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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 reactance $X_{L} = 70 Ω$ , and a capacitor of capacitive reactance $X_{C} = 130 Ω$ . The power factor of circuit is $\frac{x}{10}$ . The value of $x$ is...

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answer is 8.

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Detailed Solution

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

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