Read the following passage and answer the questions.
A student uses the laboratory mains supply of 220 V (rms) and 50 Hz. First, she joins an electric heater of resistance 110 Ω across the mains. The heater acts as a pure resistor. An ac ammeter is joined in series with the heater. She draws the source voltage and the current as phasors.
Next, she removes the heater. In its place she joins a coil of negligible resistance. The coil acts as a pure inductor, and its inductive reactance at 50 Hz is also 110 Ω. She notes the ammeter reading again and draws the phasor diagram for the coil.
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): The coil takes the same average power from the mains as the heater.
Reason (R): The average power supplied to a pure inductor over one complete cycle is zero.
In the light of the above statements, choose the most appropriate answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (A) is not correct but (R) is correct.
The heater and the coil each offer 110 Ω, so the same rms current flows in both. The power they take is still very different, because the phase between the voltage and the current is different.
Assertion (A) The coil takes the same average power from the mains as the heater. — False. The heater is a pure resistor, so it takes an average power \( P=V^{2}/R \):
\( \begin{aligned} P &= \frac{V^{2}}{R} \\ &= \frac{220^{2}}{110} \\ &= 440\ \mathrm{W} \end{aligned} \)
The coil takes no average power at all. So the two powers are not equal.
Reason (R) The average power supplied to a pure inductor over one complete cycle is zero. — True. In a pure inductor the current lags the voltage by \( \pi/2 \). The instantaneous power \( p_L=-(i_mv_m/2)\sin2\omega t \) is positive for half the time and negative for the other half, so its average over a cycle is zero.
NCERT (2026-27):
Points to Ponder – “7. There are no power losses associated with pure capacitances and pure inductances in an ac circuit. The only element that dissipates energy in an ac circuit is the resistive element.”
AC Voltage Applied to an Inductor – “Thus, the average power supplied to an inductor over one complete cycle is zero.”