Programme 19: Circuits

Background Information

Meaning of Electricity

It is unfortunate that when scientists first realised that electricity was a flow of charges they accepted a model in which positive charges travelled from the positive terminal of a power supply to the negative terminal. When the charge-carrying particle, the electron, was eventually discovered it was found to have a negative charge and to travel from the negative terminal of the power supply to the positive terminal. This is why the direction of conventional current flow is opposite to the actual flow of electrons. Students sometimes ask why this was not corrected at the time. By the time electrons were discovered electricity had moved out of the laboratory and into everyday life. It would have been difficult to get people to change, and would have been potentially dangerous if machines were connected the wrong way round.

Differences in Series and Parallel Circuits

There are three main differences between series and parallel circuits:

1. Adding more components in series reduces the current in the circuit. Adding more components in parallel draws more current from the supply so that the current through each one is unchanged.
2. If one component fails in a series circuit there is no current through any of the components. In a parallel circuit the other components are unaffected.
3. Components must all be switched on and off together in series, but can be switched on and off individually in parallel.

Note that when adding more components in parallel if the power supply is current limited (has a maximum current which can be drawn), once the maximum is reached then adding more components will lead to a reduction in current through each component.

Ohm’s Law

Ohm’s Law says that voltage (V) is directly proportional to current (I) for a conductor provided that its temperature remains constant. If V is directly proportional to I, a graph of V (in volts), against I (in amps), will be a straight line through the origin. Resistance increases with temperature, and if the conductor warms up, due to the current flowing through it, the graph will not be a straight line. The constant of proportionality is called resistance R, so V = RI where R is the gradient of the graph. R is a measure of how difficult it is for electrons to flow through the material. It is measured in ohms (W).

It is usual to plot the dependent variable (in this case I) against the independent variable (in this case V). In the case of Ohm’s Law, graphs are plotted of V against I so that the gradient gives R and not 1/R. Some devices and materials do not obey Ohm’s law, for example, thermistors.

Filament lamps are designed to heat up even at low voltages, so that the filament gives out light. The filament wire would follow Ohm’s law if the temperature was constant. At very low voltages the lamp may start off with V proportional to I, but it quickly heats up. Since it can’t be kept at constant temperature and is designed to heat up, we refer to filament lamps as non-ohmic.

Resistance

Resistance is shown to depend on the type of metal. The metal is shown to be a lattice of positive metal ions surrounded by a sea of free electrons. One reason why different metals do not have the same resistance is that they contain a different number of free electrons. There are other reasons, such that the positive ions vibrate with different amplitude or frequency for different metals.

Resistance is proportional to the length of the wire – doubling the length doubles the resistance.

Resistance also depends on the thickness of the wire. It is actually inversely proportional to the cross-sectional area of the wire: as the area doubles the resistance halves. This is demonstrated by using two wires to double the area (doubling the diameter of a circular cross-section wire would give four times the area and so one quarter of the resistance).

Temperature

Temperature affects resistance because it changes the vibration of the positive ions in the lattice. It is more difficult for the electrons to flow through a wire if the ions are vibrating more. This means that resistance increases with temperature. The demonstration shows that resistance decreases when materials are cooled. The superconductor is a ceramic which becomes superconducting at liquid nitrogen temperatures (–196°C). When a magnet is moved close to the superconductor, currents will be induced in the superconductor (by induction), to oppose the movement of the magnet. These currents will not die away due to resistance as they do in most materials, because the superconductor has no resistance. They will continue to provide a magnetic field which repels the magnet.