How does the electric field due to a point charge vary with distance? (CBSE 2020)
  The electric field due to a point charge varies inversely with the square of the distance from the charge, given by E = kq/r², where k is Coulomb’s constant, q is the charge, and r is the distance.
• 5. What is the electric field inside a uniformly charged spherical shell? (CBSE 2017)
  The electric field inside a uniformly charged spherical shell is zero, as per Gauss’s law.
• 6. State the principle of superposition for electric fields. (CBSE 2016)
  The principle of superposition states that the net electric field at a point due to multiple charges is the vector sum of the electric fields produced by each charge individually.
• 7. What is the direction of the electric field due to a positive point charge? (CBSE 2019)
  The electric field due to a positive point charge is directed radially outward from the charge.
• 8. How does the electric field change if the medium between a point charge and a test charge is changed? (CBSE 2020)
  The electric field decreases if the medium has a higher permittivity than vacuum, as E = q/(4πεr²), where ε is the permittivity of the medium.
• 9. What is the physical significance of electric field lines not intersecting? (CBSE 2018)
  Electric field lines do not intersect because at any point, the electric field has a unique direction. If lines intersected, it would imply multiple directions for the field at that point, which is physically impossible.
• 10. What is the electric field due to an infinite plane sheet of charge? (CBSE 2017)
  The electric field due to an infinite plane sheet of charge with surface charge density σ is E = σ/(2ε₀), where ε₀ is the permittivity of free space, and it is uniform and perpendicular to the sheet.

Topic 4: Electric Field Lines

• 1. What are the properties of electric field lines? (CBSE 2018)
  Electric field lines start from positive charges and end at negative charges, never intersect, and their density indicates the field strength.
• 2. Why do electric field lines never intersect? (CBSE 2019)
  Electric field lines never intersect because the electric field at any point has a unique direction. Intersection would imply multiple directions for the field at that point, which is physically impossible.
• 3. What do electric field lines indicate about the strength of the electric field? (CBSE 2020)
  The density of electric field lines indicates the strength of the electric field; closer lines represent a stronger field, while farther lines indicate a weaker field.
• 4. How do electric field lines behave near a conductor? (CBSE 2017)
  Electric field lines are perpendicular to the surface of a conductor at its surface, and no field lines exist inside a conductor in electrostatic equilibrium.
• 5. What is the direction of electric field lines for a positive point charge? (CBSE 2016)
  For a positive point charge, electric field lines are directed radially outward from the charge.
• 6. How do electric field lines differ for a negative point charge? (CBSE 2019)
  For a negative point charge, electric field lines are directed radially inward towards the charge.
• 7. What is the significance of the tangent to an electric field line? (CBSE 2021)
  The tangent to an electric field line at any point gives the direction of the electric field at that point.
• 8. Why are electric field lines continuous in a charge-free region? (CBSE 2018)
  Electric field lines are continuous in a charge-free region because the electric field is well-defined and varies smoothly without abrupt changes in the absence of charges.
• 9. How do electric field lines behave in a uniform electric field? (CBSE 2020)
  In a uniform electric field, electric field lines are straight, parallel, and equally spaced, indicating a constant field strength and direction.
• 10. What happens to electric field lines in a region with no electric field? (CBSE 2017)
  In a region with no electric field, such as inside a conductor in electrostatic equilibrium, no electric field lines exist.

Topic 5: Electric Dipole

• 1. Define an electric dipole and its moment. (CBSE 2019)
  An electric dipole is a pair of equal and opposite charges separated by a small distance. Its dipole moment is p = qd, where q is the charge and d is the separation distance, directed from the negative to the positive charge.
• 2. What is the SI unit of electric dipole moment? (CBSE 2018)
  The SI unit of electric dipole moment is coulomb-meter (C·m).
• 3. What is the electric field at a point on the axial line of an electric dipole? (CBSE 2020)
  The electric field at a point on the axial line of an electric dipole is given by E = (2kp)/r³, where k is Coulomb’s constant, p is the dipole moment, and r is the distance from the center of the dipole, directed along the dipole axis.
• 4. What is the electric field at a point on the equatorial line of an electric dipole? (CBSE 2017)
  The electric field at a point on the equatorial line of an electric dipole is given by E = kp/r³, where k is Coulomb’s constant, p is the dipole moment, and r is the distance from the center of the dipole, directed opposite to the dipole moment.
• 5. What is the torque experienced by an electric dipole in a uniform electric field? (CBSE 2016)
  The torque on an electric dipole in a uniform electric field is given by τ = p × E, where p is the dipole moment and E is the electric field, with magnitude τ = pE sinθ, where θ is the angle between p and E.
• 6. When is the torque on an electric dipole maximum in a uniform electric field? (CBSE 2019)
  The torque on an electric dipole is maximum when the dipole moment is perpendicular to the electric field (θ = 90°), giving τ = pE.
• 7. What is the potential energy of an electric dipole in a uniform electric field? (CBSE 2021)
  The potential energy of an electric dipole in a uniform electric field is given by U = -p · E, or U = -pE cosθ, where p is the dipole moment, E is the electric field, and θ is the angle between p and E.
• 8. Why is the net force on an electric dipole zero in a uniform electric field? (CBSE 2018)
  The net force on an electric dipole in a uniform electric field is zero because the equal and opposite charges experience equal and opposite forces, which cancel each other out.
• 9. How does the electric field due to a dipole vary with distance at large distances? (CBSE 2020)
  At large distances, the electric field due to an electric dipole varies inversely with the cube of the distance (E ∝ 1/r³).
• 10. What is the direction of the dipole moment of an electric dipole? (CBSE 2017)
  The dipole moment of an electric dipole is directed from the negative charge to the positive charge.

Topic 6: Gauss’s Law

• 1. State Gauss’s law. (CBSE 2020)
  Gauss’s law states that the electric flux through a closed surface is proportional to the charge enclosed, given by Φ = q/ε₀, where Φ is the electric flux, q is the enclosed charge, and ε₀ is the permittivity of free space.
• 2. What is electric flux? (CBSE 2019)
  Electric flux is a measure of the number of electric field lines passing through a given surface, defined as Φ = E · A cosθ, where E is the electric field, A is the area, and θ is the angle between the field and the normal to the surface.
• 3. What is the SI unit of electric flux? (CBSE 2018)
  The SI unit of electric flux is newton meter squared per coulomb (N·m²/C) or volt-meter (V·m).
• 4. Why is Gauss’s law useful in calculating electric fields? (CBSE 2021)
  Gauss’s law is useful for calculating electric fields in highly symmetric charge distributions (e.g., spherical, cylindrical, or planar symmetry) as it relates the electric flux through a closed surface to the enclosed charge, simplifying calculations.
• 5. What is the electric field inside a uniformly charged spherical shell? (CBSE 2017)
  According to Gauss’s law, the electric field inside a uniformly charged spherical shell is zero, as the enclosed charge is zero.
• 6. What is the electric field due to an infinite plane sheet of charge using Gauss’s law? (CBSE 2019)
  Using Gauss’s law, the electric field due to an infinite plane sheet of charge with surface charge density σ is E = σ/(2ε₀), where ε₀ is the permittivity of free space, and it is uniform and perpendicular to the sheet.
• 7. What is a Gaussian surface? (CBSE 2016)
  A Gaussian surface is an imaginary closed surface used in Gauss’s law to calculate the electric flux and determine the electric field for a given charge distribution.
• 8. Why does Gauss’s law not hold for non-closed surfaces? (CBSE 2020)
  Gauss’s law applies only to closed surfaces because it relates the total electric flux through a closed surface to the charge enclosed within it, which is not well-defined for non-closed surfaces.
• 9. What is the electric field due to a long infinite line of charge using Gauss’s law? (CBSE 2018)
  Using Gauss’s law, the electric field due to a long infinite line of charge with linear charge density λ is E = λ/(2πε₀r), where ε₀ is the permittivity of free space and r is the radial distance from the line.
• 10. How does Gauss’s law relate to Coulomb’s law? (CBSE 2017)
  Gauss’s law is a general form of Coulomb’s law; Coulomb’s law can be derived from Gauss’s law for a point charge by choosing a spherical Gaussian surface, showing that the electric field E = kq/r² is consistent with Φ = q/ε₀.

Topic 7: Applications of Gauss’s Law

• 1. How is Gauss’s law used to find the electric field due to a charged sphere? (CBSE 2021)
  Gauss’s law is applied by considering a spherical Gaussian surface around the charged sphere, leading to E = kQ/r² for points outside (where Q is the total charge and r is the distance from the center) and E = 0 inside a uniformly charged hollow sphere.
• 2. How can Gauss’s law be used to find the electric field due to an infinite plane sheet of charge? (CBSE 2019)
  Using Gauss’s law, a cylindrical Gaussian surface perpendicular to the plane sheet with surface charge density σ is chosen, yielding a uniform electric field E = σ/(2ε₀), where ε₀ is the permittivity of free space.
• 3. How is the electric field due to an infinite line of charge derived using Gauss’s law? (CBSE 2018)
  Gauss’s law is applied using a cylindrical Gaussian surface coaxial with the line of charge with linear charge density λ, resulting in an electric field E = λ/(2πε₀r), where r is the radial distance from the line.
• 4. Why is the electric field inside a uniformly charged spherical shell zero? (CBSE 2020)
  Gauss’s law shows that the electric field inside a uniformly charged spherical shell is zero because the charge enclosed by a Gaussian surface inside the shell is zero, leading to zero flux and thus E = 0.
• 5. How is Gauss’s law used to find the electric field due to a uniformly charged solid sphere? (CBSE 2017)
  For a uniformly charged solid sphere, Gauss’s law gives E = (ρr)/(3ε₀) for points inside (r < R) and E = (Q)/(4πε₀r²) for points outside (r > R), where ρ is the volume charge density, Q is the total charge, and R is the radius.
• 6. How does Gauss’s law apply to a charged conductor in electrostatic equilibrium? (CBSE 2016)
  Gauss’s law shows that the electric field inside a charged conductor in electrostatic equilibrium is zero, as all charge resides on the surface, and a Gaussian surface inside encloses no charge.
• 7. How is the electric field due to two parallel charged sheets derived using Gauss’s law? (CBSE 2019)
  Using Gauss’s law, the electric field between two parallel sheets with surface charge densities ±σ is E = σ/ε₀ (directed from positive to negative sheet), while outside both sheets, the fields cancel, giving E = 0.
• 8. Why is a Gaussian surface chosen to be symmetric with the charge distribution? (CBSE 2020)
  A symmetric Gaussian surface is chosen because it simplifies the calculation of electric flux, as the electric field is constant or zero over the surface, making Gauss’s law easier to apply.
• 9. How is Gauss’s law used to derive the electric field of a point charge? (CBSE 2018)
  By applying Gauss’s law to a spherical Gaussian surface centered on a point charge q, the electric field is derived as E = q/(4πε₀r²), consistent with Coulomb’s law.
• 10. What is the electric field due to a charged cylindrical shell using Gauss’s law? (CBSE 2017)
  Using Gauss’s law, the electric field due to a charged cylindrical shell with surface charge density σ is E = σr/(ε₀R) for points inside (r < R) and E = σR/(ε₀r) for points outside (r > R), where R is the radius of the cylinder.

Chapter–2: Electrostatic Potential and Capacitance

Topic 1: Electrostatic Potential

• 1. Define electrostatic potential at a point. (CBSE 2019)
  Electrostatic potential at a point is the work done per unit positive charge in bringing a test charge from infinity to that point, given by V = W/q.
• 2. What is the SI unit of electrostatic potential? (CBSE 2018)
  The SI unit of electrostatic potential is the volt (V), where 1 volt = 1 joule per coulomb (J/C).
• 3. What is the electrostatic potential due to a point charge? (CBSE 2020)
  The electrostatic potential due to a point charge q at a distance r is given by V = kq/r, where k is Coulomb’s constant.
• 4. How is the electric field related to the electrostatic potential? (CBSE 2017)
  The electric field E is the negative gradient of the electrostatic potential V, given by E = -∇V.
• 5. What is the electrostatic potential inside a uniformly charged spherical shell? (CBSE 2021)
  Inside a uniformly charged spherical shell, the electrostatic potential is constant and equal to V = kQ/R, where Q is the total charge and R is the radius of the shell.
• 6. What is the potential energy of a system of two point charges? (CBSE 2016)
  The potential energy of a system of two point charges q₁ and q₂ separated by a distance r is given by U = kq₁q₂/r, where k is Coulomb’s constant.
• 7. What is an equipotential surface? (CBSE 2019)
  An equipotential surface is a surface on which the electrostatic potential is the same at all points, and the electric field is perpendicular to the surface.
• 8. Why is no work done in moving a charge on an equipotential surface? (CBSE 2020)
  No work is done in moving a charge on an equipotential surface because the potential is constant, and the electric field is perpendicular to the surface, resulting in zero force component along the surface.
• 9. What is the electrostatic potential due to an electric dipole at an axial point? (CBSE 2018)
  The electrostatic potential due to an electric dipole at a point on its axial line at distance r is V = kp/r², where p is the dipole moment and k is Coulomb’s constant.
• 10. Why is the electrostatic potential due to a dipole zero at points on the equatorial plane? (CBSE 2017)
  The electrostatic potential due to an electric dipole is zero on the equatorial plane because the potentials due to the positive and negative charges cancel each other out.

Topic 2: Potential Due to a Dipole

• 1. What is the potential due to an electric dipole at an equatorial point? (CBSE 2020)
  The potential due to an electric dipole at an equatorial point is zero, as the contributions from the positive and negative charges cancel each other.
• 2. What is the potential due to an electric dipole at a point on its axial line? (CBSE 2019)
  The potential due to an electric dipole at a point on its axial line at distance r is V = kp/r², where k is Coulomb’s constant and p is the dipole moment.
• 3. How does the potential due to an electric dipole vary with distance at large distances? (CBSE 2018)
  At large distances, the potential due to an electric dipole varies inversely with the square of the distance, V ∝ 1/r².
• 4. Why is the potential due to a dipole zero on the equatorial plane? (CBSE 2021)
  The potential due to a dipole is zero on the equatorial plane because the potentials from the positive and negative charges are equal in magnitude but opposite in sign, canceling each other.
• 5. What is the general expression for the potential due to an electric dipole? (CBSE 2017)
  The general expression for the potential due to an electric dipole at a point (r, θ) is V = (kp cosθ)/r², where p is the dipole moment, k is Coulomb’s constant, r is the distance from the dipole’s center, and θ is the angle between the dipole axis and the position vector.
• 6. How does the potential due to a dipole differ from that of a point charge? (CBSE 2016)
  The potential due to a dipole falls off as 1/r² and depends on the angle θ, whereas the potential due to a point charge falls off as 1/r and is independent of direction.
• 7. What is the potential energy of an electric dipole in a uniform electric field? (CBSE 2019)
  The potential energy of an electric dipole in a uniform electric field is U = -p · E = -pE cosθ, where p is the dipole moment, E is the electric field, and θ is the angle between them.
• 8. At what angle is the potential due to an electric dipole maximum? (CBSE 2020)
  The potential due to an electric dipole is maximum when θ = 0° (along the axial line in the direction of the dipole moment), giving V = kp/r².
• 9. Why does the potential due to a dipole not depend on the medium at large distances? (CBSE 2018)
  At large distances, the potential due to a dipole depends only on the dipole moment and distance (V = kp/r²), and the effect of the medium’s permittivity cancels out due to the dipole’s neutral nature.
• 10. What is the potential due to an electric dipole at a point far away compared to its separation? (CBSE 2017)
  For a point far away compared to the dipole’s separation, the potential is approximated as V = (kp cosθ)/r², where p is the dipole moment, k is Coulomb’s constant, r is the distance, and θ is the angle with the dipole axis.

Topic 3: Electrostatic Potential Energy

• 1. Define electrostatic potential energy of a system of charges. (CBSE 2021)
  Electrostatic potential energy of a system of charges is the work done in assembling the charges from infinity to their respective positions, given by U = kq₁q₂/r for two charges, where k is Coulomb’s constant, q₁ and q₂ are the charges, and r is the separation.
• 2. What is the potential energy of a system of two point charges? (CBSE 2019)
  The potential energy of a system of two point charges q₁ and q₂ separated by a distance r is U = kq₁q₂/r, where k is Coulomb’s constant.
• 3. What is the significance of the sign of potential energy in a system of charges? (CBSE 2018)
  The sign of potential energy indicates the nature of interaction: positive for repulsive forces (like charges) and negative for attractive forces (unlike charges).
• 4. How does the potential energy change if the distance between two charges is doubled? (CBSE 2020)
  If the distance between two charges is doubled, the potential energy becomes half its original value, as U ∝ 1/r.
• 5. What is the potential energy of an electric dipole in a uniform electric field? (CBSE 2017)
  The potential energy of an electric dipole in a uniform electric field is U = -p · E = -pE cosθ, where p is the dipole moment, E is the electric field, and θ is the angle between them.
• 6. When is the potential energy of a dipole in a uniform electric field minimum? (CBSE 2019)
  The potential energy of a dipole in a uniform electric field is minimum when the dipole is aligned with the field (θ = 0°), giving U = -pE.
• 7. How is the potential energy of a system of three charges calculated? (CBSE 2016)
  The potential energy of a system of three charges q₁, q₂, and q₃ is the sum of the pairwise potential energies: U = k(q₁q₂/r₁₂ + q₁q₃/r₁₃ + q₂q₃/r₂₃), where r₁₂, r₁₃, and r₂₃ are the distances between the charges.
• 8. What is the potential energy of a charge in a uniform electric field? (CBSE 2020)
  The potential energy of a charge q in a uniform electric field is U = qV, where V is the electrostatic potential at the position of the charge.
• 9. Why is the potential energy of two unlike charges negative? (CBSE 2018)
  The potential energy of two unlike charges is negative because their interaction is attractive, requiring work to be done by an external agent to separate them, resulting in U = kq₁q₂/r being negative.
• 10. How does the potential energy change if the medium between two charges changes? (CBSE 2017)
  The potential energy decreases if the medium’s permittivity increases (e.g., from air to water), as U = q₁q₂/(4πεr), where ε is the permittivity of the medium.

Topic 4: Capacitance

• 1. What is the capacitance of a parallel plate capacitor? (CBSE 2018)
  The capacitance of a parallel plate capacitor is given by C = ε₀A/d, where ε₀ is the permittivity of free space, A is the area of the plates, and d is the separation between the plates.
• 2. Define capacitance of a capacitor. (CBSE 2019)
  Capacitance is defined as the ability of a capacitor to store charge, given by C = Q/V, where Q is the charge stored and V is the potential difference across the capacitor.
• 3. What is the SI unit of capacitance? (CBSE 2020)
  The SI unit of capacitance is the farad (F), where 1 farad = 1 coulomb per volt (C/V).
• 4. How does the capacitance of a parallel plate capacitor change if a dielectric is inserted between the plates? (CBSE 2017)
  The capacitance of a parallel plate capacitor increases by a factor of κ (dielectric constant) when a dielectric is inserted, becoming C = κε₀A/d, where κ > 1.
• 5. What is the effect on capacitance if the distance between the plates of a capacitor is doubled? (CBSE 2021)
  If the distance between the plates of a capacitor is doubled, the capacitance becomes half its original value, as C ∝ 1/d.
• 6. How is the energy stored in a capacitor calculated? (CBSE 2016)
  The energy stored in a capacitor is given by U = (1/2)CV² = (1/2)Q²/C = (1/2)QV, where C is the capacitance, V is the potential difference, and Q is the charge.
• 7. What is the equivalent capacitance of capacitors connected in series? (CBSE 2019)
  For capacitors connected in series, the equivalent capacitance is given by 1/C_eq = 1/C₁ + 1/C₂ + ... + 1/Cₙ.
• 8. What is the equivalent capacitance of capacitors connected in parallel? (CBSE 2020)
  For capacitors connected in parallel, the equivalent capacitance is the sum of individual capacitances: C_eq = C₁ + C₂ + ... + Cₙ.
• 9. Why does the capacitance of a parallel plate capacitor increase with a dielectric? (CBSE 2018)
  The capacitance increases with a dielectric because the dielectric reduces the electric field between the plates by polarization, increasing the permittivity (κε₀), thus C = κε₀A/d.
• 10. What happens to the energy stored in a capacitor if the potential difference across it is doubled? (CBSE 2017)
  If the potential difference across a capacitor is doubled, the energy stored increases fourfold, as U = (1/2)CV², and U ∝ V².

Topic 5: Combination of Capacitors

• 1. What is the equivalent capacitance when capacitors are connected in series? (CBSE 2019)
  The equivalent capacitance of capacitors in series is given by 1/C_eq = 1/C₁ + 1/C₂ + ..., where C₁, C₂, etc., are the individual capacitances.
• 2. What is the equivalent capacitance when capacitors are connected in parallel? (CBSE 2020)
  The equivalent capacitance of capacitors in parallel is the sum of individual capacitances: C_eq = C₁ + C₂ + ... + Cₙ.
• 3. How is the charge distributed in a series combination of capacitors? (CBSE 2018)
  In a series combination of capacitors, the charge on each capacitor is the same, and the total charge is equal to the charge on the equivalent capacitor.
• 4. How is the potential difference distributed in a series combination of capacitors? (CBSE 2017)
  In a series combination, the potential difference across each capacitor is inversely proportional to its capacitance, and the total potential difference is the sum of individual potential differences: V = V₁ + V₂ + ... .
• 5. How is the charge distributed in a parallel combination of capacitors? (CBSE 2021)
  In a parallel combination, the charge on each capacitor is proportional to its capacitance (Q = CV), and the total charge is the sum of the charges on individual capacitors.
• 6. What is the potential difference across capacitors in a parallel combination? (CBSE 2016)
  In a parallel combination, the potential difference across each capacitor is the same and equal to the potential difference applied across the combination.
• 7. How does the equivalent capacitance of two identical capacitors in series compare to one capacitor? (CBSE 2019)
  For two identical capacitors of capacitance C in series, the equivalent capacitance is C_eq = C/2, which is half the capacitance of one capacitor.
• 8. How does the equivalent capacitance of two identical capacitors in parallel compare to one capacitor? (CBSE 2020)
  For two identical capacitors of capacitance C in parallel, the equivalent capacitance is C_eq = 2C, which is twice the capacitance of one capacitor.
• 9. Why is the equivalent capacitance in a series combination less than the smallest individual capacitance? (CBSE 2018)
  In a series combination, the equivalent capacitance is less than the smallest individual capacitance because the reciprocal of the equivalent capacitance is the sum of the reciprocals of individual capacitances, reducing the overall ability to store charge.
• 10. How does the energy stored in a series combination of capacitors compare to a single capacitor? (CBSE 2017)
  The energy stored in a series combination of capacitors is less than that of a single capacitor with the same total charge, as the equivalent capacitance is reduced, and energy U = Q²/(2C_eq) increases with smaller C_eq.

Topic 6: Energy Stored in a Capacitor

• 1. What is the energy stored in a charged capacitor? (CBSE 2020)
  The energy stored in a charged capacitor is given by U = (1/2)CV², where C is the capacitance and V is the potential difference across it.
• 2. What are the alternative expressions for the energy stored in a capacitor? (CBSE 2019)
  The energy stored in a capacitor can also be expressed as U = (1/2)Q²/C or U = (1/2)QV, where Q is the charge, C is the capacitance, and V is the potential difference.
• 3. How does the energy stored in a capacitor change if the potential difference is doubled? (CBSE 2018)
  If the potential difference across a capacitor is doubled, the energy stored increases fourfold, as U = (1/2)CV², and U ∝ V².
• 4. What happens to the energy stored in a capacitor if the charge on it is doubled? (CBSE 2021)
  If the charge on a capacitor is doubled, the energy stored increases fourfold, as U = (1/2)Q²/C, and U ∝ Q².
• 5. How does the energy stored in a capacitor change if a dielectric is inserted between its plates? (CBSE 2017)
  If a dielectric with dielectric constant κ is inserted while keeping the potential difference constant, the capacitance increases to C' = κC, and the energy stored increases to U' = κU, where U = (1/2)CV².
• 6. Where is the energy stored in a capacitor located? (CBSE 2016)
  The energy stored in a capacitor is located in the electric field between its plates.
• 7. What is the energy density in the electric field of a capacitor? (CBSE 2019)
  The energy density in the electric field of a capacitor is given by u = (1/2)ε₀E², where ε₀ is the permittivity of free space and E is the electric field strength.
• 8. How does the energy stored in a series combination of capacitors compare to a single capacitor? (CBSE 2020)
  For a series combination of capacitors with the same total charge, the energy stored is greater than that of a single capacitor, as U = Q²/(2C_eq), and C_eq is less than the individual capacitances.
• 9. What happens to the energy stored in a capacitor if the separation between the plates is increased with the battery disconnected? (CBSE 2018)
  If the separation between the plates is increased with the battery disconnected, the capacitance decreases (C ∝ 1/d), and the energy stored increases, as U = Q²/(2C), where Q remains constant.
• 10. What is the effect on the energy stored in a capacitor if a dielectric is inserted with the battery connected? (CBSE 2017)
  If a dielectric is inserted with the battery connected, the capacitance increases to C' = κC, and the energy stored increases to U' = κU, as U = (1/2)CV² and V remains constant.

Topic 7: Dielectrics and Polarisation

• 1. What is the effect of a dielectric on capacitance? (CBSE 2021)
  The presence of a dielectric increases the capacitance of a capacitor by a factor of the dielectric constant (κ), making C = κε₀A/d, where ε₀ is the permittivity of free space, A is the plate area, and d is the separation.
• 2. What is meant by polarisation of a dielectric? (CBSE 2019)
  Polarisation of a dielectric is the process of alignment of dipole moments or separation of charges within the dielectric material in the presence of an external electric field.
• 3. What is the dielectric constant of a material? (CBSE 2018)
  The dielectric constant (κ) of a material is the ratio of the permittivity of the material (ε) to the permittivity of free space (ε₀), i.e., κ = ε/ε₀.
• 4. How does a dielectric affect the electric field between the plates of a capacitor? (CBSE 2020)
  A dielectric reduces the electric field between the plates of a capacitor by a factor of the dielectric constant (κ), as E = E₀/κ, where E₀ is the field without the dielectric.
• 5. What is the effect of a dielectric on the energy stored in a capacitor with constant voltage? (CBSE 2017)
  With constant voltage, inserting a dielectric increases the capacitance to C' = κC, and the energy stored increases to U' = κU, where U = (1/2)CV².
• 6. What is the effect of a dielectric on the energy stored in a capacitor with constant charge? (CBSE 2016)
  With constant charge, inserting a dielectric increases the capacitance to C' = κC, reducing the energy stored to U' = U/κ, where U = Q²/(2C).
• 7. What is the polarisation vector in a dielectric material? (CBSE 2019)
  The polarisation vector (P) in a dielectric is the dipole moment per unit volume, representing the extent of polarisation induced by an external electric field.
• 8. Why do dielectrics increase the capacitance of a capacitor? (CBSE 2020)
  Dielectrics increase capacitance by reducing the electric field through polarisation, which increases the effective permittivity (κε₀), leading to C = κε₀A/d.
• 9. What is the difference between polar and non-polar dielectrics? (CBSE 2018)
  Polar dielectrics have permanent dipole moments that align with an external electric field, while non-polar dielectrics have no permanent dipoles but develop induced dipoles in an external field.
• 10. How does the presence of a dielectric affect the potential difference across a capacitor with constant charge? (CBSE 2017)
  With constant charge, inserting a dielectric increases the capacitance to C' = κC, reducing the potential difference to V' = V/κ, as V = Q/C.

Chapter–3: Current Electricity

Topic 1: Electric Current

• 1. Define electric current. (CBSE 2019)
  Electric current is the rate of flow of electric charge through a conductor, given by I = Q/t, where Q is the charge and t is the time.
• 2. What is the SI unit of electric current? (CBSE 2018)
  The SI unit of electric current is the ampere (A), where 1 ampere = 1 coulomb per second (C/s).
• 3. What is the direction of conventional electric current? (CBSE 2020)
  The conventional electric current is defined to flow in the direction of positive charge movement, from the positive to the negative terminal of a circuit.
• 4. What is meant by drift velocity of electrons? (CBSE 2017)
  Drift velocity is the average velocity with which free electrons move in a conductor under the influence of an electric field, typically very small (on the order of mm/s).
• 5. How is electric current related to drift velocity? (CBSE 2021)
  Electric current is related to drift velocity by I = nqAv_d, where n is the number density of electrons, q is the charge of an electron, A is the cross-sectional area, and v_d is the drift velocity.
• 6. What is the difference between direct current (DC) and alternating current (AC)? (CBSE 2016)
  Direct current (DC) flows in one direction with constant magnitude, while alternating current (AC) periodically reverses direction and changes magnitude.
• 7. What is the role of free electrons in the conduction of electric current in metals? (CBSE 2019)
  Free electrons in metals move under an applied electric field, carrying charge and constituting the electric current in the conductor.
• 8. Why is the drift velocity of electrons in a conductor very small compared to their thermal velocity? (CBSE 2020)
  The drift velocity is small because electrons undergo frequent collisions with atoms, resulting in a net average velocity much lower than their random thermal velocity.
• 9. What is the effect of temperature on the drift velocity of electrons? (CBSE 2018)
  As temperature increases, the resistance of the conductor increases due to more frequent collisions, reducing the drift velocity for a given electric field.
• 10. What is the relationship between current density and electric current? (CBSE 2017)
  Current density (J) is the electric current per unit area of cross-section, related to current by I = J·A, where A is the cross-sectional area.

Topic 2: Ohm's Law

• 1. State Ohm's law. (CBSE 2020)
  Ohm's law states that the current through a conductor between two points is directly proportional to the voltage across the two points, given by V = IR, where V is the voltage, I is the current, and R is the resistance.
• 2. What is the SI unit of resistance? (CBSE 2019)
  The SI unit of resistance is the ohm (Ω), where 1 ohm = 1 volt per ampere (V/A).
• 3. What is meant by ohmic and non-ohmic conductors? (CBSE 2018)
  Ohmic conductors obey Ohm's law, showing a linear relationship between voltage and current (e.g., metals), while non-ohmic conductors do not, showing a non-linear relationship (e.g., diodes).
• 4. How does the resistance of a conductor affect the current according to Ohm's law? (CBSE 2021)
  According to Ohm's law, for a constant voltage, the current is inversely proportional to the resistance, I = V/R. Higher resistance results in lower current.
• 5. What is the graphical representation of Ohm's law? (CBSE 2017)
  The graphical representation of Ohm's law for an ohmic conductor is a straight line passing through the origin on a voltage (V) versus current (I) graph, with the slope equal to the resistance R.
• 6. Why do some materials not obey Ohm's law? (CBSE 2016)
  Some materials do not obey Ohm's law because their resistance varies with voltage or current due to non-linear properties, such as temperature changes or structural effects (e.g., semiconductors, gases).
• 7. How does the voltage across a conductor change if the current is doubled, according to Ohm's law? (CBSE 2019)
  According to Ohm's law, if the current is doubled while resistance remains constant, the voltage across the conductor also doubles, as V = IR.
• 8. What is the physical significance of the resistance in Ohm's law? (CBSE 2020)
  Resistance in Ohm's law represents the opposition to the flow of electric current in a conductor, measured as the ratio of voltage to current (R = V/I).
• 9. How is Ohm's law verified experimentally? (CBSE 2018)
  Ohm's law is verified experimentally by measuring the current through a conductor for different applied voltages and plotting V versus I. A straight line through the origin confirms V = IR.
• 10. What happens to the current if the resistance of a conductor is halved, keeping voltage constant? (CBSE 2017)
  If the resistance is halved while keeping the voltage constant, the current doubles, as I = V/R, according to Ohm's law.

Topic 3: Drift Velocity

• 1. What is drift velocity? (CBSE 2021)
  Drift velocity is the average velocity with which free electrons move through a conductor under the influence of an electric field, given by v_d = I/(neA), where I is current, n is electron density, e is the charge of an electron, and A is the cross-sectional area.
• 2. How is drift velocity related to electric current? (CBSE 2019)
  Drift velocity is related to electric current by the formula I = neAv_d, where I is the current, n is the electron density, e is the charge of an electron, A is the cross-sectional area, and v_d is the drift velocity.
• 3. Why is the drift velocity of electrons typically very small? (CBSE 2020)
  The drift velocity of electrons is very small because electrons undergo frequent collisions with atoms in the conductor, resulting in a slow net movement despite their high thermal velocities.
• 4. How does drift velocity depend on the electric field in a conductor? (CBSE 2018)
  Drift velocity is directly proportional to the electric field, given by v_d = (eEτ)/m, where e is the electron charge, E is the electric field, τ is the relaxation time, and m is the electron mass.
• 5. What is the effect of temperature on drift velocity? (CBSE 2017)
  As temperature increases, the drift velocity decreases for a given electric field because increased thermal agitation causes more frequent collisions, reducing the relaxation time τ.
• 6. How does the cross-sectional area of a conductor affect drift velocity? (CBSE 2016)
  For a constant current, the drift velocity is inversely proportional to the cross-sectional area of the conductor, as v_d = I/(neA), where a larger A reduces v_d.
• 7. What is the role of relaxation time in determining drift velocity? (CBSE 2019)
  Relaxation time (τ) is the average time between electron collisions; a longer τ increases drift velocity, as v_d = (eEτ)/m, where e is the electron charge, E is the electric field, and m is the electron mass.
• 8. How does drift velocity relate to the mobility of electrons? (CBSE 2020)
  Drift velocity is related to electron mobility by v_d = μE, where μ = eτ/m is the electron mobility, e is the electron charge, τ is the relaxation time, m is the electron mass, and E is the electric field.
• 9. Why is drift velocity independent of the mass of the conductor? (CBSE 2018)
  Drift velocity depends on the electron mass (m) in v_d = (eEτ)/m, but for a given material, the number density (n) and relaxation time (τ) dominate, and the conductor’s total mass does not directly affect v_d.
• 10. How does increasing the current affect the drift velocity in a conductor? (CBSE 2017)
  Increasing the current increases the drift velocity, as v_d = I/(neA), where I is the current, and n, e, and A remain constant for a given conductor.

Topic 4: Electrical Resistance

• 1. Define electrical resistance and its SI unit. (CBSE 2018)
  Electrical resistance is the opposition to the flow of electric current in a conductor, given by R = V/I, where V is voltage and I is current. Its SI unit is the ohm (Ω).
• 2. What factors affect the resistance of a conductor? (CBSE 2019)
  The resistance of a conductor depends on its length (L), cross-sectional area (A), material resistivity (ρ), and temperature, given by R = ρL/A.
• 3. What is the formula for the resistance of a conductor? (CBSE 2020)
  The resistance of a conductor is given by R = ρL/A, where ρ is the resistivity, L is the length, and A is the cross-sectional area.
• 4. How does the resistance of a conductor change if its length is doubled? (CBSE 2017)
  If the length of a conductor is doubled, its resistance doubles, as R ∝ L, according to the formula R = ρL/A.
• 5. How does the resistance change if the cross-sectional area of a conductor is halved? (CBSE 2021)
  If the cross-sectional area of a conductor is halved, its resistance doubles, as R ∝ 1/A, according to the formula R = ρL/A.
• 6. What is meant by resistivity of a material? (CBSE 2016)
  Resistivity (ρ) is a material property that quantifies how strongly it opposes the flow of electric current, given by ρ = RA/L, where R is resistance, A is cross-sectional area, and L is length.
• 7. How does temperature affect the resistance of a metallic conductor? (CBSE 2019)
  For a metallic conductor, resistance increases with temperature due to increased collisions of electrons with vibrating atoms, approximately following R = R₀(1 + αΔT), where α is the temperature coefficient of resistance.
• 8. Why do alloys have higher resistivity than pure metals? (CBSE 2020)
  Alloys have higher resistivity than pure metals because their disordered atomic structure increases electron scattering, impeding the flow of current.
• 9. What is the effect of resistance on current in a circuit according to Ohm's law? (CBSE 2018)
  According to Ohm's law, for a constant voltage, the current in a circuit is inversely proportional to the resistance, I = V/R, so higher resistance decreases current.
• 10. Why do conductors have low resistance compared to insulators? (CBSE 2017)
  Conductors have low resistance due to a high density of free electrons that facilitate current flow, whereas insulators have very few free electrons, resulting in high resistance.

Topic 5: Kirchhoff’s Laws

• State Kirchhoff’s first law. (CBSE 2019)
  Kirchhoff’s first law (junction rule) states that the algebraic sum of currents entering a junction is equal to the sum of currents leaving the junction.
• State Kirchhoff’s second law. (CBSE 2018)
  Kirchhoff’s second law (loop rule) states that the algebraic sum of potential differences in any closed loop is always zero.
• Write the conditions under which Kirchhoff’s laws are applicable. (CBSE 2020)
  Kirchhoff’s laws are valid for lumped, linear circuits and are based on conservation of charge and energy. They are not valid for circuits with rapidly changing magnetic fields.
• Using Kirchhoff’s rules, obtain the balance condition of a Wheatstone bridge. (CBSE 2017)
  By applying Kirchhoff’s loop rule, the balance condition of a Wheatstone bridge is R1/R2 = R3/R4.
• A battery of emf E is connected to resistors R1, R2 and R3 in a circuit. How can Kirchhoff’s rules be used to find the current in each resistor? (CBSE 2016)
  By applying Kirchhoff’s junction rule at nodes and loop rule in independent loops, we form equations that can be solved simultaneously to get the currents in R1, R2, and R3.
• Explain how Kirchhoff’s laws follow from the principle of conservation of charge and energy. (CBSE 2015)
  The junction rule is based on conservation of charge (no charge is lost at a junction). The loop rule is based on conservation of energy (net energy change in a closed loop is zero).
• Apply Kirchhoff’s laws to a circuit with two loops and explain the procedure. (CBSE 2019 Compartment)
  Assign currents to branches, apply junction rule at a node, and then apply loop rule in both loops. This gives simultaneous equations for calculating unknown currents.
• What is the physical significance of Kirchhoff’s first law? (CBSE 2014)
  It signifies conservation of charge at a junction: charge neither accumulates nor disappears in an electrical circuit.
• What is the physical significance of Kirchhoff’s second law? (CBSE 2013)
  It signifies conservation of energy: total emf supplied is equal to the total potential drop in a closed loop.
• State any two limitations of Kirchhoff’s laws. (CBSE 2012)
  (i) Not valid for circuits where displacement current is significant.
  (ii) Not applicable in circuits with varying magnetic flux linking the circuit.

Topic 6: Wheatstone Bridge

• What is the principle of a Wheatstone bridge? (CBSE 2020)
  The principle of a Wheatstone bridge is that when the bridge is balanced, the ratio of resistances in one arm equals the ratio in the other arm, i.e., P/Q = R/S.
• Derive the condition for balance of a Wheatstone bridge using Kirchhoff’s laws. (CBSE 2019)
  By applying Kirchhoff’s loop law to both loops of the bridge and equating the potential difference across the galvanometer to zero, we obtain the balance condition: P/Q = R/S.
• Why is Wheatstone bridge more accurate than the law of resistances in series and parallel? (CBSE 2018)
  Because it measures the unknown resistance by comparison, thereby minimizing errors due to resistance of connecting wires and contact points.
• What happens to the galvanometer current when the Wheatstone bridge is balanced? (CBSE 2017)
  When the Wheatstone bridge is balanced, the potential difference across the galvanometer becomes zero, so no current flows through it.
• Write two limitations of a Wheatstone bridge. (CBSE 2016)
  (i) It cannot be used for measuring very low resistances.
  (ii) It gives inaccurate results when the resistances are not purely ohmic or if temperature varies.
• Explain the role of the galvanometer in a Wheatstone bridge. (CBSE 2015)
  The galvanometer detects whether there is any current flowing through it. A zero deflection indicates the bridge is balanced.
• Name the practical device based on the Wheatstone bridge principle and state its use. (CBSE 2014)
  The meter bridge (slide wire bridge) is based on Wheatstone bridge principle. It is used to determine the unknown resistance of a wire.
• State the condition under which Wheatstone bridge is said to be balanced. (CBSE 2013)
  The Wheatstone bridge is balanced when the ratio of resistances in the two arms is equal, i.e., P/Q = R/S, and the galvanometer shows no deflection.
• What is the sensitivity of a Wheatstone bridge? How can it be increased? (CBSE 2012)
  Sensitivity is the deflection per unit fractional change in resistance. It can be increased by using a galvanometer of high sensitivity and by keeping resistances nearly equal.
• Why is Wheatstone bridge not suitable for AC measurements? (CBSE 2011)
  Because in AC, inductance and capacitance cause phase differences, so the simple resistance ratio principle of the Wheatstone bridge no longer holds true.

Topic 7: Electrical Energy and Power

• Define electrical power and its SI unit. (CBSE 2021)
  Electrical power is the rate of doing work or transferring energy, given by P = VI, and its SI unit is watt (W).
• Derive the relation for electrical power in terms of resistance and current. (CBSE 2020)
  Using Ohm’s law V = IR, power P = VI = I²R. Thus, electrical power can also be expressed as P = I²R.
• What do you mean by commercial unit of electrical energy? (CBSE 2019)
  Commercial unit of electrical energy is kilowatt-hour (kWh). 1 kWh = 1000 watt × 3600 seconds = 3.6 × 10⁶ J.
• An electric bulb is rated 220 V – 100 W. What does it mean? (CBSE 2018)
  It means the bulb operates at 220 volts and consumes 100 joules of energy per second when operated at rated voltage.
• A heater of resistance 50 Ω operates on 220 V. Calculate the power consumed and the energy consumed in 2 hours. (CBSE 2017)
  Power P = V²/R = (220²)/50 = 968 W (approx). Energy consumed = Pt = 968 × 7200 = 6.97 × 10⁶ J ≈ 1.94 kWh.
• Define watt-hour and kilowatt-hour. (CBSE 2016)
  One watt-hour is the energy consumed by a device of 1 W power in 1 hour. One kilowatt-hour (kWh) is the energy consumed by a 1 kW device in 1 hour (1 kWh = 3.6 × 10⁶ J).
• Two bulbs are rated 40 W – 220 V and 100 W – 220 V. Which one has higher resistance? (CBSE 2015)
  Resistance R = V²/P. For 40 W bulb, R = (220²)/40 = 1210 Ω. For 100 W bulb, R = (220²)/100 = 484 Ω. Hence, the 40 W bulb has higher resistance.
• Why is electrical energy transmitted at high voltage? (CBSE 2014)
  Power loss in transmission lines is I²R. By transmitting at high voltage, current decreases for the same power, thereby reducing energy losses.
• A 60 W bulb is used for 10 hours daily. Calculate the energy consumed in one month of 30 days. (CBSE 2013)
  Daily energy = 60 W × 10 h = 600 Wh = 0.6 kWh. Monthly energy = 0.6 × 30 = 18 kWh.
• A geyser of 1500 W is operated for 2 hours daily. Find the cost of energy used in 20 days at ₹6.50 per kWh. (CBSE 2012)
  Daily energy = 1.5 kW × 2 h = 3 kWh. For 20 days, energy = 60 kWh. Cost = 60 × 6.50 = ₹390.

Chapter–4: Moving Charges and Magnetism

Topic 1: Magnetic Force on a Charge

• What is the force on a moving charge in a magnetic field? (CBSE 2019)
  The force on a moving charge in a magnetic field is given by F = q(v × B), where q is charge, v is velocity, and B is magnetic field strength.

Topic 2: Biot-Savart Law

• State the Biot-Savart law. (CBSE 2020)
  The Biot-Savart law states that the magnetic field dB at a point due to a small current element is proportional to the current, the length of the element, and the sine of the angle between the element and the line to the point, dB ∝ Idl sinθ.

Topic 3: Ampere’s Circuital Law

• State Ampere’s circuital law. (CBSE 2021)
  Ampere’s circuital law states that the line integral of the magnetic field around a closed loop is equal to μ₀ times the total current enclosed by the loop, ∮B·dl = μ₀I.

Topic 4: Force on a Current-Carrying Conductor

• What is the force on a current-carrying conductor in a magnetic field? (CBSE 2018)
  The force on a current-carrying conductor in a magnetic field is given by F = I(L × B), where I is current, L is length, and B is magnetic field.

Topic 5: Torque on a Current Loop

• What is the torque on a current loop in a magnetic field? (CBSE 2019)
  The torque on a current loop in a magnetic field is given by τ = NIAB sinθ, where N is the number of turns, I is current, A is area, B is magnetic field, and θ is the angle.

Topic 6: Moving Coil Galvanometer

• What is the principle of a moving coil galvanometer? (CBSE 2020)
  A moving coil galvanometer works on the principle that a current-carrying coil placed in a magnetic field experiences a torque proportional to the current.

Chapter–5: Magnetism and Matter

Topic 1: Bar Magnet and Magnetic Field

• What is the magnetic field due to a bar magnet? (CBSE 2021)
  The magnetic field due to a bar magnet resembles that of a magnetic dipole, with field lines emerging from the north pole and entering the south pole.

Topic 2: Magnetic Properties of Materials

• Define magnetic susceptibility. (CBSE 2018)
  Magnetic susceptibility is a measure of how a material responds to an applied magnetic field, defined as the ratio of magnetization to the magnetic field strength, χ = M/H.

Topic 3: Earth’s Magnetism

• What are the elements of Earth’s magnetic field? (CBSE 2019)
  The elements of Earth’s magnetic field are magnetic declination, inclination (dip), and horizontal and vertical components of the field.

Topic 4: Magnetic Dipole Moment

• Define magnetic dipole moment. (CBSE 2020)
  Magnetic dipole moment is a vector quantity that measures the strength and orientation of a magnetic dipole, given by m = IA for a current loop, where I is current and A is area.

Chapter–6: Electromagnetic Induction

Topic 1: Faraday's Laws

• State Faraday's law of electromagnetic induction. (CBSE 2019)
  Faraday's law states that the induced electromotive force (EMF) in a circuit is equal to the negative rate of change of magnetic flux through the circuit, ε = -dΦ/dt.

Topic 2: Lenz's Law

• State Lenz's law. (CBSE 2020)
  Lenz's law states that the induced EMF and current in a circuit oppose the change in magnetic flux that produced them.

Topic 3: Self-Induction and Mutual Induction

• Define self-induction. (CBSE 2021)
  Self-induction is the phenomenon where a change in current in a coil induces an EMF in the same coil, given by ε = -L(di/dt), where L is inductance.

Topic 4: Energy Stored in an Inductor

• What is the energy stored in an inductor? (CBSE 2018)
  The energy stored in an inductor is given by U = (1/2)LI², where L is inductance and I is the current.

Chapter–7: Alternating Current

Topic 1: AC Voltage and Current

• What is the RMS value of an AC voltage? (CBSE 2019)
  The RMS (root mean square) value of an AC voltage is the square root of the mean of the squares of the instantaneous values, given by V_rms = V_max / √2.

Topic 2: AC Circuits with Resistance

• How does current behave in a purely resistive AC circuit? (CBSE 2020)
  In a purely resistive AC circuit, the current is in phase with the voltage, and its magnitude follows Ohm's law, I = V/R.

Topic 3: Reactance and Impedance

• Define reactance in an AC circuit. (CBSE 2021)
  Reactance is the opposition to the flow of alternating current due to capacitance or inductance, given by X_C = 1/(ωC) for capacitance and X_L = ωL for inductance.

Topic 4: Power in AC Circuits

• What is the average power in an AC circuit? (CBSE 2018)
  The average power in an AC circuit is given by P = V_rms I_rms cosφ, where cosφ is the power factor.

Chapter–8: Electromagnetic Waves

Topic 1: Properties of EM Waves

• What are electromagnetic waves? (CBSE 2021)
  Electromagnetic waves are transverse waves that consist of oscillating electric and magnetic fields, propagating through space at the speed of light.

Chapter–9: Ray Optics and Optical Instruments

Topic 1: Reflection of Light

• State the laws of reflection of light. (CBSE 2018)
  The laws of reflection state that the incident ray, the reflected ray, and the normal to the surface at the point of incidence all lie in the same plane, and the angle of incidence equals the angle of reflection.

Chapter–10: Wave Optics

Topic 1: Interference

• What is the condition for constructive interference? (CBSE 2019)
  The condition for constructive interference is that the path difference between the waves should be an integral multiple of the wavelength, i.e., Δx = nλ.

Chapter–11: Dual Nature of Radiation and Matter

Topic 1: Photoelectric Effect

• State the photoelectric effect. (CBSE 2020)
  The photoelectric effect is the emission of electrons from a material when it is exposed to light or electromagnetic radiation of sufficient frequency.

Topic 2: De Broglie Hypothesis

• State de Broglie's hypothesis. (CBSE 2021)
  De Broglie's hypothesis states that every particle or matter exhibits wave-like properties, with wavelength λ = h/p, where h is Planck's constant and p is momentum.

Chapter–12: Atoms

Topic 1: Atomic Structure

• What is the Bohr model of an atom? (CBSE 2019)
  The Bohr model of an atom describes electrons orbiting the nucleus in discrete energy levels, with transitions between levels causing absorption or emission of energy.

Chapter–13: Nuclei

Topic 1: Nuclear Reactions

• Define nuclear fission. (CBSE 2020)
  Nuclear fission is the process in which a heavy nucleus splits into two or more lighter nuclei, releasing a large amount of energy.

Chapter–14: Semiconductor Electronics

Topic 1: Semiconductors

• What are semiconductors? (CBSE 2021)
  Semiconductors are materials with electrical conductivity between conductors and insulators, such as silicon and germanium, whose conductivity can be controlled.

Topic 2: p-n Junction

• Explain the working of a p-n junction diode. (CBSE 2018)
  A p-n junction diode allows current to flow in one direction (forward bias) when the p-side is connected to the positive terminal and the n-side to the negative, due to the movement of majority charge carriers.