Which of the following is not correct for an ac circuit?

The correct answer is Option (1) → The applied rms voltage equal to algebraic sum of the rms voltages across the series elements of the circuit.

The question asks for the wrong statement. In a series ac circuit the voltages across \( R \), \( L \) and \( C \) are not in phase, so they add as phasors (vectors), not as plain numbers.

Option (1) — Incorrect statement. The applied rms voltage is the phasor sum

    \( V_{\mathrm{rms}} = \sqrt{V_R^{2} + (V_L - V_C)^{2}} \)

which is less than the algebraic sum \( V_R + V_L + V_C \), because \( V_L \) and \( V_C \) are in opposite phase and \( V_R \) is \( 90^\circ \) out of phase with them.

Option (2) — Correct statement. A capacitor is connected across the interrupter of the primary of an induction coil to reduce sparking.

Option (3) — Correct statement. The power factor is \( \cos\phi = R/Z \). It equals 1 when \( Z = R \), which is the least value of the impedance \( Z = \sqrt{R^{2} + (X_L - X_C)^{2}} \).

Option (4) — Correct statement. At resonance \( X_L = X_C \), so \( Z = R \) is minimum and the current \( I = V/R \) is maximum.

NCERT (2026-27):
Resonance – “… The algebraic sum of the two voltages, V_R and V_C is 311.3 V which is more than the source voltage of 220 V. How to resolve this paradox? As you have learnt in the text, the two voltages are not in the same phase. Therefore, they cannot be added like ordinary numbers.”