Question

A cylindrical wire is connected to opposite terminals of battery. If the diameter of the wire is reduced by a factor of two, the current through the wire is:

a) doubled

b) decreased fourfold

c) none of these are true

d) halved

e) increased fourfold

f) unchanged

*Explanation would be helpful*

Answer 1

Here,

as the resistance is given as

R = p * Length/(pi * radius^2)

when diameter is reduced to half ,

the radius is also reduced to half

which makes new Resistance 4 times

hence, for same voltage

current will be decreased four times

the correct option is b) decreased fourfold