Graph
Plot a graph of resistance, R, in 惟 on the y-axis against length, l, in cm on the x-axis. Draw the line of best fit.
Conclusion
We can see from the graph that as the length of the wire, l, increases, the resistance, R, also increases.
This agrees with our prediction.
In fact, since the line of best fit is a straight line through the origin, we can be even more precise.
We can say that, for a metal wire at constant temperature, the resistance is directly proportional to the length of the wire.
If you double the length of the wire you double its resistance.
If you triple the length of wire, you triple its resistance.
If you half the length of wire, you half its resistance, and so on.
Key points
- The resistance of a metallic conductor at constant temperature depends on the length of the conductor.
- Resistance is directly proportional to length.
Question
A 5 m length of wire is found to have a resistance of 40 \(\Omega\). What is the resistance of each of the following identical wires of different length?
a) 10 m
b) 25 m
c) 2.5 m
Since each wire is identical resistance and length are directly proportional.
a) 10 m is twice the original length, so this wire will have twice the resistance = \({2}\times{40~}\Omega{=~80~}\Omega\).
b) 25 m is five times the original length, so this wire will have five times the resistance = \({5}\times{40~}\Omega{=~200~}\Omega\)
c) 2.5 m is half the original length, so this wire will have half the resistance = \(\frac{1}{2}\times{40~}\Omega{=~20~}\Omega\).