A LCR series circuit driven with E max = 90 V at frequency f d = 30 Hz has resistance R = 80Ω , an inductance with inductive reactance X L = 20.0Ω and capacitance with capacitive reactance X C = 80.0Ω . The power factor of the circuit is

Physics · Alternating Current

JEE Main 2026 — 6 April, Morning Shift — Question 15

A LCR series circuit driven with $E_{\mathrm{max}} = 90\mathrm{V}$ at frequency $f_d = 30\mathrm{Hz}$ 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

Option A:
0.8
Correct
Option B:
0.64
Option C:
0.9
Option D:
0.5

Answer: A

Step-by-step solution

Impedance $Z = \sqrt{R^2 + (X_L - X_C)^2} = \sqrt{80^2 + (20-80)^2} = \sqrt{6400+3600}=100\Omega$ . Power factor $\cos\phi = R/Z = 80/100 = 0.8$ .

Answer key and solution verified before publishing.

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Exam: JEE Main 2026
Paper: 6 April, Morning Shift
Subject: Physics
Chapter: Alternating Current
Topic: Series LCR Circuit and Power Factor