Two concentric circular loops of radii b and 2b, made of the same type of wire, lie in the plane of the page, as shown below. The total resistance of the wire loop of radius b is R. What is the resistance of the wire loop of radius 2b? a. R2b=R/4
b. R2b=2R
c. R2b=R
d. R2b=R/2
e. R2b=4R

a. R2b = R/4

Explanation:

The total resistance of a metallic wire is given by the following formula:

R = ρL/A

where,

R = Resistance of Wire

ρ = Resistivity of the material of wire

L = Length of Wire

A = Area of Wire = πr²

Therefore,

R = ρL/πr²

for the 1st wire,

radius = r = b

Therefore,

R = ρL/πb²   equation 1

Now, for the second wire,

r = 2b

Therefore,

R2b = ρL/π(2b)²

R2b = ρL/πb²4

using equation 1:

R2b = R/4

therefore, correct option is:

a. R2b = R/4

a and b sometimes have a positive value

the amount of current in the coil