Question

The switch $S$ in the circuit shown is closed. If the value of potential at $A$ is $20\text{V}$ , then the value of current $i$ will be (Give integer value)

Answer 1

According to Kirchoff's Current law at the junction $C$

$i=i_1+i_2$

Thus, $\frac{V_C-0}{2}=\frac{V_A-V_C}{2}+\frac{V_B-V_C}{4}$

$\Rightarrow \frac{V_C}{2}=\frac{20-V_C}{2}+\frac{10-V_C}{4}$

$\Rightarrow 2V_C=40-2V_C+10-V_C$

$\Rightarrow 5V_C=50$

$\Rightarrow V_c=\frac{50}{5}=10Volt$

Then $i=\frac{V_C-0}{2}=\frac{10}{2}=5\text{A}$

Accepted answer : $5$