A series LCR circuit with L = (100)/(π)mH, C = 10 ^ - 3 π F and R =...

The capacitive reactance of the circuit is given by, 

$\begin{cases}{X}_{c} & = & \dfrac{1}{\omegaC} \\ & = & \dfrac{\pi}{2\pi \times 50 \times {10}^{- 3}} \\ & = & 10Ω\end{cases}$

The inductive reactance of the circuit is given by, 

$\begin{cases}{X}_{L} & = & \omegaL \\ & = & 2\pi \times 50 \times \dfrac{100}{\pi} \times {10}^{- 3} \\ & = & 10Ω\end{cases}$

From above calculations, it is clear that

${X}_{C} = {X}_{L}$

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