Given below are two statements:
Statement I : An AC circuit undergoes electrical resonance if it contains either a capacitor or an inductor.
Statement II : An AC circuit containing a pure capacitor or a pure inductor consumes high power due to its non-zero power factor.
In the light of above statements, choose the correct answer form the options given below:

Solution

Physics sir · 4 steps

Resonance needs L and C together, and a pure L or C draws zero average power, so both statements fall.

1. Statement I. Resonance happens when the inductive and capacitive reactances cancel, X_L = X_C, which gives ω₀ = 1/√LC. With only a capacitor or only an inductor there is nothing to cancel against, so there is no resonance. Statement I is false.
2. Phase difference. In a purely inductive or purely capacitive circuit, current and voltage are out of phase by φ = 90°. The power factor is cos φ = cos 90° = 0.

   P_(avg) = Vᵣₘₛ Iᵣₘₛ cos φ = Vᵣₘₛ Iᵣₘₛ × 0 = 0

3. Statement II. The power factor is zero, not non-zero, and the average power consumed is zero, not high. Energy stored in one quarter cycle is returned to the source in the next. Statement II is false.
4. So. Both statements are false, which is option (a).

The idea to keep. Resonance always needs both L and C so their reactances can cancel. A pure L or pure C has a 90° phase gap, power factor zero, and zero average power: a wattless current.

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