Capacitors in d.c. circuits

A capacitor is a gap in a circuit with space for charge on the 'plates' shown as the horizontal lines.

A capacitor in the shape of a T, with an up side down T shape above it. There is a small gap between them.

When a capacitor is charged, electrons on the lower plate repel electrons from the upper plate, which then move to the positive terminal of the supply.

Uncharged capacitor with + and - charges evenly distributed above top & below bottom plates. Charged capacitor with + charges above top plate & - charges below bottom plate.

The voltage applied V_{c} to charge the capacitor (circuit 1 below) is measured with a voltmeterand charge accumulated Q is measured by removing the charged capacitor from circuit 1 and connecting it to a coulomb meter (circuit 2).

Circuit diagram containing a voltage supply cell, a resistor, and a capacitor with a voltage capacitor across it.

By varying the charging voltage and measuring the associated charge Q a graph can be drawn.

The gradient of this graph is equal to the capacitance of the capacitor.

C= \frac{Q}{V}

And the area under the graph is the energy stored by the capacitor.

Graph of charge accumulated, Q, in coulombs against voltage applied, VC, in volts. The graph shows a straight line sloping diagonally upwards from the origin.

E= \frac{1}{2}QV

This can be combined with the equation for capacitance above to give two alternative equations for energy stored.

E= \frac{1}{2}\frac{Q^2}{C} and

E= \frac{1}{2}C{V^2}

Question

A 2200 \mu F capacitor is charged up with a 1.5 V cell.

(a) What charge is stored?

(b) What energy is stored?

C= 2200\mu F

=2200 \times {10^{ - 6}}F

V = 1.5 V

Q=?

a) Q=CV

=2200 \times {10^{ - 6}} \times 1.5

=0.0033C

b) E= \frac{1}{2}C{V^2}

= \frac{1}{2} \times 2200 \times {10^{-6}} \times {1.5^2}

= 0.00248J

curriculum-key-fact
  • The S.I. unit of charge is the Coulomb, C
  • The S.I. unit of capacitance is the Farad, F
  • A capacitor of capacitance 1 Farad will store 1 Coulomb of charge with the potenial difference across it is 1 volt