Question

How much energy is given to a unit charge passing through a $6V$ battery?

Answer 1

Hint: Apply the definition of voltage difference and voltage to find the expression for energy in terms of the voltage applied and the amount of charge. Out of the three variables, two variables namely voltage and charge are known and thus, the third that is energy can be found.
Formula used: The relation between voltage, charge and energy which derives from the basic definition of voltage:
$\text{energy}=\text{voltage}\times \text{charge}$

Complete step-by-step answer:
Let us first define voltage difference. Voltage difference is defined as the work a charge of 1 Coulomb has to do to travel from the initial point to the final point. The voltage difference between two points is independent of the path taken by the charge. Now, Voltage at a particular point is defined similar to the voltage difference, as the initial point is taken as infinity. The voltage at infinity is assumed zero. Therefore, the voltage at a point is the work done by a unit charge to reach that point from infinity.
For the question, a charge $Q=1C$ passes through a $V=6V$ battery which can be interpreted as the charge travels from a point where its voltage was initially zero (infinity) to a point where it has gained a voltage of $6V$.
We know that the energy consumed is the same amount as the work done. Therefore, from the basic definition of voltage explained earlier, an equation can be formulated:
$\begin{aligned} & \text{energy}=\text{voltage}\times \text{charge} \\\ & \text{energy}=6\times 1=6J \\\ \end{aligned}$
Therefore, the answer to the question is 6 Joules.

Note: The relation between energy and charge can be confusing, that is weather energy is voltage per unit charge or voltage times charge. In such situations firstly, try to understand the definition of voltage and not memorize it. Secondly, if you are still not sure, perform dimensional analysis on the expression to cross check.