A series LCR circuit is connected to an AC source of 220 V, 50 Hz. The circuit contains a resistance , an inductor of inductive reactance , and a capacitor of capacitive reactance . The power factor of the circuit is . The value of is _________.

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Solution

Q.
A series LCR circuit is connected to an AC source of 220 V, 50 Hz. The circuit contains a resistance $R = 8 Ω$ , an inductor of inductive reactance $X_{L} = 70 Ω$ , 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 _________. [2023]

Ans.
(8)

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

$\cos ϕ = \frac{80}{\sqrt{{(80)}^{2} + {(60)}^{2}}}$

$\cos ϕ = \frac{80}{100} = \frac{8}{10}$

$So, x = 8$

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