Question

If a wire of resistance 1 ohm is stretched to double its length then the resistance will become

Answer 1

Answer:

4 ohm

Explanation :

The point here to understand is when we stretch a wire we increase is its length and as the volume of the wire is kept constant, so the area of the cross-section of the wire has to be now exactly half of the initial value.

Now let us say the original length of wire is ‘l',the area of cross-section of the wire is 'A' and the resistivity of the wire is ‘P', then acc. to the formula for resistance

R=P*(l/A)

Now after stretching the wire,

Length=2*l

Area=A/2

So the new resistance

R'=P*[2l/(A/2)]

R'=4*[P*(l/A)]

R'=4R

So the new resistance is 4 times the initial resistance.