Question

a piece of wire of resistance 20 ohm is drawn out so that its length is increased to twice its original length calculate the resistance of the wire and the new position

Answer 1

R=ρl/a
if length is increased to twise of original wire then its area decrease by half (as volume is constant = lengthXarea)
so resistance is increased by 4 times
new rasistance is 80 Ω

Answer 2

Given resistance , R = 20 Ω

And we have to find the new resistance with the help of the original length .

Solution :

We know very well that ,

R = (pl/A)

We can write it as :

R = (pl²/v)

Then ,

It is given that

l' = 2l

So ,

R' = (4pl²)/V = 4R ----(eq.1)

R = 20 ohm = 20 Ω

So , putting R = 20 ohm in equation 1 ,

We have :

R' = 4R = 4(20) = 80 Ω

The required new resistance is of 80 ohm = 80Ω