Question

The potential difference between points A and B is

Answer 1

Equivalent resistance in both the branches is,

$R_{{\text{Eq}}_1}=8+6=14\Omega$

$R_{{\text{Eq}}_2}=4+3=7\Omega$

Now equivalent resitance of circuit is,

$R_{\text{eq}}=\frac{14\times 7}{14+7}=\frac{14}{3}\Omega$

Net current $=I=\frac{V}{R_{\text{eq}}}=\frac{10}{\frac{14}{3}}=\frac{15}{7}\text{A}$

From current Division,

$I_1=\frac{7}{21}\times \frac{15}{7}=\frac{5}{7}\text{A}$

$I_2=I-I_1$

$I_2=\frac{15}{7}-\frac{5}{7}=\frac{10}{7}\text{A}$

From KVL

$8I_1+V_{\text{B}}-V_{\text{A}}-4I_2=0$

$\Rightarrow V_{\text{A}}-V_{\text{B}}=8\times \frac{5}{7}-4\times \frac{10}{7}$

$\Rightarrow V_{\text{A}}-V_{\text{B}}=0$