Given below are two statements :
Statement I : The reactance of an ac circuit is zero. It is possible that the circuit contains a capacitor and an inductor.
Statement II : In ac circuit, the average power delivered by the source never becomes zero.
In the light of the above statements, choose the correct answer from the options given below.

Solution

Physics sir · 3 steps

Test each statement against the extreme case: resonance for the first, a pure L or C circuit for the second.

1. Statement I. The net reactance of a series LCR circuit is X = X_L - X_C. When ω L = 1/(ω C) the two cancel, so X = 0 even though both an inductor and a capacitor are present. This is resonance, so Statement I is true.

   P_(avg) = Vᵣₘₛ Iᵣₘₛ cos φ

2. Statement II. In a purely inductive or purely capacitive circuit the current and voltage differ in phase by 90°. Then cos φ = cos 90° = 0, so the average power is zero. Such a circuit stores energy and returns it every cycle, so Statement II is false.
3. So. Statement I is true and Statement II is false, which is option (c).

The idea to keep. Zero reactance means X_L and X_C cancel at resonance, not that L and C are absent. Average power is zero whenever cos φ = 0, as in a pure L or pure C circuit.

Answer from the NTA final answer key. Solution by PrepWiser.