Question

a wire is drawn such that its radius changes from r to 2r . The new resistance is : (a) 1 tiem (b) 4 times (c) 8 times (d) 1/16 times

Answer 1

None of the above.

If a wire is drawn it gets smaller.

From r to r/2 resistance increases 4 times because

area is reduced by four times.

If it is expanded to 4 times area (double radius) the

resistance is ¼.

Answer 2

Answer:

4 times

Solution:

The resistance of the wire will become four times the previous.

The volume of the wire remains same because the material of the wire neither increases nor decreases.

So, V = V’  

$A \times L=A^{\prime} \times L^{\prime}$

$A \times r=A^{\prime} \times 2 r$

$\frac{A}{2}=A^{\prime}$

So, the new area of cross section is half the previous one.

Resistance of a wire $=\frac{\rho L}{A}$

$R=\frac{\rho r}{A}$

$R^{\prime}=\frac{\rho 2 r}{\frac{A}{2}}$

$R^{\prime}=\frac{\rho 4 r}{A}$

So, from these equations,

R = 4r

So, the resistance is four times the previous one.