In the shown AC circuit phase different between currents I_1 and … - Vidyadip

MCQ

In the shown $AC$ circuit phase different between currents $I_1$ and $I_2$ is

A
$\frac{\pi }{2} - {\tan ^{ - 1}}\,\frac{{{x_L}}}{R}$
B
${\tan ^{ - 1}}\,\frac{{{x_L} - {x_C}}}{R}$
✓
$\frac{\pi }{2} + {\tan ^{ - 1}}\,\frac{{{x_L}}}{R}$
D
${\tan ^{ - 1}}\,\frac{{{x_L} - {x_C}}}{R} + \frac{\pi }{2}$

✓

Answer

Correct option: C.

$\frac{\pi }{2} + {\tan ^{ - 1}}\,\frac{{{x_L}}}{R}$

c
Current leads the voltage by $\frac{\pi}{2}$ in capacitor and by $\frac{\tan ^{-1} X_{L}}{R}$ in $R L$ circuit phase difference in $I_{1}$ and $I_{2}$

$=\frac{\pi}{2}+\frac{\tan ^{-1} X_{L}}{R}$

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