Question

All resistances in the circuit are of $2\Omega$ each. The current in the resistance between $D$ and $E$ is

• A. $5\text{A}$
• B. $2.5\text{A}$
• C. $1\text{A}$
• D. $7.5\text{A}$

Answer 1

The correct option is B $2.5\text{A}$

$R_{AB}$ has no significance because $R_{DE},R_{GH},R_{CD},R_{FG}$ make a balanced wheatstone bridge.
$R_w$ (due to wheatstone bridge)$=R$
Now,
$R_{eq}=R_w$ (due to wheatstone bridge) || $R$ (between $DG)=\frac{R}{2}=1\Omega$
$\therefore$ Total current in the circuit, $I=\frac{10}{1}\text{A}$
Again,
$\because R_w=R_{DG}=R$
$\therefore I_1=I_2=\frac{10}{2}=5\text{A}$(using current division)
Also,
Current in wheatstone bridge,$I_{DE}=I_{DC}$
$\therefore I_{DE}=\frac{5}{2}=2.5\text{A}$ (using current division)