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Q.
The potential difference $V_{A}-V_{B}$ for the circuit shown in figure is $-\frac{22}{x} V$. The value of $x$ is____.
Current Electricity
Solution:
At junction $C : i_{1}+i_{2}=i$,
where $i_{1}=\frac{0-x}{1}, i_{2}=\frac{1-x}{1}$
At $D: 4 i+i_{1}=0$, solve to get $x=\frac{4}{9}$
Now
$V_{A}-i_{1}+1+i=V_{B} \Rightarrow V_{A}-V_{B}$
$=-\left(2+\frac{4}{9}\right)=-\frac{22}{9} V$
