A LCR series circuit driven with Erms = 90 V at frequency fd = 30 Hz has resistance R = 80 Ω, an inductance with inductive reactance XL = 20.0 Ω and capacitance with capacitive reactance XC = 80.0 Ω. The power factor of the circuit is ______. (a) 0.8 (b) 0.64 (c) 0.9 (d) 0.5

Answer: (a). Z = √(R² + (XC - XL)²) = √(80² + 60²) = 100 Ω. Power factor cos φ = R/Z = 80/100 = 0.8. So the answer is (a) 0.8.

A LCR series circuit driven with Erms = 90 V at frequency fd = 30 Hz… | JEE Main 2026 (6 Apr, Shift 1)

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Power, Power Factor & Wattless Current

A LCR series circuit driven with $E_{rms} = 90\text{ V}$ at frequency $f_{\text{d}} = 30\text{ Hz}$ has resistance $R = 80\ \Omega$ , an inductance with inductive reactance $X_L = 20.0\ \Omega$ and capacitance with capacitive reactance $X_C = 80.0\ \Omega$ . The power factor of the circuit is ______.

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Answer: (a)

$Z = \sqrt{R^2 + (X_C - X_L)^2} = \sqrt{80^2 + 60^2} = 100\ \Omega$ .
Power factor $\cos\phi = \frac{R}{Z} = \frac{80}{100} = 0.8$ .
So the answer is (a) 0.8.

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