Question

An electric circuit is shown in the figure. The potential difference between the points $A$ & $B$ is:

• A. $\frac{10}{3}V$
• B. $\frac{20}{3}V$
• C. $\frac{5}{3}V$
• D. $\frac{7}{3}V$

Answer 1

The correct option is A

$\frac{10}{3}V$

Step 1: Given Data

$$\begin{gathered} R_1=1\Omega \\ {R}_2=1\Omega \\ {R}_3=1\Omega \\ {R}_4=1\Omega \end{gathered}$$

Step 2: Find potential differences between the points $A$ & $B$

Let Node $B$ be the reference node hence the voltage of this node will be zero and the potential at $A$gives the potential difference between $A$ and $B$.

Applying Kirchhoff's current law at the node, we get

$\Rightarrow$$\frac{V_A-2}{2}+\frac{V_A-4}{2}+\frac{V_A-4}{2}=0$

$\Rightarrow$ $V_A\left(\frac{1}{2}+\frac{1}{2}+\frac{1}{2}\right)=5$

$\Rightarrow$ $V_A\left(\frac{3}{2}\right)=5$

$\Rightarrow$ $V_A=\frac{10}{3}V$

Hence, option (A) is correct.