JEE Main 2026 · 24 January · morning · Single correct · +4 / −1
For the series LCR circuit connected with 220 V,50 Hz a.c source as shown in the figure, the power factor is α/10. The value of α is ____ .
- (a) 4
- (b) 8
- (c) 6
- (d) 10
Answer and solution
Answer (c) 6
Solution
Physics sir · 3 steps
Subtract the two reactances first, then build Z like a right triangle with R as the base.
- Net reactance. In series, the inductor and capacitor voltages are opposite in phase, so their reactances subtract: X_C - X_L = 150 - 70 = 80 Ω.
- Impedance. The resistance and the net reactance are at right angles, so Z = √(R² + (X_C - X_L)²) = √(60² + 80²) = √10000 = 100 Ω.
cos φ = R/Z = 60/100 = 6/10
- So. The power factor is 6/10, so α = 6. The supply values of 220 V and 50 Hz are not needed, because the reactances are already given.
The idea to keep. Power factor is always R/Z. In a series LCR circuit, find the net reactance |X_L - X_C| first, and look out for 3-4-5 triangles in the numbers.
Answer from the NTA final answer key. Solution by PrepWiser.