Question

Two wires are made up of different materials whose specific resistance are in the ratio of $2:3$, length $3:4$, area $4:5$. The ratio of their resistance is

• A. $6:5$
• B. $6:8$
• C. $5:8$
• D. $1:2$

Answer 1

The correct option is C $5:8$

$\text{Step 1: Resistance of wires}$

Resistance of wire can be given by: $R=\frac{\rho l}{A}$

$\Rightarrow$ For both the wires we can write:

$R_1=\frac{\left({\rho }_1\right)\left(l_1\right)}{A_1}$ $....\left(1\right)$

$R_2=\frac{\left({\rho }_2\right)\left(l_2\right)}{A_2}$ $....\left(2\right)$

$\text{Step 2: Solving equations}$

Dividing equations $\left(1\right)$ and $\left(2\right)$, we get

$\frac{R_1}{R_2}=\left(\frac{{\rho }_1}{{\rho }_2}\right)\left(\frac{l_1}{l_2}\right)\left(\frac{A_2}{A_1}\right)$

$\Rightarrow \frac{R_1}{R_2}=\left(\frac{2}{3}\right)\left(\frac{3}{4}\right)\left(\frac{5}{4}\right)$

$\Rightarrow \frac{R_1}{R_2}=\frac{5}{8}$

Hence, Option(C) is correct.