Question

Two copper wires are of same length one of the twice as thick as the other. Then the resistance of the two wires are in the ratio of:

• A. 1:16
• B. 1:8
• C. 1:4
• D. 1:2

Answer 1

Answer: (C)

Here : Thickness of first wire $r_1=2r$
The thickness of second wire $r_2=r$
Using the selation for resistance of wire is,
$R=\frac{S\times l}{A}=S\times \frac{l}{\pi r^2}\propto \frac{l}{r^2}$
Hence $\frac{R_1}{R_2}={\left(\frac{r_2}{r_1}\right)}^2$
$=\frac{(r{)}^2}{(2r{)}^2}=\frac{1}{4}$