How is total energy in an RLC circuit calculated?

The total energy in an RLC circuit is primarily associated with the energy stored in the inductor and capacitor. In such circuits, the inductor stores energy in its magnetic field when current flows through it, while the capacitor stores energy in its electric field when it is charged. The formula for the energy stored in an inductor is given by ( \frac{1}{2} L I^2 ) where ( L ) is the inductance and ( I ) is the current. Similarly, the energy stored in a capacitor is calculated using ( \frac{1}{2} C V^2 ) where ( C ) is the capacitance and ( V ) is the voltage across the capacitor.

In a steady-state alternating current (AC) RLC circuit, these two components oscillate energy back and forth between each other, leading to a situation where the total energy can be viewed as the sum of the energy stored in both the inductor and capacitor at any point in time. Therefore, this sum correctly represents the total energy within the circuit itself, distinct from the energy dissipated by resistors or other elements.