Question

In the given circuit below, the points $A,B$ and $C$ are at same potential. If the potential difference between $B$ and $D$ is $30V$, then the potential difference between $A$ and $O$ is

• A. 7.5 V
• B. 10 V
• C. 15 V
• D. 5 V
• E. 3.75 V

Answer 1

Answer: (A)

Potential difference between the points $O$ and $D$ $\left(V_{OD}\right)$ is 3 times the potential difference between $B$ and $O\left(V_{BO}\right)$.
From the figure,

$V_{BD}=V_{BO}+V_{OD}$ [Given]
$\Rightarrow V_{BD}=V_{BO}+3V_{BO}\left[V_{OD}=3V_{BO}\right]$
$\Rightarrow V_{BD}=4V_{BO}$
$=V_{BO}=\frac{30}{4}=7.5V$
Now, points $A$ and $D$ have same potential.
So, $V_{AO}=V_{OD}=V_{BO}=7.5V$