Question

Wires A and B are made from the same material. Wire A has length 12m and weight 50 g, while wire B is 18 m long and weighs 40 g. Then the ratio $\left(R_A/R_8\right)$ of their resistances will be

• A. 16 / 45
• B. 4 / 5
• C. 8 / 15
• D. 4 / 9

Answer 1

Answer: (A)

same material implies same $\rho$ and density.
$R=\rho \frac{l}{A}(A=\frac{V}{l}V=\frac{m}{d})$
since $\rho$ and density. are same.
$R\propto \frac{l^2}{m}$
$\frac{R_A}{R_B}=\frac{{12}^2}{{18}^2}\times \frac{40}{50}=\frac{160}{450}=\frac{16}{45}$