Question 37

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______.

$$ R = 60 \, \Omega, \quad X_L = 70 \, \Omega, \quad X_C = 150 \, \Omega $$

$$ Z = \sqrt{R^2 + (X_L - X_C)^2} $$

$$ Z = \sqrt{60^2 + (70 - 150)^2} $$

$$ Z = \sqrt{3600 + 6400} = \sqrt{10000} = 100 \, \Omega $$

power factor ($$\cos \phi$$)

$$ \cos \phi = \frac{R}{Z} $$

$$ \cos \phi = \frac{60}{100} = \frac{6}{10} $$

$$ \frac{\alpha}{10} = \frac{6}{10} $$

$$ \alpha = 6 $$

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