A circuit connected to an ac source of emf e = e0sin(100t) with t in… | JEE Main 2019 (8 Apr, Shift 2)

Q49JEE Main 2019 · 8 APR · SHIFT 2Medium

RL and RC Series Circuits

A circuit connected to an ac source of emf e = e0sin(100t) with t in seconds, gives a phase difference of $\pi$ /4 between the emf e and current i. Which of the following circuits will exhibit this?

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Answer: (c)

Phase difference $\frac{\pi}{4}$ needs reactance $X = R$ ; here $\omega = 100\text{ rad/s}$ .
RL: $X_L = \omega L = 100 \times 10^{-3}$ or $100 \times 10^{-2}$ , i.e. $0.1$ or $1\ \Omega \ne 1000\ \Omega$ .
RC with $C = 10\ \mu\text{F}$ : $X_C = \frac{1}{100 \times 10^{-5}} = 1000\ \Omega = R$ . (With $1\ \mu\text{F}$ , $X_C = 10^4\ \Omega$ .)
So the answer is (c) RC circuit with $R = 1\text{ k}\Omega$ , $C = 10\ \mu\text{F}$ .

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