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

Answer:

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

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 $\frac{\rho l_A}{a_A}=4\frac{\rho l_B}{a_B}$ ( As $l_A=l_B$ )

$\frac{a_A}{a_B}=\frac{1}{4}$

$\frac{d_A^2}{d_B^2}=\frac{1}{4}$

$\frac{d_A}{d_B}=\frac{1}{2}$

$d_B=2d_A$

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