Question 46 of 190

In the above circuit, $C=\dfrac{\sqrt{3}}{2}\mu F, {R}_{2}=20\Omega , L=\dfrac{\sqrt{3}}{10}H$ and ${R}_{1}=10\Omega .$ Current in $L\text{-}{R}_{1}$ path is ${I}_{1}$ and in $C-{R}_{2}$ path it is ${I}_{2}.$ The voltage of $AC source is given by, V=200 2  sin( 100 t )$ volts. The phase difference between ${I}_{1}$ and ${I}_{2}$ is:

A${60}^{o}$B${0}^{o}$C${30}^{o}$D${150}^{o}$

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Answer: (D) ${150}^{o}$

Inductive reactance ${X}_{L}=\omega L=100\dfrac{\sqrt{3}}{10}\Omega$

$=10 \sqrt{3} \Omega$

Capacitive reactance

${X}_{c}=\dfrac{1}{\omega C}=\dfrac{1}{100\times \dfrac{\sqrt{3}}{2}\times {10}^{-6}}\Omega =\dfrac{20000}{\sqrt{3}}\Omega$

For ${i}_{1}$, phase difference between ${i}_{1}$ & voltage$tan{\phi }_{1} =\dfrac{{x}_{L}}{R}=\dfrac{10\sqrt{3}}{10}=\sqrt{3}$

$\Rightarrow {\phi }_{1} = {60}^{o},$ current lagging

For ${i}_{2}$ , phase difference
$tan{\phi }_{2}=\dfrac{{X}_{C}}{R}=\dfrac{20000}{\sqrt{3}\times 20}=\dfrac{1000}{\sqrt{3}}$

$\Rightarrow {\phi }_{1} \approx {90}^{o},\text{current leading}$

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