An inductance coil of reactance 30 Ω, a resistor of resistance 40 Ω and a capacitor of reactance 50 Ω are connected in series across an a.c. source. The current flowing in the circuit is 5 A. The effective potential difference across points \( A \) and \( C \) is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 250 V
In a series a.c. circuit the voltages across L and R are 90° out of phase, so they add as phasors, not arithmetically. From the figure, points A and C take in only the inductor and the resistor; the capacitor lies between C and D.
\( \displaystyle V_{AC} = I\sqrt{X_L^{2} + R^{2}} \)
\( \displaystyle V_{AC} = 5\,\mathrm{A} \times \sqrt{(30\,\Omega)^{2} + (40\,\Omega)^{2}} = 5\,\mathrm{A} \times 50\,\Omega \)
\( V_{AC} = 250\,\mathrm{V} \)
The current of 5 A is an effective (rms) value, so this is the effective voltage and no factor \( \sqrt{2} \) enters.