Question

Q2. If a wire of resistance 1 ohm is stretched till its length is doubled. Find the
new resistance. ​

Answer 1

Answer:The new resistance will be 4 ohm.

Explanation:

Given that,  

Resistance R = 1 ohm

Length L = 2l

We know that,

R = \rho \dfrac{L}{A}.....(I)

Where, A = area

\rho = resistivity

A = \rho l.....(II)

After stretch,

The new resistance is

R'=\rho \dfrac{l'}{A'}.....(III)

The volume is constant after and before stretch

So, Al= A'l'

Al= A'2l

A'= \dfrac{A}{2}

Now , put the value off A' and l in equation (III)

R' = \rho\dfrac{2l}{\dfrac{A}{2}}

R' = \rho\dfrac{4l}{A}.....(IV)

Now, divided equation (IV) by equation (I)

\dfrac{R'}{R} = \dfrac{\rho 4lA}{A\rho l}

R' = 4 ohm

Hence, the new resistance will be 4 ohm.