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

Question

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

Professor PC Thomas Classes · Answer

(a) :\ Current through arm CAD, $I=\frac{V}{8}$ amp\ Potential difference between $C$ and $A=V_{C}-V_{A}$ $$ =\frac{V}{8} 	imes 4=\frac{V}{2} 	ext { volt } $$ Current through CBD, $I^{\prime}=\frac{V}{4}$ amp\ Potential difference between $C$ and $B=V_{C}-V_{B}$ $$ =\frac{V}{4} 	imes 1=\frac{V}{4} 	ext { volt. } $$ Potential between $A$ and $B=V_{A}-V_{B}$\ $	herefore \quad V_{A}-V_{B}=V_{C}-V_{B}-\left(V_{C}-V_{A}ight)=\frac{V}{4}-\frac{V}{2}=-\frac{V}{4}$.\ $\Rightarrow \quad V_{A}-V_{B}<0$ or, $V_{A}<V_{B}$\ As $V_{A}<V_{B}$, so direction of current will be from $B$ to $A$.\