Question

An electric current of $5A$ is divided into three branches forming a parallel combination. The length of the wire in three branches in the ratio $2:3:4$ and their diameter ratio $3:4:5$. Find the current ratio in three branches.

• A. $1.5:2:1.3$
• B. $1.4:1.66:1.94$
• C. $1:2:1$
• D. $1:1:1$

Answer 1

The correct option is B $1.4:1.66:1.94$

Resistance $R=\rho l/A,A=\pi d^2/4$ is directly proportional to the length and inversely proportional to the Area, i.e., directly proportional to the square of the diameter.

As length are in ratio $2:3:4$ and diameter are in ratio $3:4:5$.

So the resistance are in ratio $2/3^2:3/4^2:4/5^2=2/9:3/16:4/25$

By ohm's law, current is inversely proportional to the resistance, so current is

in ratio $9/2:16/3:25/4$

Dividing the total current $5A$ in this ratio, we get current ratios as:

$1.4:1.66:1.94$