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 \(40 \Omega\) = \(20 \Omega\)