Question

The potential difference (in V) between points $a$ and $b$ when switch $S$ is open,is $(10+x)$. Find the value of $x$.

Answer 1

For path pag: current $i_1=\frac{36}{6+3}=4A$
Potential across $6\Omega$ is $V_p-V_a=6i_1=6\times 4=24V...\left(1\right)$
For path pbg: current $i_2=\frac{36}{3+6}=4A$
Potential across $3\Omega$ is $V_p-V_b=3i_1=3\times 4=12V....\left(2\right)$
$\left(1\right)-\left(2\right)\Rightarrow V_b-V_a=24-12=12V$