Describe a capacitor as a charge-storing component, define capacitance, and apply the relationship between charge, capacitance and voltage

What this dot point is asking

SEAB wants you to describe a capacitor as a component that stores electric charge, to define capacitance, and to use the relationship between charge, capacitance and voltage. The central insight is that a capacitor stores energy by holding charge on two plates separated by an insulator, and that capacitance measures how much charge it holds for each volt applied.

The answer

What a capacitor is

A capacitor is two conducting plates separated by an insulating layer called the dielectric. When connected to a supply, electrons pile onto one plate and leave the other, so one plate becomes negative and the other positive. The capacitor stores this separated charge, and with it a store of electrical energy. No charge crosses the dielectric, so a steady direct current cannot flow through a charged capacitor.

Capacitance defined

Capacitance is the charge stored per unit voltage across the capacitor:

The unit is the farad ($\text{F}$): one farad stores one coulomb per volt. The farad is very large, so practical capacitors are marked in microfarads ($\mu\text{F}$), nanofarads ($\text{nF}$) or picofarads ($\text{pF}$). A larger capacitance stores more charge for the same voltage.

The charge relationship

Rearranging the definition gives the working equation:

So the charge stored is the capacitance multiplied by the voltage across the plates. Doubling the voltage doubles the stored charge for a fixed capacitor.

Charging and discharging

When a capacitor charges through a resistor:

• At first it is empty, so the current is large and the voltage across it is zero.
• As charge builds, the capacitor's voltage rises and opposes the supply, so the current falls.
• Eventually the capacitor voltage equals the supply voltage and the current stops.

When discharging through a resistor, the stored charge flows out, the voltage falls from its starting value towards zero, and the current also decays to zero. The rate of charging or discharging is set by the resistance and capacitance, which is the basis of time-delay circuits.

Types of capacitor

Small-value capacitors are often non-polarised and can be connected either way. Large-value electrolytic capacitors are polarised: they have a marked positive and negative lead and must be connected the correct way round, or they can be damaged.

Examples in context

Example 1. Smoothing a power supply. After a diode rectifier turns alternating current into a bumpy direct current, a large electrolytic capacitor across the output charges up on the peaks and discharges into the load between them. This smooths the ripples into a steadier voltage, a direct use of charge storage that appears in nearly every mains-powered device.

Example 2. A camera flash. A flash gun charges a capacitor slowly from a small battery, then dumps the stored charge into the flash tube in an instant to give a bright burst. The capacitor lets a weak source deliver a large surge of energy when needed, which is the whole point of storing charge.

Try this

• Cue. A $2200\ \mu\text{F}$ capacitor stores $11\ \text{mC}$ of charge. Find the voltage across it. Rearrange $Q = CV$ to $V = Q/C = 0.011 / (2200 \times 10^{-6}) = 5.0\ \text{V}$.

• Cue. Explain why a charged capacitor blocks a steady direct current. Charge cannot cross the insulating dielectric, so once the plates are fully charged no further current flows.

• Cue. State one reason an electrolytic capacitor must be connected the right way round. It is polarised, so reversing the polarity can damage the dielectric and destroy the capacitor.