Question

A uniform wire of length l and radius r has resistance 100 ohm. If the radius is reduced to r/2, the resistance of the new wire is

Answer 1

Hello friend,

◆ Answer-

R' = 400 ohm

◆ Explaination-

# Given-

R = 100 ohm

r' = r/2

# Solution-

Let ρ be resistivity of wire material.

Resistance of wire is calculated by-

R = ρl / A

R = ρl / πr^2

When radius is halved -

R' = ρl / πr'^2

R' = ρl / π(r/2)^2

R' = 4 (ρl/πr^2)

R' = 4 R

R' = 4 × 100

R' = 400 ohm

Therefore, resistance of new wire is 400 ohm.

Hope this helps...