JEE Main 2023 · 30 January · evening · Single correct · +4 / −1
In the given circuit, rms value of current (Iᵣₘₛ) through the resistor R is:
- (a) 2 √2 A
- (b) 2 A
- (c) 1/2 A
- (d) 20 A
Answer and solution
Answer (b) 2 A
Solution
Physics sir · 3 steps
It is a series circuit, so find the impedance first, then divide the rms voltage by it.
- Net reactance. In series, the inductor and capacitor voltages are opposite in phase, so their reactances subtract: X_L - X_C = 200 - 100 = 100 Ω.
Z = √(R² + (X_L - X_C)²) = √(100² + 100²) = 100√2 Ω
- Same current everywhere. One current flows through every element of a series circuit, including R. So Iᵣₘₛ = Vᵣₘₛ/Z = 200√2/100√2.
- So. Iᵣₘₛ = 2 A through the resistor, which is option (b).
The idea to keep. In a series LCR circuit, never divide by R alone. Subtract X_C from X_L, combine with R by Pythagoras to get Z, and I = V/Z holds for rms values directly.
Answer from the NTA final answer key. Solution by PrepWiser.