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 $50\text{Hz}$ frequency (the next three circuits) in different ways as shown in Column II. When a current $I$ (steady state for DC or rms for AC) 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. A(r,s,t),B(q,r,s,t),C(p,q),D(q,r,s,t)
• B. Option c missing
• C. Option d missing
• D. Option b missing

Answer 1

The correct option is A A(r,s,t),B(q,r,s,t),C(p,q),D(q,r,s,t)

(p) $V_1=0,V_2=V(\because X_L=0)$
(q) $X_L=0,V_1=0,V_2=V$
(r) $X_L=\omega L=2\pi fL=1.884\Omega$
$V_1=I{X}_L$
$V_2=IR$
$V_1<V_2$
(s) $X_L=1.884\Omega$
$X_C=\frac{1}{\omega L}=\frac{10}{3\pi }\times {10}^3\Omega$
$X_C>>X_L$
$V_2=I{X}_C,V_1=I{X}_L$
(t) $R=1\text{k}\Omega$
$X_C=\frac{10}{3\pi }\times {10}^3\Omega$
$\Rightarrow X_C>R\Rightarrow V_2>V_1$
Also, $V_2=I{X}_L,V_1=IR$