Question

Potential difference between two points is equal to
A. $\dfrac{\text{electric charge}}{\text{time}}$
B. $\dfrac{\text{work done}}{\text{time}}$
C. $\dfrac{\text{work done}}{\text{charge}}$
D. $\text{work done }\times \text{ charge}$

Answer 1

Electric potential at a point is the potential energy of a unit charge placed at that point. Potential difference between two different points will be equal to the change in potential energy of a unit charge when it moves from one point to the other.

Formula used:
$\Delta U=-W$

Complete step by step answer:
Let us first understand what is meant by electric potential at a point.

Electric potential at a point is the potential energy of a unit charge placed at that point. Suppose at some point P, the electric potential V. If we place a unit charge (point charge), then the potential energy of the charge will be equal to V. (numerical value)

Therefore, we can write electric potential as $\dfrac{\text{energy}}{\text{charge}}$.
Now, we can understand that potential difference two different points will be equal of the change in potential energy of a unit charge when it moved from one point to the other.

Suppose there is some potential difference between point A and point B. If a unit point charge is taken from point A and point B, then the change in potential energy is equal to the potential difference between points A and B.

Therefore, we can say that if a point charge q is taken from point A to point B then the change in potential energy ($\Delta U$) per unit charge is equal to the potential difference ($\Delta V$) between the two points.

i.e. $\Delta V=\dfrac{\Delta U}{q}$.

Since electric force is a conservative force, $\Delta U=-W$, where W is work done by the electric force.

Hence, $\Delta V=-\dfrac{W}{q}$.

Therefore, potential difference between two points is equal to $\dfrac{\text{work done}}{\text{charge}}$.

Hence, the correct option is C.

Note:(i) The flow of electric charge from a given cross per unit time is defined to be electric current.
i.e. $\text{current}=\dfrac{\text{electric charge}}{\text{time}}$

Therefore, the option A is equal to electric current.
(ii) Work done per unit time is defined to be power.
i.e. $\text{power =}\dfrac{\text{work done}}{\text{time}}$