You are given many resistances, capacitors and inductors. These are connected to a variable DC voltage source (the first two circuits) or an AC voltage source of 50 Hz frequency (the next three circui

Question

You are given many resistances, capacitors and inductors. These are connected to a variable DC voltage source (the first two circuits) or an AC voltage source of $50 Hz$ frequency (the next three circuits) in different ways as shown in Column II. When a current $I$ (steady state for DC or rms for $A C$ ) flows through the circuit, the corresponding voltage $V_{1}$ and $V_{2}$ (indicated in circuits) are related as shown in Column I. Match the two

TestHub · Accepted Answer

In circuit (P), I can't be non zero in steady state. In circuit (Q) : V 1 ​ = 0 and V 2 ​ = 2 I = V (also) ​ In circuit (R): V 1 ​ = X L ​ I = ( 2 π f L ) I = ( 2 π × 50 × 6 × 1 0 − 3 ) I = 1.88 I V 2 ​ = 2 I ​ In circuit (S): V 1 ​ = X L ​ I = 1.88 I V 2 ​ = X C ​ I = ( 2 π f C 1 ​ ) I = ( 2 π × 50 × 3 × 1 0 − 6 1 ​ ) I = ( 1061 ) I ​ In circuit (T): ​ V 1 ​ = I R = ( 1000 ) I V 2 ​ = X C ​ I = ( 1061 ) I ​ Therefore the correct options are as under (A) → R, S, T (B) → Q, R, S, T (C) → Q or P , Q (D) → Q, R, S, T

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