When is Maximum Power Dissipated in an AC Circuit?

In a purely resistive circuit. Average power in AC is P = Vrms x Irms x cos phi. The power factor cos phi is largest (equal to 1) only when the phase angle phi = 0, which happens when there is no net reactance. A pure resistor has phi = 0, so all the supplied power is dissipated. This is exactly what NEET 2023 asked - the answer is the resistive circuit.

Because average power = Vrms x Irms x cos phi. Vrms and Irms are fixed by the source and the circuit, so the only way to make P as large as possible is to make cos phi as large as possible. The maximum value cos phi can take is 1 (when phi = 0). At that point current and voltage rise and fall together, so power (which is voltage times current) is always positive and never returns energy to the source.

Both give cos phi = 1, so both give maximum power for a given source. In a plain resistor there is no L or C at all. In a series LCR circuit at resonance, XL = XC, so the inductive and capacitive effects cancel and the net reactance is zero. The circuit then behaves like a pure resistance R, impedance Z = R, phi = 0, and power is maximum. So resonance is the way an LCR circuit reaches its maximum-power condition.

No. A pure inductor and a pure capacitor have phi = 90 degrees, so cos phi = 0 and average power P = Vrms x Irms x 0 = 0. They store energy in one quarter cycle and return all of it in the next. The current through them is called wattless current. Only resistance converts electrical energy into heat, so only resistance dissipates power.

At resonance Z = R (smallest possible impedance), so current is maximum, Irms = Vrms / R. The maximum average power is P_max = Vrms^2 / R = Irms^2 x R. Lowering R would raise this value, but for a fixed R the power is largest exactly at resonance where the reactances cancel.

The condition is cos phi = 1, meaning the phase angle between current and voltage is zero. This happens when the circuit is purely resistive, or when a series LCR circuit is at resonance (XL = XC), so the net reactance is zero and impedance Z = R.

P_max = Vrms x Irms (since cos phi = 1), which equals Vrms^2 / R = Irms^2 x R. Power is dissipated only across the resistance R.

For a pure inductor or capacitor the current is 90 degrees out of phase with the voltage, so cos phi = 0 and average power = Vrms x Irms x 0 = 0. They store energy for a quarter cycle and return all of it, so the average heat dissipated is zero.

Yes, at resonance. Resonance makes Z minimum (Z = R), so Irms = Vrms/R is maximum, and since power = Irms^2 x R, the power dissipated is also maximum for that fixed R.

Yes. Average power = Vrms x Irms x (power factor). Since power factor cos phi can be at most 1, power is maximum exactly when cos phi = 1, that is, in a resistive or resonant circuit.