Alternating CurrentHard

Question

For the series LCR circuit connected with 220 V , 50 Hz a.c source as shown in the figure, the power factor is $\frac{\alpha}{10}$. The value of $\alpha$ is $\_\_\_\_$

Options

A.4
B.10
C.6
D.8

Solution

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

$$\begin{matrix} Z & \ = \sqrt{R^{2} + \left( X_{L} - X_{C} \right)^{2}} \\ & \ = \sqrt{60^{2} + (150 - 70)^{2}} = 100\Omega \\ \therefore & \text{~}\text{Power factor}\text{~} = \frac{60}{100} = \frac{6}{10} \end{matrix}$$

Then $a = 6$

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