Question 85: AC fundamentals

Question

A series LCR circuit with $$\mathrm{L}=\frac{100}{\pi} \mathrm{mH}, \mathrm{C}=\frac{10^{-3}}{\pi} \mathrm{F}$$ and $$\mathrm{R}=10 \Omega$$, is connected across an ac source of $$220 \mathrm{~V}, 50 \mathrm{~Hz}$$ supply. The power factor of the circuit would be ________.

Accepted Answer

$$\begin{aligned}
& \mathrm{X}_{\mathrm{c}}=\frac{1}{\omega \mathrm{C}}=\frac{\pi}{2 \pi 	imes 50 	imes 10^{-3}}=10 \Omega \
& \mathrm{X}_{\mathrm{L}}=\omega \mathrm{L}=2 \pi 	imes 50 	imes \frac{100}{\pi} 	imes 10^{-3} \
& =10 \Omega \
& \because \mathrm{X}_{\mathrm{C}}=\mathrm{X}_{\mathrm{L}}, 	ext { Hence, circuit is in resonance } \
& 	herefore 	ext { power factor }=\frac{\mathrm{R}}{\mathrm{Z}}=\frac{\mathrm{R}}{\mathrm{R}}=1
\end{aligned}$$

AC fundamentals

A series LCR circuit with $\mathrm{L}=\frac{100}{\pi} \mathrm{mH}, \mathrm{C}=\frac{10^{-3}}{\pi} \mathrm{F} and \mathrm{R}=10 \Omega, is connected across an ac source of 220 \mathrm{~V}, 50 \mathrm{~Hz}$ supply. The power factor of the circuit would be ________.

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