Alternating Current

JEE Main level, numerical answer, medium

163 of 190

Question 163 of 190

A series LCR circuit with L=100πmH,C=10−3πFL=\dfrac{100}{\pi }mH,C=\dfrac{{10}^{-3}}{\pi }F and R=10ΩR=10\Omega, is connected across an AC source of 220V,50Hz220V,50Hz supply. The power factor of the circuit would be ____.

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Answer: 1

The capacitive reactance of the circuit is given by,
Xc=1ωC=π2π×50×10−3=10Ω\begin{matrix}{X}_{c} & = & \dfrac{1}{\omega C} \\ & = & \dfrac{\pi }{2\pi \times 50\times {10}^{-3}} \\ & = & 10\Omega \end{matrix}
The inductive reactance of the circuit is given by,
XL=ωL=2π×50×100π×10−3=10Ω\begin{matrix}{X}_{L} & = & \omega L \\ & = & 2\pi \times 50\times \dfrac{100}{\pi }\times {10}^{-3} \\ & = & 10\Omega \end{matrix}
From above calculations, it is clear that
XC=XL{X}_{C}={X}_{L}
∴∴ Power factor =RZ=RR=1=\dfrac{R}{Z}=\dfrac{R}{R}=1

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