IIT-JEE 2010 · Paper 2 · Physics Q57 · Dronacharya Exams

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PhysicsMatrix match+8Question 57 of 57

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 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.

Column I

A
$I\ne0$ , $V_1$ is proportional to $I$
B
$I\ne0$ , $V_2>V_1$
C
$V_1=0$ , $V_2=V$
D
$I\ne0$ , $V_2$ is proportional to $I$

Column II

P
Q
R
S
T

Answer and worked solution

Official answer: A → R, S, T; B → Q, R, S, T; C → P, Q; D → Q, R, S, T

Steady DC. An inductor has no voltage across it; a capacitor blocks current.

P (L + C on DC): $I=0$ , $V_1=0$ , $V_2=V$ .
Q (L + 2 Ω on DC): $I=V/2$ , $V_1=0$ , $V_2=V=2I$ .

AC at 50 Hz. $X_L=2\pi\times50\times6\times10^{-3}\approx1.9\ \Omega$ , $X_C=\dfrac1{2\pi\times50\times3\times10^{-6}}\approx1061\ \Omega$ .

R (L + 2 Ω): $V_1=1.9I$ , $V_2=2I$ .
S (L + C): $V_1=1.9I$ , $V_2=1061I$ .
T (1 kΩ + C): $V_1=1000I$ , $V_2=1061I$ .

Matching.

A ( $I\ne0$ , $V_1\propto I$ ): R, S, T. (In Q, $V_1=0$ .)
B ( $I\ne0$ , $V_2>V_1$ ): Q, R, S, T.
C ( $V_1=0$ , $V_2=V$ ): P, Q.
D ( $I\ne0$ , $V_2\propto I$ ): Q, R, S, T.

Answer: A → R, S, T; B → Q, R, S, T; C → P, Q; D → Q, R, S, T

Topics:Reactance and impedance Ohm's law and resistivity RC circuits

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