Question

The resistance of metal wire is 4ohm if the wire is stretchrd uniformly untill the length becomes twice that of original length what is new resistance

Answer 1

Answer = 16 ohm

STEP-BY-STEP EXPLANATION :-

Resistance = 4 ohm

Now,

$\frac{ \rho \: l}{a} = 4$

Now,

The wire is stretched to the length which is twice the original length.

So,

Length = 2l

And area will become half the initial area because volume of wire remains constant.

So

Area = a/2

Now ,

Applying the formula for resistance :-

$r = \frac{\rho \: \times 2l}{ \frac{a}{2} } \\ \\ \\ = \frac{ \rho \: \times4l }{a} \\ \\ \\ 4 \frac{ \rho \times l}{a}$

Now,

We already know that rho*l/a is equal to 4 ohm as it is already given...

Thus,

New Resistance of the wire =

$4 \times 4 \\ \\ = 16 \: ohm$

Thus,

Answer is 16 ohm