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A circuit has three parallel branches between nodes A-B (top) and A-E (bottom rail): left branch has 2 ohm resistor (B to A), middle branch has 4 ohm resistor (C to F), right branch has variable finite resistance R (D to E). Bottom rail connects A-F (4 V cell) and F-E (variable cell V2). Match the statements in List-I with the circuit configurations in List-II where V2 takes values 6V (P,T), 8V (Q), 4V (R), and 14/3 V (S). List-I: (I) Current through 4 ohm resistance can be zero. (II) Current through 4 ohm resistance can be from F to C. (III) Current through 2 ohm resistance can be from B to A. (IV) Current through R will be zero.

1. I -> P,Q,R,S,T; II -> Q; III -> P,Q,R,S,T; IV -> S
2. I -> Q; II -> P,Q,R,S,T; III -> P,Q,R,S,T; IV -> S
3. I -> P,Q,R; II -> P,Q,R,S,T; III -> T; IV -> P,Q,R,S,T
4. I -> T; II -> Q; III -> P,Q,R,S,T; IV -> P,Q,R,S,T

Correct answer: I -> Q; II -> P,Q,R,S,T; III -> P,Q,R,S,T; IV -> S

Solution

The voltage across the 4 ohm (node voltage V_CF) depends on the two EMFs and the other resistors. Since R is variable, node voltages shift. Current through 4 ohm = 0 when V_C = V_F exactly — this happens for specific V2. Direction of current in 4 ohm (F to C) is the typical direction for most V2 values. Current in 2 ohm (B to A) direction holds for all configurations since left branch is driven by the 4V cell. Current through R = 0 when the two branches on either side are balanced — happens for V2 = 14/3 V (case S). This matches option B.

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