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Electrostatic Potential and Capacitance

Class 12th Physics Chapter Assertion and Reason


Assertion and Reason Questions Chapter-2  Electrostatic Potential and Capacitance

Assertion (A) and other labelled Reason (R). Select the correct answer to these questions from the options as given below.

A. Both A and R are true, and R is the correct explanation of A.

B. Both A and R are true, but R is not the correct explanation of A.

C. A is true, but R is false.

D. A is false, but R is true.


1. Assertion (A): The electrostatic potential at any point on the equatorial plane of an electric dipole is zero.

Reason (R): The potential due to equal and opposite charges of the dipole cancels out at every point on the equatorial plane.

  • (a) Both A and R are true, and R is the correct explanation of A.
  • Answer: (a)
    Explanation: At any point on the equatorial plane, the potentials due to the two charges of the dipole are equal in magnitude but opposite in sign, canceling each other.

2. Assertion (A): The electric potential at a point midway between two like charges is not zero.

Reason (R): The potentials due to two like charges at the midpoint add up.

  • (a) Both A and R are true, and R is the correct explanation of A.
  • Answer: (a)
    Explanation: The potential is a scalar quantity and does not cancel out like vectors. Hence, the potentials due to both charges add up.

3. Assertion (A): The work done in moving a charge in an electrostatic field from one point to another depends only on the initial and final positions.

Reason (R): The electrostatic force is a conservative force.

  • (a) Both A and R are true, and R is the correct explanation of A.
  • Answer: (a)
    Explanation: Since the electrostatic force is conservative, the work done depends only on the initial and final positions, not on the path taken.

4. Assertion (A): A charged particle can move on an equipotential surface without any work being done.

Reason (R): The electric field is always perpendicular to the equipotential surface.

  • (a) Both A and R are true, and R is the correct explanation of A.
  • Answer: (a)
    Explanation: No work is done when a charge moves along an equipotential surface, as there is no component of the electric field in the direction of motion.

5. Assertion (A): The electric potential due to a point charge decreases as the distance from the charge increases.

Reason (R): The electric potential is inversely proportional to the distance from the charge.

  • (a) Both A and R are true, and R is the correct explanation of A.
  • Answer: (a)
    Explanation: The formula for electric potential is V= \(\frac{kq}{r}\)​, so the potential decreases with an increase in distance.

6. Assertion (A): Two equipotential surfaces can never intersect.

Reason (R): At the point of intersection, the electric field would have two different directions, which is not possible.

  • (a) Both A and R are true, and R is the correct explanation of A.
  • Answer: (a)
    Explanation: If two equipotential surfaces intersect, it would imply two values of potential at the point of intersection, which is impossible.

7. Assertion (A): The potential inside a hollow charged conductor is constant.

Reason (R): The electric field inside a hollow charged conductor is zero.

  • (a) Both A and R are true, and R is the correct explanation of A.
  • Answer: (a)
    Explanation: Inside a conductor, the electric field is zero in electrostatic equilibrium, leading to a constant potential throughout the volume.

8. Assertion (A): The electric potential at a point due to a dipole is zero if the point is on the equatorial line.

Reason (R): The potentials due to the positive and negative charges of the dipole cancel each other on the equatorial line.

  • (a) Both A and R are true, and R is the correct explanation of A.
  • Answer: (a)
    Explanation: On the equatorial line, the distances from both charges of the dipole are equal, and the potentials due to them are equal and opposite, leading to a net zero potential.

9. Assertion (A): The potential due to a uniformly charged spherical shell is zero at its center.

Reason (R): The electric field inside a uniformly charged spherical shell is zero.

  • (b) Both A and R are true, but R is not the correct explanation of A.
  • Answer: (b)
    Explanation: The potential inside a spherical shell is constant, and at the center, the potential is non-zero. However, the electric field is zero.

10. Assertion (A): The capacitance of a parallel plate capacitor increases if a dielectric material is inserted between the plates.

Reason (R): A dielectric material reduces the electric field between the plates of the capacitor.

  • (a) Both A and R are true, and R is the correct explanation of A.
  • Answer: (a)
    Explanation: The dielectric material reduces the electric field, increasing the capacitance, as C= \(\frac{Q}{V}\), and V decreases with the dielectric.

11. Assertion (A): The potential energy of a system of two opposite charges is negative.

Reason (R): The potential energy of the system is proportional to the product of the charges.

  • (a) Both A and R are true, and R is the correct explanation of A.
  • Answer: (a)
    Explanation: Since the charges are opposite, the potential energy is negative as the product of the charges is negative.

12. Assertion (A): The electrostatic potential energy of a system of two like charges increases as the distance between them decreases.

Reason (R): Like charges repel each other, and work is done to bring them closer.

  • (a) Both A and R are true, and R is the correct explanation of A.
  • Answer: (a)
    Explanation: As the charges are brought closer, work has to be done against the repulsive force, increasing the potential energy.

13. Assertion (A): The work done in moving a charge between two points on an equipotential surface is zero.

Reason (R): The potential difference between two points on an equipotential surface is zero.

  • (a) Both A and R are true, and R is the correct explanation of A.
  • Answer: (a)
    Explanation: Since the potential difference is zero, no work is done in moving a charge between two points on an equipotential surface.

14. Assertion (A): The electrostatic potential is constant throughout the interior of a conductor in electrostatic equilibrium.

Reason (R): The electric field inside a conductor is zero in electrostatic equilibrium.

  • (a) Both A and R are true, and R is the correct explanation of A.
  • Answer: (a)
    Explanation: Since the electric field inside a conductor is zero, the potential remains constant throughout the interior.

15. Assertion (A): The electric potential of a charged spherical conductor is the same at all points on its surface.

Reason (R): The electric field inside a spherical conductor is zero.

  • (b) Both A and R are true, but R is not the correct explanation of A.
  • Answer: (b)
    Explanation: The potential on the surface of a conductor is constant, but the reason for this is not related to the electric field inside being zero.

16. Assertion (A): The capacitance of a capacitor depends on the geometry of the plates and the dielectric medium between them.

Reason (R): Capacitance is a function of the charge and potential difference between the plates.

  • (b) Both A and R are true, but R is not the correct explanation of A.
  • Answer: (b)
    Explanation: The capacitance depends on the area of the plates, distance between them, and the dielectric constant, not just the charge and potential difference.

17. Assertion (A): The potential inside a conductor in electrostatic equilibrium is the same as the potential on its surface.

Reason (R): The electric field inside a conductor in electrostatic equilibrium is zero.

  • (a) Both A and R are true, and R is the correct explanation of A.
  • Answer: (a)
    Explanation: Since the electric field is zero inside the conductor, there is no potential difference between any two points inside it, making the potential constant throughout.

18. Assertion (A): The energy stored in a capacitor is directly proportional to the square of the charge on the plates.

Reason (R): The energy stored in a capacitor is given by \(\frac{1}{2} \frac{Q^2}{C}\)​.

  • (a) Both A and R are true, and R is the correct explanation of A.
  • Answer: (a)
    Explanation: The energy stored in a capacitor is proportional to the square of the charge as given by the formula U=\(\frac{Q^2}{2C}\)​.

19. Assertion (A): The potential energy of a charged capacitor increases if the charge on the plates increases.

Reason (R): The potential energy of a capacitor is proportional to the square of the charge on its plates.

  • (a) Both A and R are true, and R is the correct explanation of A.
  • Answer: (a)
    Explanation: Since the potential energy of a capacitor is proportional to \(\ Q^{2}\), an increase in charge increases the potential energy.

20. Assertion (A): A capacitor stores energy by storing charge on its plates.

Reason (R): The energy stored in a capacitor is given by \(\frac{1}{2}\) QV .

  • (b) Both A and R are true, but R is not the correct explanation of A.
  • Answer: (b)
    Explanation: The energy is stored in the electric field between the plates, not directly by storing charge. However, the formula U= \(\frac{1}{2}\) QV is correct.

21. Assertion (A): The potential at infinity is defined to be zero in electrostatics.

Reason (R): This is done for mathematical convenience and consistency in calculations.

  • (a) Both A and R are true, and R is the correct explanation of A.
  • Answer: (a)
    Explanation: Defining the potential at infinity as zero allows for a consistent reference point for measuring potential differences.

22. Assertion (A): A capacitor can store energy even when it is not connected to a battery.

Reason (R): A charged capacitor retains its charge indefinitely in ideal conditions.

  • (a) Both A and R are true, and R is the correct explanation of A.
  • Answer: (a)
    Explanation: Once charged, an ideal capacitor retains its charge and thus can store energy until it is discharged.

23. Assertion (A): The capacitance of a capacitor increases if the distance between the plates decreases.

Reason (R): The capacitance is inversely proportional to the distance between the plates.

  • (a) Both A and R are true, and R is the correct explanation of A.
  • Answer: (a)
    Explanation: The capacitance is given by C= \(\frac{εA}{d}\)​, where ddd is the distance between the plates, confirming that capacitance increases as distance decreases.

24. Assertion (A): The potential difference across a capacitor is directly proportional to the charge on its plates.

Reason (R): This relationship is given by the equation Q=CV.

  • (a) Both A and R are true, and R is the correct explanation of A.
  • Answer: (a)
    Explanation: The relationship V= \(\frac{Q}{C}\) shows that potential difference V is directly proportional to the charge Q.

25. Assertion (A): A capacitor with a dielectric has a higher capacitance than the same capacitor without a dielectric.

Reason (R): The dielectric reduces the electric field between the plates, allowing more charge to be stored.

  • (a) Both A and R are true, and R is the correct explanation of A.
  • Answer: (a)
    Explanation: A dielectric increases capacitance by reducing the electric field, allowing the capacitor to store more charge.

26. Assertion (A): The potential energy of a capacitor is maximum when it is fully charged.

Reason (R): At maximum charge, the voltage across the capacitor is at its peak value.

  • (a) Both A and R are true, and R is the correct explanation of A.
  • Answer: (a)
    Explanation: The potential energy is given by U=\(\frac{1}{2} CV^{2}\), which is maximum when the charge is maximum.

27. Assertion (A): The capacitance of a parallel plate capacitor can be increased by increasing the area of the plates.

Reason (R): Capacitance is directly proportional to the plate area.

  • (a) Both A and R are true, and R is the correct explanation of A.
  • Answer: (a)
    Explanation: The capacitance formula C=\(\frac{εA}{d}\)​ shows that capacitance increases with an increase in plate area.

28. Assertion (A): The energy density in an electric field is directly proportional to the square of the electric field strength.

Reason (R): The formula for energy density is given by \(\frac{1}{2} εE^{2}\).

  • (a) Both A and R are true, and R is the correct explanation of A.
  • Answer: (a)
    Explanation: The energy density is indeed proportional to the square of the electric field strength as derived from the energy density formula.

29. Assertion (A): A capacitor will discharge faster if it is connected to a resistor with a lower resistance.

Reason (R): Lower resistance allows a higher current to flow, resulting in a quicker discharge.

  • (a) Both A and R are true, and R is the correct explanation of A.
  • Answer: (a)
    Explanation: A lower resistance allows for a higher current, leading to a faster discharge of the capacitor.

30. Assertion (A): The electric field inside a conductor in electrostatic equilibrium is zero.

Reason (R): This is because the charges reside on the surface of the conductor.

  • (a) Both A and R are true, and R is the correct explanation of A.
  • Answer: (a)
    Explanation: The charges redistribute themselves on the surface to cancel out the electric field inside the conductor.

31. Assertion (A): The potential difference across a capacitor is independent of the dielectric material used.

Reason (R): The potential difference depends only on the charge and capacitance.

  • (b) Both A and R are true, but R is not the correct explanation of A.
  • Answer: (b)
    Explanation: The potential difference V depends on charge Q and capacitance C, which changes with the dielectric. Thus, the assertion is false.

32. Assertion (A): When a dielectric material is inserted into a capacitor, the charge on the plates increases.

Reason (R): The dielectric increases the capacitance of the capacitor.

  • (a) Both A and R are true, and R is the correct explanation of A.
  • Answer: (a)
    Explanation: Inserting a dielectric increases capacitance, which allows the capacitor to store more charge for the same potential difference.

33. Assertion (A): The energy stored in a capacitor is released when it discharges.

Reason (R): The discharge of a capacitor converts electrical energy into other forms of energy.

  • (a) Both A and R are true, and R is the correct explanation of A.
  • Answer: (a)
    Explanation: The stored energy is converted into electrical energy, which can do work in the circuit during discharge.

34. Assertion (A): The electric potential due to a positive charge is positive.

Reason (R): The electric potential is defined as the work done in bringing a unit positive charge from infinity to that point.

  • (a) Both A and R are true, and R is the correct explanation of A.
  • Answer: (a)
    Explanation: The potential is defined as positive since work is done against the electric field to bring a positive charge from infinity.

35. Assertion (A): Capacitors in series have the same charge on each capacitor.

Reason (R): The charge on capacitors in series is the same because the current through each capacitor is the same.

  • (a) Both A and R are true, and R is the correct explanation of A.
  • Answer: (a)
    Explanation: In series, the same charge flows through each capacitor, resulting in equal charges on all.

36. Assertion (A): The total capacitance of capacitors in series is less than the smallest capacitance in the series.

Reason (R): The formula for total capacitance in series results in a smaller value than any individual capacitance.

  • (a) Both A and R are true, and R is the correct explanation of A.
  • Answer: (a)
    Explanation: The formula \(\frac{1}{C_{\text{total}}} = \frac{1}{C_1} + \frac{1}{C_2} + ...\) confirms that the total capacitance is always less than the smallest individual capacitance.

37. Assertion (A): The total capacitance of capacitors in parallel is equal to the sum of the individual capacitances.

Reason (R): In parallel, each capacitor experiences the same potential difference, allowing the total charge to be additive.

  • (a) Both A and R are true, and R is the correct explanation of A.
  • Answer: (a)
    Explanation: In parallel, the voltage across each capacitor is the same, and thus the total capacitance is \(\ C_{\text{total}} = C_1 + C_2 + ...\)

38. Assertion (A): If the distance between the plates of a capacitor is doubled, the capacitance is halved.

Reason (R): Capacitance is inversely proportional to the distance between the plates.

  • (a) Both A and R are true, and R is the correct explanation of A.
  • Answer: (a)
    Explanation: According to C= \(\frac{εA}{d}\)​, doubling the distance ddd results in halving the capacitance.

39. Assertion (A): A capacitor can be charged to a higher voltage than its rated voltage without any damage.

Reason (R): Exceeding the rated voltage can lead to breakdown of the dielectric material.

  • (b) Both A and R are true, but R is not the correct explanation of A.
  • Answer: (b)
    Explanation: The assertion is false; exceeding the rated voltage can damage the capacitor.

40. Assertion (A): A charged capacitor behaves like a battery when it discharges.

Reason (R): The capacitor provides a steady voltage until it is fully discharged.

  • (b) Both A and R are true, but R is not the correct explanation of A.
  • Answer: (b)
    Explanation: While a charged capacitor discharges voltage, it does not maintain a steady voltage like a battery.

41. Assertion (A): The capacitance of a capacitor depends on the geometry of its plates.

Reason (R): The area of the plates and the distance between them affect the capacitance value.

  • (a) Both A and R are true, and R is the correct explanation of A.
  • Answer: (a)
    Explanation: The capacitance is directly influenced by the area and the separation of the plates.

42. Assertion (A): The potential energy stored in a capacitor can be expressed in terms of charge and capacitance.

Reason (R): The energy can be given by U=\(\frac{1}{2} QV\) and U=\(\frac{1}{2} CV^{2}\)​.

  • (a) Both A and R are true, and R is the correct explanation of A.
  • Answer: (a)
    Explanation: Both formulas express potential energy stored in a capacitor and relate charge and capacitance.

43. Assertion (A): The electric field between the plates of a capacitor is uniform.

Reason (R): This uniformity is due to the parallel nature of the plates.

  • (a) Both A and R are true, and R is the correct explanation of A.
  • Answer: (a)
    Explanation: The parallel plates create a uniform electric field in the region between them.

44. Assertion (A): The energy stored in a capacitor is independent of the dielectric constant of the material used.

Reason (R): The dielectric constant affects capacitance, which in turn affects the energy stored.

  • (b) Both A and R are true, but R is not the correct explanation of A.
  • Answer: (b)
    Explanation: The assertion is false; the energy stored is dependent on capacitance, which varies with the dielectric constant.

45. Assertion (A): Capacitors are used in electronic circuits to smooth out voltage fluctuations.

Reason (R): Capacitors can release energy quickly, which stabilizes voltage.

  • (a) Both A and R are true, and R is the correct explanation of A.
  • Answer: (a)
    Explanation: Capacitors can store and release energy quickly, helping to stabilize voltage in circuits.

46. Assertion (A): The dielectric strength of a material determines its effectiveness as a dielectric in a capacitor.

Reason (R): Higher dielectric strength allows a capacitor to operate at higher voltages without breakdown.

  • (a) Both A and R are true, and R is the correct explanation of A.
  • Answer: (a)
    Explanation: Dielectric strength is crucial for determining the maximum operating voltage of a capacitor without breakdown.

47. Assertion (A): A capacitor acts as an open circuit after being fully discharged.

Reason (R): There is no charge stored on its plates in a fully discharged state.

  • (a) Both A and R are true, and R is the correct explanation of A.
  • Answer: (a)
    Explanation: A fully discharged capacitor has no stored charge, acting like an open circuit.

48. Assertion (A): The total charge in a closed circuit with capacitors is conserved.

Reason (R): Capacitors can only store charge but cannot create it.

  • (a) Both A and R are true, and R is the correct explanation of A.
  • Answer: (a)
    Explanation: Charge conservation is a fundamental principle, and capacitors store charge without creating or destroying it.

49. Assertion (A): The breakdown of a dielectric occurs at a certain critical electric field strength.

Reason (R): When the electric field exceeds the dielectric strength, it leads to ionization of the dielectric material.

  • (a) Both A and R are true, and R is the correct explanation of A.
  • Answer: (a)
    Explanation: Breakdown happens when the electric field surpasses the dielectric strength, causing ionization.

50. Assertion (A): Increasing the temperature of a dielectric material generally decreases its capacitance.

Reason (R): Increased temperature reduces the dielectric constant of the material.

  • (a) Both A and R are true, and R is the correct explanation of A.
  • Answer: (a)
    Explanation: As temperature rises, many dielectric materials exhibit a decrease in their dielectric constant, leading to reduced capacitance.