Question

In an ac circuit, why is the average power for an inductor and a capacitor zero, but not for a resistor?

Short answer

In AC circuit the average power in capacitor and inductor is zero because both of them store energy in half cycle and releases the same in other cycle.

Step-by-step solution

Define energy in capacitor, inductor and resistor

Capacitor stores the electrostatics energy. This energy is due to electric field between capacitor which is generated by voltage of ac power supply. For example in parallel plate capacitor, electrostatics energy is expressed as

${\mathit{U}}_{\mathbf{E}}\frac{\mathbf{1}}{\mathbf{2}}\mathit{c}{\mathit{V}}^{\mathbf{2}}$where c is capacitance and$\mathit{V}$ is voltage.

Inductor stores electromagnetic energy. This energy is due to presence of magnetic field inside inductor which generates due to alternating current supply by the ac power source. For example in inductor, electromagnetic energy is expressed as

${\mathit{U}}_{\mathbf{B}}\mathbf{=}\frac{\mathbf{1}}{\mathbf{2}}\mathit{L}{\mathit{l}}^{\mathbf{2}}$where $\mathit{L}$is the inductance and I is the current.

Resistor when connected in circuit despites heat or power loss as per joule’s law of heating which is mathematically expressed as

$\mathit{H}\mathbf{=}{\mathit{l}}^{\mathbf{2}}\mathit{R}\mathit{t}$where $\mathit{H}$is the heat loss, $\mathit{R}$is the resistance and t is time for which current is flowing.

LCR circuit with AC power supply – AC circuit

In LCR circuit, inductor, resistance and capacitor are connected in series with an ac power supply. AC power supply keeps on changing the current in circuit which induces energy in inductor and capacitor.

Their energies keep on changing such that in first half cycle of AC supply, the energies are stored in capacitor and inductor while in other half cycle, these energies are released. It makes the average power of both capacitor and inductor zero.

Meanwhile in resistor, power will only generate and keep on in form of heat.

Hence, the average power for an inductor and a capacitor is zero, but not for a resistor.