# Capacitor potential energy Formula

The energy stored on a capacitor or potential energy can be expressed in terms of the work done by a battery, where the voltage represents energy per unit charge. The voltage V is proportional to the amount of charge which is already on the capacitor. It's expression is:

Capacitor energy = 1/2 (capacitance) * (voltage)^{2}

The equation is:

U = 1/2 C V^{2}

Where:

C: Capacitance

V: Voltage

U: Energy stored in the capacitor

Capacitor Potential Energy Formula Questions:

1) A capacitor is connected to a battery with a voltage of 5 V. Its capacitance is 2 μF. What is the energy stored in the capacitor?

Answer:

From the energy capacitor formula:

U= 1/2 C V^{2} = 1/2 (2*10^{(-6)} F)* (5 V)^{2}

U= 25 * 10^{(-6)} J

2) A capacitor is connected to a battery with a voltage of 5 V. It storage 0.5 μ J of energy. What is its capacitance?

Answer:

From the energy capacitor formula:

U= 1/2 C V^{2} → C = 2 U /V^{2}

C = 2* 0.5 *10^{(-6)} J / (5 V)^{2}

C= 0.04 * 10^{(-6)} F = 0.04 μ F

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