First slide

Alternating Current and voltage

Question

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 $π / 4$ , as shown in the diagram. If the circuit consists possibly only of RC or LC in series, find the relationship between the two elements

Moderate

A

$R = 1 kΩ, C = 10 μF$
B

$R = 1 kΩ, C = 1 μF$
C

$R = 1 kΩ, L = 10 H$
D

$R = 1 kΩ, L = 1 H$

Solution

As the current i leads the voltage by $\frac{π}{4},$ it is an RC circuit, hence $tanφ = \frac{X_{C}}{R} \Rightarrow \tan \frac{π}{4} = \frac{1}{ω CR}$
$\Rightarrow ω CR = 1 as ω = 100 rad / \sec$
$\Rightarrow CR = \frac{1}{100} \sec^{- 1} .$
From all the given options only option (a) is correct.

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