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  4. In an L-C-R circuit, if impedance is √3 times of resistance and capacitive reactance is zero. Find the phase difference.

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Q. In an L-C-R circuit, if impedance is $\sqrt{3}$ times of resistance and capacitive reactance is zero. Find the phase difference.

Alternating Current

Solution:

The phasor diagram of L-C-R circuit shows that phase angle $\phi$ is given by
image
$ \tan \phi = \frac{ V_L - V_C}{ V_R} = \frac{ X_L - X_C}{ R} $
Given, $ X_C = 0, \, X_L = \sqrt 3 R$
$\therefore \phi = \tan^{ - 1} \bigg( \frac{ \sqrt 3 R}{ R} \bigg) $
$\Rightarrow \phi = \tan^{ - 1} \, ( \sqrt 3) = 60^\circ$