Question

A wire of resistance 10 ohm is stretched to such a length that its radius becomes half. What will be its new resistance

Answer 1

Explanation:

This is simple. The resistance is inversly proportional to cross section Area of the conductor and Directly proportional to length

There are two points here

Stretching [ Theoretically ] without increasing length

Now radius has become half

Area = Pi x R^2;

When R has become 1/2 ; The square of R become 1/4

Since it is inversly proportional the resistance becomes 4 times ; i.e. 4 x 10 = 40 Ohms

2. When stretching the volume remains same; [ Practically ] ; When radius becomes half the area becomes proportional to 1/4th [ Pi *r^2] the length become four times

Resistance is proportional to the length; Hence when length becomes double, the resistance also becomes two times more ; Hence it will be 160 Ohms .