The circuit involves two ideal cells connected to a 1 μ F capacitor via a key K. Initially the key K is in position 1 and the capacitor is charged fully by 2V cell. The key is pushed to position 2. Li

Question

The circuit involves two ideal cells connected to a 1 $μ F$ capacitor via a key K. Initially the key K is in position 1 and the capacitor is charged fully by 2V cell. The key is pushed to position 2. List-I gives physical quantities involving the circuit after the key is pushed from position 1. List-II gives corresponding results. Match the statements in List-I with the corresponding values in List-II.

List-I	List-II
(I) The net charge crossing the 4 volt cell in $μ C$ is	(P) 2
(II) The magnitude of work done by 4 Volt cell in $μ J$ is	(Q) 6
(III) The gain in potential energy of capacitor in $μ J$ is	(R) 8
(IV) The net heat produced in circuit in $μ J$ is	(S) 16
	(T) 20

TestHub · Accepted Answer

Initial charge on capacitor (key at 1): $q_{i} = C V_{i} = 1 \times 2 = 2 μ C$

Final charge (key at 2): $q_{f} = C V_{f} = 1 \times 4 = 4 μ C$

Net charge crossing the 4 V cell: $q_{f} - q_{i} = 4 - 2 = 2 μ C$ → I → P (2).

Work done by the 4 V cell: $W = (q_{f} - q_{i}) \times 4 = 8 μ J$ → II → R (8).

Gain in potential energy: $Δ U = \frac{1}{2} C (V_{f}^{2} - V_{i}^{2}) = \frac{1}{2} [4^{2} - 2^{2}] = 6 μ J$ → III → Q (6).

Net heat produced: $Δ H = W - Δ U = 8 - 6 = 2 μ J$ → IV → P (2).

Hence I → P; II → R; III → Q; IV → P, option (D).

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