Question

The given four terminal network is part of a larger circuit. The points $A,B,C$ are at the same potential. The potential difference between any one of $A,B$ or $C$ and $D$ is $40\text{V}$. The potential difference between $A$ and $O$ is

• A. $10\text{V}$
• B. $15\text{V}$
• C. $18\text{V}$
• D. $20\text{V}$

Answer 1

The correct option is A $10\text{V}$

According to Kirchhoff's Junction Law:

$I_{CO}+I_{BO}+I_{AO}=I_{OD}$

$\Rightarrow \frac{V_C-V_O}{R}+\frac{V_B-V_O}{R}+\frac{V_A-V_O}{R}=\frac{V_O-V_D}{R}$
$(\because V_A=V_B=V_C)$

$\Rightarrow 3\left(\frac{V_A-V_O}{R}\right)=\frac{V_O-V_A+V_A-V_D}{R}$

$\Rightarrow 3\left(\frac{V_A-V_O}{R}\right)=-\left(\frac{V_A-V_O}{R}\right)+\left(\frac{V_A-V_D}{R}\right)$

$\Rightarrow 4\left(\frac{V_A-V_O}{R}\right)=\frac{V_A-V_D}{R}$

$\Rightarrow 4(V_A-V_O)=40$

$\Rightarrow V_A-V_O=10\text{V}$

Hence, the correct answer is (A).