For an ac source rated at 220 V , 50 Hz , which of the following stat…

The correct answer is Option (3) → The average value over a period of (1/50) s is \( 0\,\mathrm{V} \).

The rating of an ac source gives its rms value. The time period is \( T = 1/f = 1/50\,\mathrm{s} \), so (1/50) s is one full cycle.

    \( \displaystyle V_{\mathrm{peak}} = \sqrt{2}\,V_{\mathrm{rms}} = 220\sqrt{2} \approx 311\,\mathrm{V} \)

Over a complete cycle the positive half and the negative half of the sine wave cancel, so the average value is zero.

Option (1) The peak value over a period of (1/50) s is \( 220\,\mathrm{V} \). — Incorrect. The rated \( 220\,\mathrm{V} \) is the rms value; the peak value is \( 220\sqrt{2}\,\mathrm{V} \).

Option (2) The average value over a period of (1/50) s is \( 220\,\mathrm{V} \). — Incorrect. The average over a full cycle is zero, not the rms value.

Option (3) The average value over a period of (1/50) s is \( 0\,\mathrm{V} \). — Correct. The average over one full period is zero.

Option (4) The average value over a period of (1/50) s is \( 220\sqrt{2}\,\mathrm{V} \). — Incorrect. \( 220\sqrt{2}\,\mathrm{V} \) is the peak value, not the average over a period.

NCERT (2026-27):
AC Voltage Applied to a Resistor – “… We see that, like the applied voltage, the current varies sinusoidally and has corresponding positive and negative values during each cycle. Thus, the sum of the instantaneous current values over one complete cycle is zero, and the average current is zero.”

AC Voltage Applied to a Resistor – “… It is customary to measure and specify rms values for ac quantities. For example, the household line voltage of 220 V is an rms value with a peak voltage of

    \( \displaystyle v_m = \sqrt{2}\,V = (1.414)(220\ \mathrm{V}) = 311\ \mathrm{V} \)”