To an ac power supply of 220 V at 50 Hz , a resistor of $20 \Omega$, a capacitor of reactance $25 \O

Question

To an ac power supply of 220 V at 50 Hz , a resistor of $20 \Omega$, a capacitor of reactance $25 \Omega$ and an inductor of reactance $45 \Omega$ are connected in series. The corresponding current in the circuit and the phase angle between the current and the voltage is, respectively

Professor PC Thomas Classes · Answer

$\begin{aligned} & 	ext { (d) : Given, } V=220 \mathrm{~V}, v=50 \mathrm{~Hz} \ & R=20 \Omega, X_L=45 \Omega 	ext { and } X_C=25 \Omega \ & 	ext { Current, } I=\frac{V}{Z}=\frac{220}{\sqrt{R^2+\left(X_L-X_Cight)^2}}=\frac{220}{\sqrt{400+400}} \ & =\frac{220}{20 \sqrt{2}}=\frac{11}{\sqrt{2}}=7.8 \mathrm{~A} \ & 	ext { Phase angle, } \phi=	an ^{-1}\left(\frac{X_L-X_C}{R}ight)=	an ^{-1}\left(\frac{45-25}{20}ight)\end{aligned}$ $=	an ^{-1}\left(\frac{20}{20}ight)$ or $\phi=45^{\circ}$