Question

Find the current $i$ in the circuit shown below :

• A. $\frac{3}{2}\text{A}$
• B. $\frac{5}{2}\text{A}$
• C. $\frac{7}{2}\text{A}$
• D. $\frac{1}{2}\text{A}$

Answer 1

The correct option is C $\frac{7}{2}\text{A}$


From the circuit diagram it is clear that all the resistances are connected parallel to each other.
Therefore, the net resistance of the circuit is given by :
$\frac{1}{R_{eq}}=\frac{1}{10}+\frac{1}{5}+\frac{1}{2}$

$\Rightarrow R_{eq}=\frac{10}{8}\Omega$

Therefore, the current flowing through the battery is given by :
$I=\frac{V}{R}=\frac{5}{\frac{10}{8}}=4\text{A}$

Assigning potential to the various points of circuit :


From the figure we can say that $i$ is given by :
$i=4-\frac{1}{2}=\frac{7}{2}\text{A}$