Question

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

Answer 1

Answer:The new resistance is 1/4th of the original resistance.

Explanation:

The resistance can be determined by the formula R = rho* L/A where rho is the resistivity of the material, L is the length and A is the cross-sectional area of the wire.

The resistance of the wire is given as R.

So this can be written as:

R = rho* L/(π r^2).

After the radius of its cross-section is doubled, we get the new resistance as:

R' = rho* L / ( π(2r)^2) = rho* L/( π (4*r^2))

So, on comparing the initial and final resistance, we find that the new resistance is 1/4th of the original resistance.

Explanation: