Question

The potential difference between A and B in the following situation is:

Answer 1

Step 1: Finding current through $1\Omega$resistance

As seen from the given circuit, it is clear that at point B, $3-\mathrm{ampere}$ current flows to C, and $4-\mathrm{ampere}$ current flows to point E. This means the total outgoing current at point B is $7\mathrm{ampere}$.

According to the junction rule, the current at junction B must be zero. So, the incoming current at junction B must be $7-\mathrm{ampere}$. Therefore, the $7-\mathrm{ampere}$current comes from point F to point B.

$$\begin{gathered} {\mathrm{V}}_{\mathrm{A}}=\mathrm{Voltage}\mathrm{at}\mathrm{A} \\ {\mathrm{V}}_{\mathrm{B}}=\mathrm{Voltage}\mathrm{at}\mathrm{B} \end{gathered}$$

Step 2: Applying Kirchhoff's Voltage Law

Applying Kirchhoff's Voltage Law from A to B

$$\begin{gathered} {\mathrm{V}}_{\mathrm{A}}–2\times 5+10–1\times 7–5={\mathrm{V}}_{\mathrm{B}} \\ {\mathrm{V}}_{\mathrm{A}}–10+10–7–5={\mathrm{V}}_{\mathrm{B}} \\ {\mathrm{V}}_{\mathrm{A}}–{\mathrm{V}}_{\mathrm{B}}=12 \end{gathered}$$

Hence, the potential difference between A and B is $12\text{Volts}$.