Given below are two statements:
Statement I : Maximum power is dissipated in a circuit containing an inductor, a capacitor and a resistor connected in series with an AC source, when resonance occurs
Statement II : Maximum power is dissipated in a circuit containing pure resistor due to zero phase difference between current and voltage.
In the light of the above statements, choose the correct answer from the options given below:

Solution

Physics sir · 4 steps

Power depends on cos φ; both statements are really saying the same thing: make φ = 0.

1. Average power. In any AC circuit the average power is P = Vᵣₘₛ Iᵣₘₛ cos φ, where φ is the phase difference between current and voltage. For fixed Vᵣₘₛ, power is largest when Iᵣₘₛ is largest and cos φ = 1.

   P = (Vᵣₘₛ² R)/Z², Z = √(R² + (X_L - X_C)²)

2. Statement I. At resonance X_L = X_C, so Z = R takes its smallest value and the current is maximum. Also φ = 0, so cos φ = 1 and the power Vᵣₘₛ²/R is the maximum possible. Statement I is true.
3. Statement II. In a pure resistor, current and voltage are in phase, so φ = 0 and cos φ = 1. The full product Vᵣₘₛ Iᵣₘₛ is dissipated as heat, unlike an inductor or capacitor where φ = 90° and the average power is zero. Statement II is true.
4. So. Both statements are true, which is option (d).

The idea to keep. Average AC power is Vᵣₘₛ Iᵣₘₛ cos φ. Whenever current and voltage are in phase, as in a pure resistor or an LCR circuit at resonance, cos φ = 1 and power is maximum.

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