Question

The current $\left(i_1\right)$ (in $A$) flowing through $1\Omega$ resistor in the following circuit is

• A. $0.40A$
• B. $0.20A$
• C. $0.25A$
• D. $0.5A$

Answer 1

The correct option is B $0.20A$

$$\begin{array}{cc}& \text{Net resistance across CD}=\frac{1}{2}\Omega \\ & \text{Net resistance across BE}=2+\frac{1}{2}=\frac{5}{2}\Omega \\ & \text{Net resistance across BE}=\frac{\frac{5}{2}\times 2}{\frac{5}{2}+2}=\frac{10}{9}\Omega .\\ & \text{Total current in circuit}=\frac{V}{R}=\frac{9}{10}A\\ & \text{In the given circuit,voltage across BE = voltage across BF}=1V\\ & \text{Current across BE}=\frac{V_{BE}}{R}=\frac{2}{5}A\\ & \text{Current across CD and DE will be same which is}\frac{2}{5}A.\\ & \text{Now, current across any}1\Omega \text{resistor will be same and given by}=I=\frac{1}{2}\times \frac{2}{5}=\frac{1}{5}=0.20A\end{array}$$