Question

In the given circuit ,which is a part of a closed circuit. find the currents $i_1$ and $i_2$.

• A. $0.4\text{A};0.5\text{A}$
• B. $0.4\text{A};0.8\text{A}$
• C. $0.6\text{A};0.4\text{A}$
• D. $0.4\text{A};0.6\text{A}$

Answer 1

The correct option is D $0.4\text{A};0.6\text{A}$


Let the potential at $O$ be $x$

Applying Kirchoff's junction law at $O$, $i=i_1+i_2$

$\frac{30-x}{10}=\frac{x-12}{20}+\frac{x-2}{30}$

$\Rightarrow 6(30-x)=3(x-12)+2(x-2)$

$\Rightarrow 220=11x\Rightarrow x=20\text{V}$

So, $i_1=\frac{x-12}{20}=\frac{20-12}{20}=\frac{8}{20}=0.4\text{A}$

$i_2=\frac{x-2}{30}=\frac{20-2}{30}=\frac{18}{30}=\frac{6}{10}=0.6\text{A}$

Hence, option (d) is the correct answer.