Electronics - AS Module 1 & 2

Capacitors

Capacitors are used to store charge. The capacitance of a capacitor is the measure of its ability to store charge.

All capacitors consist of two parallel plates, which sandwich an insulator, known as the dielectric. Opposite charges are stored on the plates of the capacitor, resulting in apotential difference accross the plates.

A capacitor stores equal amounts of opposite charge on its two plates.

If you plot a graph of the potential difference across the plates against charge stored on the plate you find:

As charge builds up, so does the pd across the plates (in a directly proportional way).

V~Q

Also, if then,V~Q then,

Q/V = a constant.

We call the constant which relates the two, C, the capacitance because it is “the charge stored per unit pd across the plates”, i.e. the capacity of the plates to store charge.

C = Q/V

C - Capacitance in Farads

Q - Charge in Coulombs

V - Potential Difference in Volts

Units of Capacitance

The unit of Capacitance is the Farad.

A capacitor has a capacitance of 1 Farad if a Potential Difference of 1 Volt gives a charge on each plate of 1 Coulomb.

1 Farad is a very large Capacitance.

1µ F = 1 x 10-6 F

1pF = 1 x 10-12 F

The Effect Of Time

What happens to current as time passes?

As explained above, current falls away as it becomes less attractive for electrons to move to the plate from battery.

What happens to the charge on the plate?

Charge builds up - quickly at first (a lot of electrons arriving each second) and then more slowly. We have already said that voltage is proportional to charge, so the voltage - time graph is exactly the same as the charge - time graph.

When the capacitor is fully charged, the pd across the plates will equal the emf of the cell charging it.

Energy stored in a capacitor

The area under this graph gives the energy stored in a capacitor

Energy = Area = 1/2 Q.V

or

Energy = 1/2 C.V^2

or

Energy = 1/2 (Q^2)/C

Capacitors in Series

The charge on each capacitor in series must be the same.

(Think about the middle part of the circuit - the total charge must be zero.)

The total potential difference is equal to the sum of the potential differences across the capacitors.

VT = V1 + V2 + V3

But Q=CV and V=Q/C

Q/CT = Q/C1 + Q/C2 + Q/C3

Dividing through by Q

1/CT = 1/C1 + 1/C2 + 1/C3

Capacitors in Parallel

The total charge is the sum of the charges on the capacitors.

The potential difference across each capacitor is the same.

(They are all connected to the same points in the circuit)

QT = Q1 + Q2 + Q3

But Q = CV

And so

CTV = C1V + C2V + C3V

Dividing through by V

CT = C1 + C2 + C3