Question

Two nichrome wires $A$ and $B$, each of length $5cm$ and of radius $1cm$ and $3cm$ respectively are connected to each other in series. If a current of $5A$ flows through the combination of wires, the ratio of potential difference across wire $A$ to that across wire $B$ will be

• A. $1:3$
• B. $3:1$
• C. $9:1$
• D. $1:9$

Answer 1

Answer: (C)

$9:1$

Ratio of potential difference in series
$\frac{V_1}{V_2}=\frac{I{R}_1}{I{R}_2}=\frac{R_1}{R_2}$
$\frac{V_1}{V_2}=\frac{\rho \frac{l_1}{A_1}}{\rho \frac{l_2}{A_2}}[\because l_1=l_1=5cm]$
$\left[\begin{array}{c}{A}_1=\pi (r_1{)}^2=\pi (1{)}^2\\ A_2=\pi (r_2{)}^2=\pi (3{)}^2\end{array}\right]$
$\therefore \frac{V_1}{V_2}=\frac{A_2}{A_1}=\frac{\pi (3{)}^2}{\pi (1{)}^2}=9:1$.