Electric circuits

Resistance and thickness of wire (cross-sectional area).

Compare two circuits with batteries of the same voltage, with the same length of wire, made of the same material, but one wire is thicker than the other. The concentration gradient will be the same in both wires. To show the different thicknesses of the two wires we need to add an extra axis to our graphs:

Graphs showing the potential energies of electrons dropping along a thin wire and a thick wire.

The average speed of the electrons will be the same in both wires – the gradient is the same. However, we must think of electrons moving down each slope across the width of each slope (the cross-sectional area of each wire). This means there will be more electrons, in total, passing a line across slope (4) than slope (3). There is a higher current in the thicker wire (although per unit area, of course, each wire carries the same current). In a sense, we can think of the electrons moving down in ‘lanes’, with each ‘lane’ carrying the same number of electrons per second past a line. A thicker wire simply has more ‘lanes’ on the go at once. A higher current for a given voltage means a lower resistance. The thicker wire in (4) has a lower resistance than the thinner wire in (3).

The resistance of a wire decreases with increasing thickness.

 

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