First slide

Phasors and Phasor Diagrams

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 RL 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, $tanϕ = \frac{X_{C}}{R} \Rightarrow \tan \frac{π}{4} = \frac{1}{ωCR}$
$\Rightarrow ωCR = 1 as ω = 100 rad / \sec$
$\Rightarrow CR = \frac{1}{100} \sec^{- 1}$
From all the given options only option (1) is correct.

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