Energy Stored in Capacitor — Core Principles

Core Principles

The energy stored in a capacitor is the electrical potential energy accumulated in its electric field when it is charged. This energy originates from the work done by an external source, like a battery, to separate charges and place them on the capacitor plates.

As charge accumulates, the potential difference across the plates increases, requiring more work to transfer additional charge. The total work done is stored as potential energy. The fundamental formulas for this stored energy are $U = \frac{1}{2}CV^2$, $U = \frac{Q^2}{2C}$, and $U = \frac{1}{2}QV$, where $C$ is capacitance, $V$ is voltage, and $Q$ is charge.

The energy is actually stored in the electric field itself, with an energy density of $u = \frac{1}{2}epsilon E^2$. When a dielectric is introduced, the stored energy changes: it increases if the capacitor remains connected to the battery (constant $V$), and it decreases if the battery is disconnected (constant $Q$).

A crucial point for NEET is that only half the work done by the battery is stored as energy, with the other half dissipated as heat during charging. Also, when charged capacitors are connected, total charge is conserved, but energy is typically lost due to resistance.

Important Differences

vs Energy Stored in an Inductor

Aspect	This Topic	Energy Stored in an Inductor
Storage Medium	Electric field between plates	Magnetic field around coils
Energy Formula	$U = \frac{1}{2}CV^2 = \frac{Q^2}{2C}$	$U = \frac{1}{2}LI^2$
Proportionality	Proportional to $V^2$ or $Q^2$	Proportional to $I^2$
Energy Density	$u_E = \frac{1}{2}\epsilon E^2$	$u_B = \frac{1}{2\mu}B^2$
Charging/Discharging	Stores charge, opposes voltage changes	Stores current, opposes current changes
Role in AC Circuits	Introduces capacitive reactance ($X_C = 1/\omega C$)	Introduces inductive reactance ($X_L = \omega L$)

While both capacitors and inductors are energy storage devices, they store energy in fundamentally different forms and fields. A capacitor stores electrical potential energy in its electric field, arising from charge separation, with energy proportional to the square of voltage or charge. An inductor, on the other hand, stores magnetic potential energy in its magnetic field, generated by current flow, with energy proportional to the square of the current. Their energy density formulas also reflect this difference, involving electric field strength for capacitors and magnetic field strength for inductors. Understanding these distinctions is crucial for analyzing AC circuits and transient responses.