A series LCR circuit with L = π 100 mH , C = π 1 0 − 3 F and R = 10Ω , is connected across an AC source of 220 V , 50 Hz supply. The power factor of the circuit would be ____.

Question

A series LCR circuit with L = π 100 ​ mH , C = π 1 0 − 3 ​ F and R = 10Ω , is connected across an AC source of 220 V , 50 Hz supply. The power factor of the circuit would be ____.

TestHub · Accepted Answer

The capacitive reactance of the circuit is given by,

$X_{c} = \frac{1}{ω C} = \frac{π}{2 π \times 50 \times 1 0 ^{- 3}} = 10Ω$ The inductive reactance of the circuit is given by,

$X_{L} = ω L = 2 π \times 50 \times \frac{100}{π} \times 1 0^{- 3} = 10Ω$ From above calculations, it is clear that

$X_{C} = X_{L}$

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

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