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Physics Question 45 – JEE-MAIN 2026

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A LCR series circuit driven with Erms=90 V at frequency f0=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 _______.

The power factor of an AC circuit describes the ratio of real power to apparent power, indicating how effectively electrical power is being converted into useful work.

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Ninja Strategy•Pythagorean Triple Recognition

Recognize that the resistance R=80 and net reactance |XL−XC|=60 form a 3-4-5 Pythagorean triple scaled by 20 (i.e., 3×20=60, 4×20=80), implying the impedance Z will be 5×20=100 without extensive calculation.

Step 1: Calculate Net Reactance✦ Active

Determine the difference between inductive and capacitive reactances.

XL−XC=20.0 Ω−80.0 Ω=−60.0 Ω
Step 2: Calculate Impedance○ Expand

Use the resistance and net reactance to find the total impedance of the circuit.

Z=R2+(XL−XC)2=(80 Ω)2+(−60 Ω)2=6400+3600=10000=100 Ω
Step 3: Calculate Power Factor○ Expand

Divide the resistance by the impedance to find the power factor.

cos⁡ϕ=RZ=80 Ω100 Ω=0.8
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