Question

In the circuit shown, if a conducting wire is connected between points $A$ and $B$, the current in this wire will -

• A. flow from B to A
• B. flow from A to B
• C. flow in the direction which will be decided by the value of V
• D. be zero

Answer 1

Answer: (A)

Current through arm $C A D, I=\frac{V}{8}$ amp
Potential difference between $C$ and $A=V_{C}-V_{A}$
$=\frac{V}{8} \times 4=\frac{V}{2} \text { volt }$
Current through $C B D, I^{\prime}=\frac{V}{4} amp$
Potential difference between $C$ and $B=V_{C}-V_{B}$
$=\frac{V}{4} \times 1=\frac{V}{4} \text { volt. }$
Potential between $A$ and $B=V_{A}-V_{B}$
$\therefore \quad V_{A}-V_{B}=V_{C}-V_{B}-\left(V_{C}-V_{A}\right)=\frac{V}{4}-\frac{V}{2}=-\frac{V}{4}$
$\Rightarrow V_{A}-V_{B}<0$
or, $V_{A}< V_{B}$
A s $V_{A}< V_{B}$,
so direction of current will be from $B$ to$A$.