A series LCR circuit is connected to an AC source of 220 V , 50 Hz. The circuit contains a resistance $R = 80 Ω$ , an inductor of inductive resistance $X_{L} = 70 Ω$ and a capacitor of capacitive reactance $X_{C} = 130 Ω .$ The power factor of the circuit is $\frac{X}{10} .$ The value of x is …..

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answer is 8.

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Detailed Solution

$\cos ϕ = \frac{R}{Z} = \frac{R}{\sqrt{R^{2} + {(X_{C} - X_{L})}^{2}}}$
$\Rightarrow \cos ϕ = \frac{80}{\sqrt{80^{2} + {(130 - 70)}^{2}}} \Rightarrow \cos ϕ = \frac{8}{10}$

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