When an ac source is connected to a capacitor, which of the following…

The correct answer is Option (2) → The capacitor limits the current but does not completely prevent the flow of charge.

With an ac source, the capacitor is alternately charged and discharged as the current reverses every half cycle. So charge keeps flowing in the connecting wires, though no charge crosses the gap between the plates.

Option (1) No current flows, as a capacitor offers infinite resistance to an ac source. — Incorrect. The opposition of a capacitor to ac is its reactance \( X_C=1/\omega C \). It has a finite value for any ac frequency. The current stops only with a dc source, once the capacitor is fully charged.

Option (2) The capacitor limits the current but does not completely prevent the flow of charge. — Correct. The capacitive reactance limits the current amplitude to \( i_m=v_m/X_C \), like a resistance. The repeated charging and discharging keeps an alternating current flowing in the circuit.

Option (3) The current is hindered at first and later flows smoothly. — Incorrect. The current \( i=i_m\sin(\omega t+\pi/2) \) oscillates with the same amplitude in every cycle. It is never held back for a while and then released.

Option (4) The current flows smoothly at first and is hindered later. — Incorrect. With a dc source, current flows while the capacitor charges and falls to zero when it is fully charged. With ac the source reverses every half cycle, so the capacitor never stays charged.

NCERT (2026-27):
AC Voltage Applied to a Capacitor – “When the capacitor is connected to an ac source, … it limits or regulates the current, but does not completely prevent the flow of charge. The capacitor is alternately charged and discharged as the current reverses each half cycle.”