A series LCR circuit is connected to an a.c. source of 230 V, 50 Hz. The circuit contains resistance of 80 Ω an inductor having inductive reactance 70 Ω and a capacitor of capacitive reactance 130 Ω. The power factor of the circuit is x. The value of x is (a) 0.4 (b) 0.8 (c) 0.6 (d) 0.9

Answer: (b). R = 8060Z = 100φ Power factor cos φ = R/Z, with Z = √(R² + (XC - XL)²). XC - XL = 130 - 70 = 60 Ω Z = √(80² + 60²) = 100 Ω x = 80/100 = 0.8. So the answer is (b) 0.8.

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Series LCR Circuit

A series LCR circuit is connected to an a.c. source of $230\text{ V},\ 50\text{ Hz}$ . The circuit contains resistance of $80\ \Omega$ an inductor having inductive reactance $70\ \Omega$ and a capacitor of capacitive reactance $130\ \Omega$ . The power factor of the circuit is $x$ . The value of $x$ is

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Answer: (b)

Power factor $\cos\phi = \dfrac{R}{Z}$ , with $Z = \sqrt{R^2 + (X_C - X_L)^2}$ .
$X_C - X_L = 130 - 70 = 60\ \Omega$
$Z = \sqrt{80^2 + 60^2} = 100\ \Omega$
$x = \dfrac{80}{100} = 0.8$ . So the answer is (b) 0.8.

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