Question

In the circuit shown if $R_1:R_2:R_3:R_4=1:2:3:4$ then_____

• A. Ratio of current in $R_2$ and $R_3$ is $3:1$
• B. Ratio of current in $R_1$ and $R_3$ is $3:1$
• C. Ratio of current in $R_1$ and $R_2$ is $4:5$
• D. current in $R_1$ is more than one in $R_2$

Answer 1

The correct option is A Ratio of current in $R_2$ and $R_3$ is $3:1$

$R_1$ is short circuited as potential difference across it $=0.$

Let $R_{1}bek$

$R_{2}be2k$

$R_{3}be3k$

$R_{4}be4k$

So equivalent circuit is drawn in pic,

Applying Kirchoff's voltage law in ABCD

$i_1{R}_2=2V$-----(1)

Applying Kirchoff's voltage law in AFED

$-3+i_2{R}_3+2=0$

$i_2{R}_3=1$-----(2)

Divide $1$ and $2$

$\frac{i_1{R}_2}{i_2{R}_3}=2$

$\frac{i_1}{i_2}\ast \frac{2}{3}=2$

$\frac{i_1}{i_2}=\frac{3}{1}$

$i_1:i_2=3:1$