Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): In a series LCR circuit connected to an ac source, electrical energy is dissipated only in the resistor.
Reason (R): The average power supplied to a pure inductor, and to a pure capacitor, 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 1
The correct answer is Option (1) → Both (A) and (R) are correct and (R) is the correct explanation of (A).
Assertion (A) In a series LCR circuit connected to an ac source, electrical energy is dissipated only in the resistor. — True. The source supplies an average power \( P=VI\cos\phi \). All of this power appears as heat in the resistor.
Reason (R) The average power supplied to a pure inductor, and to a pure capacitor, over one complete cycle is zero. — True. In each of them the current and the voltage differ in phase by \( \pi/2 \). So \( \cos\phi=0 \) for each of them.
Why Reason (R) explains Assertion (A)?
The power supplied to the inductor or the capacitor is positive for half the time and negative for the other half. Over a full cycle, they take no net energy from the source.
So the resistor is the only element that takes power from the source. The whole average power of the circuit, \( P=I^{2}R \), is dissipated in it.
NCERT (2026-27):
Power in AC Circuit: the Power Factor – “Case (iii) LCR series circuit: … So, φ may be non-zero in a RL or RC or RCL circuit. Even in such cases, power is dissipated only in the resistor.”
Points to Ponder – “7. There are no power losses associated with pure capacitances and pure inductances in an ac circuit. …”