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

Answer 1

The correct option is A $7.5V$

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