Energy of a capacitor

A capacitor of capacitance $50\ \mu$F is charged to $1000$ V. Calculate the stored energy.

Solution

Setup. The energy stored in a capacitor of capacitance $C$ charged to voltage $V$ is $U = \tfrac{1}{2}\,C\,V^2$ Data. $C = 50 \ \mu\text{F} = 50\cdot 10^{-6}$ F, $V = 1000 \ \text{V} = 10^3$ V. Substitution. $U = \tfrac{1}{2}\,(50\cdot 10^{-6})\,(10^3)^2 = \tfrac{1}{2}\,(50\cdot 10^{-6})\,(10^6)$ Result. $\ev{U = 25 \ \text{J}}$ That’s 25 joules releasable almost instantaneously in a discharge: it’s the principle behind the camera flash and the defibrillator.

Links

Topics: Electric field and potential Concepts: Capacitance and capacitor · Field energy density Skills: Conservation of energy Methods: Gradient method Objects: Parallel-plate capacitor