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 $40\, V$. The potential difference between $A$ and $O$ is

• A. 10V
• B. 15V
• C. 18V
• D. 20V

Answer 1

The Correct Option is A

According to Kirchhoff's junction law
$I_{C O}+I_{O B}+I_{A O}=I_{O D} $
$\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} $
$\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} $
$\Rightarrow 4\left(V_{A}-V_{O}\right)=40$
$\Rightarrow V_{A}-V_{O}=10\, V$