When an ac source of e.m.f. e = E_0 (100 ,t) is connected across … - Vidyadip

MCQ

When an ac source of $e.m.f$. $e = {E_0}$$\sin (100\,t)$ is connected across a circuit, the phase difference between the $e.m.f$. $e$ and the current $i$ in the circuit is observed to be $\pi /4$, as shown in the diagram. If the circuit consists possibly only of $RC$ or $LC$ in series, find the relationship between the two elements

✓
$R = 1k\Omega ,\,C = 10\mu F$
B
$R = 1k\Omega ,\,C = 1\mu F$
C
$R = 1k\Omega ,\,L = 10H$
D
$R = 1k\Omega ,\,L = 1H$

✓

Answer

Correct option: A.

$R = 1k\Omega ,\,C = 10\mu F$

a
(a) As the current i leads the voltage by $\frac{\pi }{4},$ it is an $RC$ circuit, hence $\tan \phi = \frac{{{X_C}}}{R}$==> $\tan \frac{\pi }{4} = \frac{1}{{\omega \,CR}}$
==> $\omega \,CR = 1$ as $\omega$ $= 100 \,rad/sec$
==> $CR = \frac{1}{{100}}se{c^{ - 1}}$.
From all the given options only option $(a)$ is correct.

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