In an a.c. circuit, a resistor, a capacitor and an inductor are conne…

The correct answer is Option (3) → \( R \)

In a series LCR circuit the inductive and capacitive reactances act in opposite directions in the phasor diagram, so only their difference adds to the resistance.

    \( \displaystyle Z = \sqrt{R^{2} + (X_L - X_C)^{2}} \)

Putting \( X_L = X_C \):

    \( \displaystyle Z = \sqrt{R^{2} + 0} = R \)

This is the resonance condition: the reactances cancel and the impedance is just the resistance.

Note: This question is from NCERT (2026-27). NTA sets numerical questions from NCERT too, so do not ignore NCERT while practising numericals.

NCERT (2026-27):
Resonance – “… For an RLC circuit driven with voltage of amplitude v_m and frequency ω, we found that the current amplitude is given by

    \( \displaystyle i_m = \frac{v_m}{Z} = \frac{v_m}{\sqrt{R^2 + (X_C - X_L)^2}} \)

with X_c = 1/ωC and X_L = ωL. So if ω is varied, then at a particular frequency ω₀, X_c = X_L, and the impedance is minimum

    \( \displaystyle Z = \sqrt{R^2 + 0^2} = R \)”