Question

1. Two wires - A and B - with circular cross-sections have identical lengths and are made of the same material. Yet, wire A has four times the resistance of wire B. How many times greater is the diameter of wire B than wire A?

Answer 1

Diameter of wire B is 2 times the diameter of wire A

Step-by-step explanation:

We have given two wire A and B

They are made up of same material and length of both the wire is sane

So
`l_A=l_B`

Let the resistivity of both the wire is
`\rho`

It is given that wire A has 4 times the resistance as wire B

So
`R_A=4R_B`

So
`(\rho l_A)/(a_A)=4(\rho l_B)/(a_B)` ( As
`l_A=l_B` )

`(a_A)/(a_B)=(1)/(4)`

`(d_A^2)/(d_B^2)=(1)/(4)`

`(d_A)/(d_B)=(1)/(2)`

`d_B=2d_A`

So diameter of wire B is 2 times the diameter of wire A