You are given many resistances, capacitors and inductors. These are connected to a variable DC voltage…
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 $50 \mathrm{~Hz}$ 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
(A) R,S,T, (B) Q,R,T, (C) P, (D) Q,R,S
(A) R,S,T, (B) Q,R,S,T, (C) P,Q, (D) Q,R,S,T
(A) S,T, (B) Q,R,T, (C) P,Q, (D) Q,R,S,T
(A) S,T, (B) Q,R,S,T, (C) P, (D) Q,R,S
Solution
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)
$
\begin{aligned}
& \text { In circuit (R): } V_1=X_L I=(2 \pi f \mathrm{~L}) I \\
& \quad=\left(2 \pi \times 50 \times 6 \times 10^{-3}\right) I \\
& \quad=1.88 I \\
& V_2=2 I
\end{aligned}
$
In circuit (S): $V_1=X_L I=1.88 I$
$
\begin{array}{r}
V_2=X_C I=\left(\frac{1}{2 \pi f C}\right) I \\
=\left(\frac{1}{2 \pi \times 50 \times 3 \times 10^{-6}}\right) I=(1061) I
\end{array}
$
In circuit (T):
$
\begin{aligned}
& V_1=I R=(1000) I \\
& V_2=X_C I=(1061) I
\end{aligned}
$
Therefore the correct options are as under
(A) $\rightarrow$ R, S, T $\quad$ (B) $\rightarrow$ Q, R, S, T
(C) $\rightarrow$ Q or $P, Q \quad$ (D) $\rightarrow$ Q, R, S, T
!
