Consider the following statements about alternating current:
(A) The household supply voltage of 220 V is an rms value.
(B) The average of an alternating current over one complete cycle is equal to its peak value.
(C) The rms current is the equivalent dc current that would produce the same average power loss as the alternating current.
(D) The average power consumed in an ac circuit over a complete cycle can be negative.
Which of the above statements are incorrect?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (B) and (D) only
Ac values are usually given as rms values. The rms value is fixed by the heating effect of the current, and this effect does not depend on the direction of the current.
(A) The household supply voltage of 220 V is an rms value. — Correct statement. The 220 V of the mains is an rms value. Its peak value is about 311 V.
(B) The average of an alternating current over one complete cycle is equal to its peak value. — Incorrect statement. The current is positive for one half of the cycle and negative for the other half. The two halves cancel, so the average current over one cycle is zero.
(C) The rms current is the equivalent dc current that would produce the same average power loss as the alternating current. — Correct statement. This is what the rms current means. A dc current equal to \( I \) gives the same average power loss \( I^{2}R \) in a resistor.
(D) The average power consumed in an ac circuit over a complete cycle can be negative. — Incorrect statement. Power is used up only in the resistance. In a pure inductor or capacitor the average power is zero. So the average power over a cycle is positive or zero.
NCERT (2026-27):
AC Voltage Applied to a Resistor – “… For example, the household line voltage of 220 V is an rms value with a peak voltage of”
\( v_m=\sqrt{2}\,V=(1.414)(220\ \mathrm{V})=311\ \mathrm{V} \)
AC Voltage Applied to a Resistor – “… 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 – “In fact, the I or rms current is the equivalent dc current that would produce the same average power loss as the alternating current.”
Points to Ponder – “3. The power consumed in an ac circuit is never negative.”