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 reactanc

Question

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 x 10 . The value of x is:

TestHub · Accepted Answer

Power factor in LCR circuit is given by,

$\cos ϕ = \frac{R}{Z}$ , where, $Z$ is the total impedance of the circuit.

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

Putting the values, we have

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

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

Thus, the value of $x = 8$ .

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