First slide

Phasors and Phasor Diagrams

Question

In a circuit, L, C and R are connected in series with an alternating voltage source of frequency f. The current lags the voltage by 45⁰. The value of C is

Moderate

A

$\frac{1}{2 πf (2 πfL + R)}$
B

$\frac{1}{πf (2 πfL + R)}$
C

$\frac{1}{2 πf (2 πfL - R)}$
D

$\frac{1}{πf (2 πfL - R)}$

Solution

$tanϕ = \frac{ωL - \frac{1}{ωC}}{R}$
$ϕ$ being the angle by which the current lags the voltage.
Given, $ϕ = 45^{\circ}$
$∴ \tan 45^{\circ} = \frac{ωL - \frac{1}{ωC}}{R}$
$\Rightarrow 1 = \frac{ωL - \frac{1}{ωC}}{R}$
$\Rightarrow R = ωL - \frac{1}{ωC}$
$\Rightarrow C = \frac{1}{ω (ωL - R)} = \frac{1}{2 πf (2 πfL - R)}$

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