C = Q/V — Capacitance

Capacitance — charge stored per volt — with a worked millifarad example.

C = \frac{Q}{V}

Capacitance equals charge stored divided by voltage across the capacitor.

What it means

Capacitance measures a capacitor's appetite for charge: how many coulombs it stores per volt across it. Bigger plates and smaller gaps mean bigger $C$ . The stored energy (½CV²) is what makes capacitors useful for smoothing power and firing camera flashes.

Variables

Symbol	Name	Unit	Meaning
$C$	Capacitance	F (farads)	Charge stored per volt
$Q$	Charge	C	Charge on one plate
$V$	Voltage	V	Potential difference between plates

Assumptions

Capacitor is charged and isolated
Q is the charge on one plate
V is the voltage between the plates

Worked example

Problem

A capacitor stores 0.01 C of charge at 5 V. What is its capacitance?

Given:

Q = 0.01 C
V = 5 V

Write the formula: $C = Q/V$
Substitute: $C = 0.01 / 5$
Calculate: $C = 0.002\ \mathrm{F} = 2\ \mathrm{mF}$

2 mF (0.002 F)

The capacitor holds 2 millifarads — a large value for electronics (typical capacitors are microfarads). Double the voltage and the same capacitor stores double the charge.