Question

. A wire in drawn such that its radius changes from r to 2 r. The new resistance is :
(a) 1 time
(b) 4 times
(c) 8 times
(d) (1/16) times
please answer with full explanation​

Answer 1

Answer:

(b) 4 times

THIS IS THE ANSWER

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×L=A

′

×L

′

A \times r=A^{\prime} \times 2 rA×r=A

′

×2r

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

2

A

=A

′

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

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

A

ρL

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

A

ρr

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

′

=

2

A

ρ2r

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

′

=

A

ρ4r

So, from these equations,

R = 4r

So, the resistance is four times the previous one.