An inductor 20 mH , a capacitor $100 \mu \mathrm{~F}$ and a resistor $50 \Omega$ are connected in se

Question

An inductor 20 mH , a capacitor $100 \mu \mathrm{~F}$ and a resistor $50 \Omega$ are connected in series across a source of emf, $V=10 \sin 314 t$. The power loss in the circuit is\

Professor PC Thomas Classes · Answer

(a) : Impedance $Z$ in an ac circuit is\ $Z=\sqrt{R^{2}+\left(X_{C}-X_{L}ight)^{2}}$; where $X_{C}=$ capacitive reactance and $X_{L}=$ inductive reactance.\ Also $X_{C}=\frac{1}{\omega C}$ and $X_{L}=\omega L$\ $	herefore \quad Z=\sqrt{(50)^{2}+\left(\frac{1}{314 	imes 100 	imes 10^{-6}}-314 	imes 20 	imes 10^{-3}ight)^{2}}$\ or $Z=56 \Omega$\ The power loss in the circuit is $P_{a v}=\left(\frac{V_{r m s}}{Z}ight)^{2} R$\ $	herefore \quad P_{a v}=\left(\frac{10}{(\sqrt{2}) 56}ight)^{2} 	imes 50=0.79 \mathrm{~W}$\