Question

The potential difference between the point A and B is:

A) $5\,V$
B) $4\,V$
C) $3\,V$
D) $2\,V$

Answer 1

Consider the potential at any one of the four points to be zero. Accordingly, there will be potential drop or potential gain as we move towards another point through the battery. With the assumed point find the potentials at all other points and thus the potential at A and B can be found. Then we can simply find the difference between the potentials of A and B.

Complete step by step solution:
There is a battery connected between two points. The battery will create the potential difference across the points equal to the potential of the battery. Thus, we can assume the potential at some point to be zero and accordingly calculate the potential across the adjacent battery.

Let the potential at point D be zero. Consider the following diagram:

We have considered the potential at point D to be zero. There is a battery of $4V$ between point D and B thus, there must be a potential difference of $4V$ between point D and B. As point D is at zero potential thus, point B must be at $4V$ potential.

Similarly, point C ${V_C}$ will be at ${V_{C = }}6V$ .
Now, there is a battery of $2V$ between points C and A. So, there must be potential difference between points C and A. Thus, the potential at point A can be of $4V$ or $8V$ . But we know that when we are moving from negative terminal of battery towards positive terminal there is gain in potential therefore, there must be a gain of $2V$ when moving from point C towards point A.
As a result, the potential at point A will be ${V_A} = 8V$ and potential at point B ${V_B}$ is ${V_B} = 4V$
The potential difference between point A and B will be:
$\Rightarrow$ ${V_A} - {V_B} = 8V - 4V = 4V$
The potential difference between the points A and B is $4V$.

Therefore, option B is the correct option.

Note: When we move from negative terminal to positive terminal of the battery there is a gain in potential. As the battery provides a potential difference between two points therefore, we can consider the potential at any point to be zero and accordingly calculate the potential at other points.