Question

Value of i₁ (Ampere) when the switch is closed is.

• A. 2A
• B. 5A
• C. 10 A
• D. 1A

Answer 1

The correct option is B

5A

Step 1: Given data

From the given circuit diagram

The voltage $V$ is 0
The voltage $V_1$ is 20V
The voltage $V_2$ is 10V
The resistance $R$ is 2$\Omega$
The resistance $R_1$ is 2$\Omega$
The resistance $R_2$ is 4$\Omega$

Let the voltage at the junction be $X$.

Step 2: Formula used

Current in terms of voltage and resistance is$I=\frac{V}{R}$

Step 3: Calculating the value of $i$

The values (clear from the figure) will be-

$$\begin{gathered} i=\frac{X-V}{R} \\ {i}_1=\frac{V_1-X}{R_1} \\ {i}_2=\frac{V_2-X}{R_2} \end{gathered}$$

Now when we apply the junction rule at point C, we get,

$\mathrm{i}={\mathrm{i}}_1+{\mathrm{i}}_2$

Putting these values into the formula for total current, we get-

$$\begin{gathered} \frac{X-V}{R}=\frac{V_1-X}{R_1}+\frac{V_2-X}{R_2} \\ \frac{X-0}{2}=\frac{20-X}{2}+\frac{10-X}{4} \\ 2X=2(20-X)+10-X \\ 5X=50 \\ X=10V \end{gathered}$$

Thus, the value of the current will be

$$\begin{gathered} i=\frac{X-0}{2} \\ i=\frac{10}{2} \\ i=5A \end{gathered}$$

Hence, option B is the correct option.