Question

One unit of electric energy is equal to:
A. One kilowatt hour
B. One watt hour
C. 100 Joules
D. None of these

Answer 1

Hint: Apply the definition of one unit of electricity and describe the amount of power used for a duration of time to produce one-unit electrical energy. Convert this unit to find the relation between a unit electrical energy and the SI unit of energy that is Joules.
Formula used: The formula for power
$\text{Power}={\displaystyle \frac{\text{Energy consumed}}{\text{Time}}}$

Complete step-by-step answer:
One unit of electrical energy is defined as the quantity of energy required when we use power of 1 kilowatt for an hour. You might recall the term ‘unit from your electricity bill’. We pay our electricity bills according to the amount of energy we used in a period of time, usually a month. As the definition suggests one unit of electrical energy is called one kilowatt hour. ‘One kilowatt’ representing the 1kW power and ‘hour’ representing the duration of an hour.
Let us calculate the value of 1 unit of electrical energy in terms of the SI unit of energy which is joules.
Power is defined as the work done per unit time. In other words, it is the ratio of energy consumed to the time taken. The formula for power is
$\text{Power}={\displaystyle \frac{\text{Energy consumed}}{\text{Time}}}$
Converting the equation in terms of energy gives us:
$\text{Energy consumed}=\text{Power}\times \text{Time}$.
We know that the power is one kilo watt. That is
$\text{Power}=1kW=1000W$
And it is used for one hour. Since, the SI unit of time is second, we convert hours to seconds:
$\text{Time}=1hr=60\times 60s=3600s$
Therefore, the energy consumed is:
$\begin{array}{rl}& \text{Energy consumed}=\text{Power}\times \text{Time}\\ & \Rightarrow \text{1kW}\times 1hr\\ & \Rightarrow 1000\times 3600W\sec \\ & \Rightarrow 3.6\times {10}^{6}J\end{array}$
One unit of electrical energy is equal to $3.6\times {10}^{6}J$ of energy.
The answer to this question is option A.

Note: Since, unit electrical energy is essentially a form of energy its dimensional formula is the same as that of energy which is $[M^1{L}^2{T}^{-2}]$. This is similar to how power is measured in Watts as well as horsepower, which are just different units of the quantity power.