Question

Solve the following problem.
The resistance of a 1m long nichrome wire is 6 $\Omega$. If we reduce the length of the wire to 70 cm. what will its resistance be ?

Answer 1

Resistance of a wire is directly proportional to its length.
Let $R_{1}and{R}_2$ be the resistance of the nichrome wire at 100 cm (1 m) and 70 cm, respectively. Therefore,
$R_1\propto 100$ ........... (i)
and
$R_2\propto 70$ ............(ii)
Dividing (ii) by (i), we get
$\frac{R_2}{R_1}=\frac{70}{100}$
$⟹R_2=\frac{70}{100}\times R_1$

Now, $R_1=6$
$⟹R_2=\frac{70}{100}\times 6=4.2\Omega$