Question

Calculate the potential difference between points $A$ and $B$. (in $V$ )

Answer 1

In Circuit $3\, \Omega, 10\, \Omega$ and $15\, \Omega$, resistance is in parallel
So $\frac{1}{ R _{1}}=\frac{1}{3}+\frac{1}{10}+\frac{1}{15}$
$R _{1}=2\, \Omega$
$6\, \Omega$ and $3\, \Omega$ Resistance are in parallel
$\frac{1}{R_{2}}=\frac{1}{6}+\frac{1}{3}$
$R_{2} =2\, \Omega$
Then $R_{\text {eq }}$ between $A$ and $B$
$R_{\text {eq }}=4+2+2+2=10\, \Omega$
Current in $15\, \Omega$ resistor
$I =\frac{ V }{ R }=\frac{10}{15}=\frac{2}{3} A$
Then current in $10\, \Omega$
$I=\frac{15}{10} \times \frac{2}{3}=1\, A$
and current in
$3\, \Omega=\frac{15}{3} \times \frac{2}{3}=\frac{10}{3} A$
Total current in circuit
$=\frac{2}{3}+1+\frac{10}{3}$
$I =5\, A$
Potential difference between $A$ and $B$
$V _{ AB } =$ Total Resistance $ \times$ Current
$=R_{ eq } \times I$
$=10 \times 5$
$V _{ AB } =50$ Volt
Hence $V _{ AB }=50$ volt