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

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TestHub · Accepted Answer

The capacitive reactance of the circuit is given by,

$\begin{array}{rcl} X_{c} & = & \frac{1}{ω C} \\ = & \frac{π}{2 π \times 50 \times 10^{- 3}} \\ = & 10 Ω \end{array}$

The inductive reactance of the circuit is given by,

$\begin{array}{rcl} X_{L} & = & ω L \\ = & 2 π \times 50 \times \frac{100}{π} \times 10^{- 3} \\ = & 10 Ω \end{array}$

From above calculations, it is clear that

$X_{C} = X_{L}$

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

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