Question

Why does an LC circuit not consume any power?

Answer 1

LC Circuit:

An LC Circuit only comprises an inductor and a capacitor component along with a supply.

1. Inductor: An inductor, also called a coil, choke, or reactor, is a passive two-terminal electrical component that stores energy in a magnetic field when electric current flows through it. An inductor typically consists of an insulated wire wound into a coil
2. Capacitor: A capacitor is a device that stores electrical energy in an electric field. It is a passive electronic component with two terminals. The effect of a capacitor is known as capacitance.

Explanation:

1. The expression for power for any electrical circuit is generally given by:
2. In an LC circuit $\theta$ is 90. Therefore, power is zero.
3. It has a minimum impedance Z=R at the resonant frequency, and the phase angle is equal to zero at resonance.
4. An ideal inductor and ideal capacitor will not consume any power.
5. So there is no internal resistance in a LC circuit.
6. The phase angle between current and voltage is chosen to range from $+\raisebox{1ex}{$\mathrm{\pi }$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$ to $-\raisebox{1ex}{$\mathrm{\pi }$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$.
7. Hence by convention the phase angle between current and voltage is never larger than $+\raisebox{1ex}{$\mathrm{\pi }$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$ and never smaller than$-\raisebox{1ex}{$\mathrm{\pi }$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$
8. This is because while the voltage on the resistance is in phase with the current the voltage on the capacitor lags 90 degrees from the same current.
9. Hence the internal resistance will be zero. If the inductor and capacitor are not ideal then they will consume power.

Hence, the power consumed in an LC circuit is zero.