Question

In $5s$, a charge of $25C$ leaves a battery and $100J$ of energy is delivered to an outside circuit. What is the potential difference across the battery?
A) $20V$
B) $125V$
C) $4V$
D) $8V$

Answer 1

Hint- The potential difference is the difference of potential across two points. The amount of energy required in moving charges in between the two points is called potential energy. The potential difference is measured in volt and the potential energy is measured in Joule. One volt is defined as the one joule of energy is required in moving unit positive charge from one place to another.

Formula used:
$I = \dfrac{q}{t}$
Where $I$is the current flowing, $q$is the charge and $t$is the time.
$W = V.I.t$
Where $W$is the work done, $V$is the potential difference, $I$is the current and $t$ is the time.

Complete step by step answer:
If the charge is moving in a specific period of time it is called current. Therefore current, $I = \dfrac{q}{t}$
Substituting the values of charge and the time in the given formula we get,
$\rightarrow I = \dfrac{{25}}{5}$
$\therefore I = 5A$
The work done is the product of power and time. Therefore, work done, $W = V.I.t$ As we want to find the potential difference, $V = \dfrac{W}{{I.t}}$
Applying all the known values in the above equation.
$V = \dfrac{{100}}{{5 \times 5}}$
$\rightarrow V = \dfrac{{100}}{{25}}$
$\therefore V = 4V$

Hence the correct option is C.

Additional information:
If the potential difference at two surfaces is equal, those two surfaces are equipotential surfaces. And the difference between the work-done on two surfaces is zero. The unit of potential difference is Volt.

Note: The amount of work done transferred in a period of time is called power. Hence the work done is the product of power and time. It is measured in Joule, erg, electron volt etc. Among these, the SI unit of potential energy or work done is Joule. One joule of work is equal to $6.24 \times {10^{18}}eV$.