Physics - Capacitors

What is capacitance?

The capacitance C of a capacitor is defined as the charge stored per unit p.d..

C = Q/V

The unit of capacitance is the farad (F) which is equal to 1 coulomb per volt.

What are the uses of capacitors?

• Smoothing circuits

• Back up power supplies

• Timing circuits

• Pulse producing circuits

• Tuning circuits

• Filter circuits

What is the energy stored in a capacitor?

E = ½ QV

E = ½ CV² or E = ½ Q²/C

In the charging process, the battery forces charge Q through pd V round the circuit an therefore transfers energy QV to the circuit. Thus, 50% of the energy supplied by the batter is stored in the capacitor. The other 50% is wasted due to resistance in the circuit as it is transferred to the surroundings when the charge flows in the circuit.

What are the decay and charging equations for charge, current and voltage of a capacitor?

Discharge:

• Q = Q₀e^-t/RC

• V = V₀e^-t/RC

• I = I₀(1-e^-t/RC)

Charge:

• Q = Q₀(1- e^-t/RC)

• V = V₀(1 - e^-t/RC)

• I = I⁰e^-t/RC

What do the charging and discharging graphs of a capacitor look like for current, voltage and charge with respect to time?

What is the time constant?

The quantity RC is called the time constant for the circuit. At time t = RC after the start of the discharge, the charge falls to 0.37 of its initial value.

What is a dielectric?

The charge stored on the plates can be increased by inserting a dielectric between the plates. Dielectrics are electrically insulating materials that increase the ability of a parallel-plate capacitor to store charge when a dielectric is placed between the plates of the capacitor. Polythene and waxed paper are examples of dielectrics.

Why do dielectrics allow a capacitor to store more charge?

When a dielectric is placed between two oppositely charged plates, each molecule of the dielectric becomes polarised. This means that its electrons are pulled slightly towards the positive plate. So the surface of the dielectric facing the positive plate gains negative charge at the expense of the other side of the dielectric that faces the negative plate. The other surface of the dielectric loses negative charge, so some positive charge is left on its surface.

• The positive side of the dielectric attracts more electrons from the battery onto the negative plate.

• The negative side of the dielectric pushes electrons back to the battery from the positive plate.

So more charge can be stored.

What is relative permittivity?

For a fixed pd across a parallel-plate capacitor with an empty space between its plates, the charge stored is increased by inserting a dielectric substance between the plates. The ratio of the charge stored with the dielectric to the charge stored without the dielectric may be defined as the relative permittivity, ε_r, of the dielectric substance.

relative permittivity ε_r = Q/Q₀

ε_r = C/C₀

It is also called dielectric constant.

What is a capacitor designed as?

For a parallel-plate capacitor with dielectric filling the space between the plates, its capacitance C = (Aε₀ε_r)/d where A is the surface area of each plate and d is the spacing between the plates.

This shows that a large capacitance can be achieved by:

• Making the area A as large as possible

• Making the plate spacing d as small as possible

• Filling the space between the plates with a dielectric which has a relative permittivity as large as possible.

What is the orientation polarisation mechanism?

This occurs in substances which contain molecules where covalent bonds are formed between atoms of different elements. The electrons in each covalent bond are shared unequally between the two atoms joined by the bond. The two atoms form a permanent electric dipole in which one atom is positively charge and the other is negatively charged. When the electric field is applied, the two atoms in each bond are displaced in opposite direction so the dipole tends to align with the field by turning slightly. However, when the field is absent, the dipoles lie in random directions.

What is the ionic polarisation mechanism?

It happens in substances where ions are held together by ionic bonds. The oppositely-charged ions of each ionic bond are displaced in opposite directions when an electric field is applied. As a result, the ions of each bond form a dipole that tends to align with the field.

What is the electronic polarisation mechanism?

It happens where the electrons of each atom are displaced relative to the nucleus of the atom when an electric field is applied. The centre of the electron distribution therefore no longer coincides with the nucleus. As a result, the electron distribution and the nucleus form a dipole that tends to align with the field.

How does relative permittivity change as the frequency of the applied field increases?

The mass of the particles being moved by the field determines which mechanisms ceases first as the frequency increases. The greater the mass of each particle, the greater its inertia is, and so the frequency at which it ceases to contribute is lower. Orientation polarisation therefore ceases first as the frequency increases then ionic polarisation, then electric polarisation.