Physics - EMI/AC Question with Solution | TestHub

Inductive reactance $X_L=\omega L=100\frac{\sqrt{3}}{10} \Omega$

$=10\sqrt{3}\Omega$

Capacitive reactance

$X_c=\frac{1}{\omega C}=\frac{1}{100\times \frac{\sqrt{3}}{2}\times {10}^{-6}} \Omega =\frac{20000}{\sqrt{3}} \Omega$

For $i_1$, phase difference between $i_1$ & voltage${t}{a}{n}{\varphi }_1=\frac{x_L}{R}=\frac{10\sqrt{3}}{10}=\sqrt{3}$

$\Rightarrow {\varphi }_1={60}^o,$ current lagging

For $i_2$ , phase difference

${t}{a}{n}{\varphi }_2=\frac{X_C}{R}=\frac{20000}{\sqrt{3}\times 20}=\frac{1000}{\sqrt{3}}$

$\Rightarrow {\varphi }_1\approx {90}^o,\text{\hspace{0.17em}\hspace{0.17em}current leading}$

$\therefore$ difference in phase $={90}^o+{60}^o={150}^o$