A series LCR circuit with , and , is connected across an ac source of 220V, 50 Hz supply. The power factor of the circuit would be

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Solution

Q.
A series LCR circuit with $L = \frac{100}{π} m H$ , $C = \frac{10^{- 3}}{π} F$ and $R = 10 Ω$ , is connected across an ac source of 220V, 50 Hz supply. The power factor of the circuit would be _________ . [2024]

Ans.
(1) $X_{c} = \frac{1}{ω C} = \frac{π}{2 π \times 50 \times 10^{- 3}} = 10 Ω$

$X_{L} = ω L = 2 π \times 50 \times \frac{100}{π} \times 10^{- 3} = 10 Ω$

$∵ X_{C} = X_{L}, Hence, circuit is in resonance$

$∴ power factor = \frac{R}{Z} = \frac{R}{R} = 1$

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