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