Example

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

Answer

Since each wire is identical resistance and length will be directly proportional.

a. 10 m is twice the original length, so this wire will have twice the resistance = 2 x 40 \Omega = 80 \Omega

b. 25 m is five times the original length, so this wire will have five times the resistance = 5 x 40 \Omega = 200 \Omega

c. 2.5 m is half the original length, so this wire will have half the resistance = \frac {1}{2} x 40 \Omega = 20 \Omega