Question

a wire is drawn such that radius changes from r to 2r what is the new resistance

Answer 1

New radius =2r
New area =4 pi r^2
Area is inversely proportional to resistance
New resistance would be 1/4of the original resistance

Answer 2

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.