Assertion (A): If separation between plates of a parallel plate isolated charged capacitor is increased, its energy stored will be increased.
Reason (R): Work done to separate the plates get converted in electrostatic potential energy.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
For an isolated capacitor, charge (Q) is constant. Energy stored is \(U = \frac{Q^2}{2C}\). If separation (d) increases, capacitance \(C = \frac{\epsilon_0 A}{d}\) decreases. Therefore, (U) increases. This increase in energy comes from the work done by an external agent to separate the plates against attractive electrostatic forces.
Assertion (A): After charging a capacitor of capacitance (C) from a battery, it is connected to the same battery of potential difference (V) with reverse polarity. Loss of energy in this process is \(2CV^2\).
Reason (R): Work done by the battery is equal to loss of energy in the given case.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
Initially, the capacitor stores energy \(U_i = \frac{1}{2}CV^2\) with charge \(Q_i = CV\). When connected with reverse polarity, the capacitor eventually charges to (-V\), and final stored energy is \(U_f = \frac{1}{2}C(-V)^2 = \frac{1}{2}CV^2\). The net change in stored energy is \(0\). The charge that flows from the battery is \(Q_f - Q_i = (-CV) - (CV) = -2CV\), meaning (2CV) charge flows. The work done by the battery is \(W_B = (2CV) \cdot V = 2CV^2\). Since \(W_B = \Delta U + Q_{\text{loss}}\), and ( \Delta U = 0\), the loss of energy is \(Q_{\text{loss}} = W_B = 2CV^2\). Both A and R are true and R explains A in this specific case.
Assertion (A): A capacitor of a certain capacity, whenever charged, will always store the same amount of charge.
Reason (R): A definite capacity implies always a same definite value of charge.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
A: False. The charge stored by a capacitor is \(Q = CV\). For a given capacitance \(C\), the charge \(Q\) depends on the applied voltage \(V\), which can vary.\nR: False. A definite capacity \(C\) does not imply a definite charge \(Q\), as \(Q\) is also proportional to the voltage \(V\) across the capacitor, which can be varied.\nTherefore, both (A) and (R) are false.
Assertion (A): Two protons placed at different distances, between the plates of a parallel plate capacitor experience the same force.
Reason (R): The electric field between the plates of parallel plate capacitor is constant.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
Assertion (A) is true because the electric field (E) in a parallel plate capacitor is uniform. The force on a proton (q) is F = qE , which is constant. Reason (R) is true as the electric field between plates of an ideal parallel plate capacitor is constant. (R) correctly explains (A).
A capacitor of capacitance C is connected across a battery of potential difference V.
Assertion (A): The energy stored in capacitor is \( \frac{1}{2} CV^2 \).
Reason (R): The energy supplied by the battery is \( CV^2 \).
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
Assertion (A) is true: energy stored in a capacitor is \( U = \frac{1}{2} CV^2 \). Reason (R) is true: the total work done by the battery (energy supplied) is \( W = CV^2 \). However, (R) is not the correct explanation for (A), as half of the supplied energy is dissipated as heat.
Assertion (A): If the distance between parallel plates of a capacitor is halved and dielectric constant is three times, then the capacitor becomes 6 times.
Reason (R): Capacity of a capacitor depends upon the nature of the plate material.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
Assertion (A) is true. For a parallel plate capacitor, \( C = \frac{\kappa \epsilon_0 A}{d} \). If ( d to d/2 ) and \( \kappa to 3\kappa \), then \( C' = \frac{3\kappa \epsilon_0 A}{d/2} = 6 \frac{\kappa \epsilon_0 A}{d} = 6C ). Reason (R) is false as capacitance depends on the dielectric medium, not the plate material.
Assertion (A): In parallel plate capacitor separation ‘d’ should be smaller than the linear dimension of the plates \( d^2 << A\).
Reason (R): For \( d^2 << A \) a fringing effect can be ignored in the region sufficiently far from the edge.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
Assertion (A) is true; for a parallel plate capacitor, 'd' must be much smaller than plate dimensions for the uniform field approximation. Reason (R) is also true. The condition \( d^2 << A \) (implying \( d << \sqrt{A} )\) allows ignoring fringing effects. Thus, (R) is the correct explanation for (A).