Question

An electric current of $5A$ is passing through a circuit containing three wires arranged in parallel. If the lengths and radii of the wires are in the ratio 2: 3: 4 and 3: 4: 5 , then the ratio of currents passing through wires would be

• A. 3: 6: 10
• B. 4: 9: 16
• C. 9: 16: 25
• D. 54: 64: 75

Answer 1

Answer: (D)

Given $,l_1:l_2:l_3=2:3:4=2l:3l:4l$
$r_1:r_2:r_3=3:4:5=3r:4r:5r$
Resistance of a wire, $R=\frac{\rho l}{\pi r^2}$
$R_1=\frac{\rho 2l}{\pi (3r{)}^2}=\frac{2}{9}\frac{\rho l}{\pi r^2}=\frac{2}{9}R,$
$R_2=\frac{\rho 3l}{\pi (4r{)}^2}=\frac{3}{16}\frac{\rho l}{\pi r^2}=\frac{3}{16}R$
$R_3=\frac{\rho 4l}{\pi (5r{)}^2}=\frac{4}{25}\frac{\rho l}{\pi r^2}=\frac{4}{25}R$
$I_1=\frac{V}{R_1};I_2=\frac{V}{R_2}$ and $I_3=\frac{V}{R_3}$
$\therefore I_1:I_2:I_3=\frac{1}{R_1}:\frac{1}{R_2}:\frac{1}{R_3}$
$=\frac{9}{2R}:\frac{16}{3R}:\frac{25}{4R}=\frac{9}{2}:\frac{16}{3}:\frac{25}{4}$
$=54:64:75$