17.2. Capacitance

Capacitors

A capacitor consists of two conductors that are close but not touching. A capacitor has the ability (capacity) to store electric charge and electric potential energy.

Capacitors (Condensers)

Even two insulated wires twisted together!

Capacitors

Circuit diagram

When the plates of a capacitor are connected to the terminals of a battery, they become charged. The voltage across the capacitor is the voltage of the battery.

Capacitance

When a capacitor is connected to a battery, the charge on each plate is proportional to the voltage:

The quantity C is called the capacitance. It indicates the amount of charge stored per volt.

Unit of capacitance: the farad (F), 1 F = 1 C/V

Michael Faraday (1793-1867), a pioneering

researcher of electricity and magnetism

Capacitance

The capacitance is a function of the geometry and materials of the capacitor. It is always a positive quantity.

For a parallel-plate capacitor with a vacuum between the plates:

Capacitors and Dielectrics

A dielectric is an insulator; when placed between the plates of a capacitor its molecules polarize, reducing the internal electric field – and thus the voltage – for a given charge. For a given voltage, it allows a greater charge to exist on both plates.

Capacitors and Dielectrics

Dielectrics also allow the plates to be placed closer together without touching – which also increases the capacitance – and allow a greater voltage to be used without the charge jumping the gap.

Dielectrics A dielectric is characterized by its dielectric constant K, which is the (non-dimensional) factor by which a dielectric increases the capacitance.

The capacitance of a parallel-plate capacitor filled with dielectric is:

Dielectrics

Break down

Lightening is an example of breakdown across a dielectric (air).

When a capacitor breaks down, you can generally smell the burning of the dielectric.

For a spark to jump a 1 km gap of air requires: 3 × 109 V A 1 mm gap: 3000 V A 0.5 μm gap: 1.5 V

Example 1

Capacitors

Storage of Electric Energy

Storage of Electric Energy

Capacitors: Applications

Capacitors can provide a large burst of energy to a circuit.

Capacitors are also used to protect delicate circuits from excess charge accumulation and power surges by diverting and storing extra charge.

Capacitors: Applications

Heart defibrillators use electric discharge to “jump-start” the heart, and can save lives.

Camera flashes also use capacitors. The charge accumulates over several seconds, and is released in a millisecond.

Computer Keyboards

The keys on a computer keyboard is connected to the upper plate of a parallel-plate capacitor. When you press on a key, the plates move closer together, changing the capacitance which the circuitry of the computer detects.

Capacitors: Applications

Capacitors are also use in DRAM (Dynamic Random Access Memory) chips in computers to store data:

0000 = 0

0001 = 2

0010 = 3

0011 = 4

0100 = 5

0101 = 6

0110 = 7

0111 = 8

1000 = 9

Capacitors can be dangerous

Capacitors can retain their charge for a very long time, even when disconnected from a voltage source – e.g. when an electrical device is turned off and unplugged from the wall. The sudden discharge of electric energy can be harmful or fatal – so be careful of capacitors!

A capacitor may be discharged by putting a screwdriver across the leads, which should be done before working on a circuit.