Question

The resistance of a $1$ long nichrome wire is $6$ if we reduce the length of the wire to $70$ cm what will its resistance be?

Answer 1

Length = 1 m.

Resistance = 6 Ω.

Area if cross section = a

Now, Resistivity = $Ra/l$

$p=\frac{6\ast a}{1}$

$p=6a$

In second case :-

Length = 70 cm = 0.7 m

Resistance = R

Area of cross section = a

Now, Resistivity =$Ra/l$

$p=Ra/0.7$

Since for the same material the resitivity will be same whether the area or the length either decrease or increase, therefore . from eq I and ii

$6a=Ra/0.7$

R = 6 × 0.7

R = 4.2 Ω.