Capacitors

Capacitance and Energy

A capacitor is a device that stores charge and energy. The unit of capacitance is the farad (F).

• Capacitance: C = q/U.
• Parallel-plate capacitor: C = ε·ε₀·S/d.
• Energy: W = CU²/2 = qU/2 = q²/(2C).
• If a dielectric is inserted between the plates, the capacitance increases ε times.

Connections

Connection	Total capacitance	Same quantity
Parallel	C = C₁ + C₂	voltage U
Series	1/C = 1/C₁ + 1/C₂	charge q

For capacitors, the formulas are the opposite of those for resistors: in a parallel connection the capacitances add, and in a series connection the reciprocals add.

Examples

• C = 5 μF, U = 20 V: q = 5·20 = 100 μC.
• 2 μF and 4 μF in parallel: C = 2 + 4 = 6 μF.
• C = 2 μF, U = 20 V: W = 2·400/2 = 400 μJ.
• 4 μF and 12 μF in series: C = 4·12/(4 + 12) = 3 μF.

1. Determine the type of connection: parallel or series
2. Find the total C
3. Calculate q = CU or W = CU²/2