Question

As the switch $S$ is closed in the circuit shown in figure, current passing through it will be

• A. $8/25\text{A}$
• B. $6.0\text{A}$
• C. $25/8\text{A}$
• D. $4.5\text{A}$

Answer 1

The correct option is C $25/8\text{A}$

Let at junction $\text{C}$, potential is $V$


Applying Kirchhoff's junction law at $\text{C}$.

$i_1+i_2=i_3$

$\Rightarrow \frac{V_A-V_C}{4}+\frac{V_B-V_C}{4}=\frac{V_C-V_D}{2}$

putting the given values, we get

$\Rightarrow \frac{20-V}{4}+\frac{5-V}{4}=\frac{V-0}{2}$

$\Rightarrow 4V=25$

$\therefore V=\frac{25}{4}\text{V}$

Therefore, current through switch $S$ will be

$i_3=\frac{V}{R}=\frac{25/4-0}{2}=\frac{25}{8}\text{A}$

Hence, option $\left(d\right)$ is correct.