An LCR series circuit is driven by an alternating voltage source having:

• E_rms = 40 V
• Frequency, f = 50/π Hz
• Resistance, R = 30 Ω
• Inductive reactance, X_L = 20 Ω
• Capacitive reactance, X_C = 60 Ω

Find the power factor of the circuit.

The power factor of an AC circuit is given by:

Power Factor = cos φ = R/Z

where Z is the impedance of the circuit.

First calculate the net reactance:

X = X_L − X_C

= 20 − 60

= −40 Ω

The negative sign indicates that the circuit behaves as a capacitive circuit.

Now calculate impedance:

Z = √(R² + X²)

= √(30² + 40²)

= √(900 + 1600)

= √2500

= 50 Ω

Therefore:

Power Factor

= R/Z

= 30/50

= 0.6

Since the circuit is capacitive, the current leads the voltage, but the magnitude of the power factor remains 0.6.

Final Answer

Power Factor = 0.6