6.1.1 Capacitors

Capacitors are electrical components which separate charge. They consist of two metallic plates separated by an insulator (a dielectric - e.g air/ceramic/paper/mica). When a capacitor is connected to a cell of e.m.f Є (for example) the electrons only flow from the cell for a short time as they cannot travel between plates (because of the insulator). During the brief current, electrons from the cell flow onto one plate (they are deposited onto a plate, this plate has a net negative charge as it gains electrons) and this repels electrons from the other plate so electrons are removed from the other plate (this plate has a net positive charge as it is deficient in electrons). Charge is always conserved - we can confirm this as the current in the circuit must be the same at all points. The same amount of electrons that has been deposited onto one plate has left the other plate so the have an equal but opposite charge (they have a net charge of 0). This means there is a p.d. across the plates. When the p.d. across the plates is equal to the e.m.f (Є) of the cell, the current in the circuit falls to 0 and the capacitor is fully charged.

The capacitance of a capacitor is defined as the charge stored per unit p.d. across it. It is measured in farads (F). From the equation below we can see that one Farad equates to one coulomb per volt. We can use the following equation to determine capacitance:

Q = V C

The greater the amount of positive and negative charge stored on the plates the greater the p.d. across them. This means that charge is proportional to p.d meaning that, from the equation above, capacitance is constant.

Okay so when we are connecting capacitors in circuits we cannot get them mixed up with resistors!! This is a big no no, they have the opposite rules...

• In parallel the total capacitance is C = C1 + C2.....
• This is because the pd. across each capacitor is the same and charge is conserved so total Q (total charge stored) equates to the sum of the individual charges stored by each capacitor....Q = Q1 + Q2... Therefore since Q = VC and V is constant then C = C1 + C2....
• In series the total capacitance is 1/C = 1/C1 + 1/C2.......
• This is because in series the sum of the p.d.s around each loop equals the e.m.f so V = V1 + V2.... We know that the charge stored in each capacitor is the same so Q is constant. Q = VC so V = Q/C so 1/C = 1/C1 + 1/C2...

There's a little bit more about capacitors in circuits. Firstly, how to investigate combinations/perhaps an unknown capacitor value. Set up a circuit with a safety resistor, an ammeter, a few capacitors and a voltmeter across each capacitor and a variable power supply (a power supply where we can vary the output voltage) and also a switch. Close the switch - current will briefly flow through the circuit. We can determine the charge stored in each capacitor by measuring the voltage across it and multiply it by the capacitor reading (Q = V C). You will see that in each instance in SERIES the charge stored in each capacitor will be the same for a certain voltage (this value will vary as voltage across the circuit varies).

To determine the series rule for capacitors (1/C = 1/C1 + 1/C2...) connect a multimeter set to capacitance across two capacitors in series. The reading will show the figure obtained is we were to do the sum 1/C = 1/C1 + 1/C2...