JEE Main 2021 · 31 August · morning · Single correct · +4 / −1
In an ac circuit, an inductor, a capacitor and a resistor are connected in series with X L = R = X C . Impedance of this circuit is :
- (a) 2R²
- (b) Zero
- (c) R
- (d) R√2
Answer and solution
Answer (c) R
Solution
Physics sir · 3 steps
When X_L = X_C, the inductor and capacitor cancel each other, so only R is left to oppose the current.
- Impedance formula. In a series RLC circuit, R adds at right angles to the net reactance X_L - X_C, because the voltage across R is 90° out of phase with the voltage across L and C.
Z = √(R² + (X_L - X_C)²)
- Reactances cancel. Here X_L = X_C, so X_L - X_C = 0. The inductor and capacitor voltages are equal and opposite, so they cancel. This is the resonance condition.
- So. Z = √(R² + 0) = R. The answer is (c).
The idea to keep. Inductive and capacitive reactance subtract, they never add. When they are equal, the circuit is at resonance and Z = R, its minimum value.
Answer from the NTA final answer key. Solution by PrepWiser.