Question

The resistance of a certain length of wire is 12 ȍ. If the wire is replaced with another wire of the same substance but half the length and twice the diameter, what will be the new resistance?  

Answer 1

We have the resistance $R$ of the wire to be $12Ω$ and let the length of the wire be $l(m)$

Since we have the resistance of a substance to be

$R=\frac{\rho*l}{A}$

From the above expression, we can deduce lll the resistance $R$ is proportional to length $l$ of the wire. That is

$R∝l$

Now, we have the resistance of the wire to be 12Ω when the length is $l$ .

If the length is then halved, implies the resistance would also be halved since we claimed earlier from the expression for equation for resistance that, $R∝l$

Hence, when length is halved, the resistance would be 6Ω.