Question

What is the commercial unit of electrical energy?

Answer 1

Hint: The total work done (or the total energy supplied) by the source emf in maintaining an electric current in the circuit for a given time is called electric energy. So the unit of electrical energy is nothing but the unit of work done i.e. Joule.

Formula used: Electric power, $P=VI={{I}^{2}}R=\dfrac{{{V}^{2}}}{R}$
Electric energy, $W=Pt=VIt={{I}^{2}}Rt$
Where the symbols carry their usual meaning.

Complete step by step answer:
Electric power: The rate of doing work is called power. So for an electric circuit, “The rate at which work is done by a source emf in maintaining the electric current through an electric circuit is called electric power of the circuit.”
If a current $I$ flows through a circuit for time $t$ at a constant potential difference $V$ then the work done or energy consumed through a resistance $R$ is given by
$W=VIt\text{ Joule}$
So electric power, $P=\dfrac{W}{t}=VI={{I}^{2}}R$,so
$\text{Power=Current }\!\!\times\!\!\text{ Voltage}$
Unit of electric power: The S.I unit of electric power is ‘Watt’.
Electric energy: The total work done by the source emf in maintaining the electric current in circuit for a given time is known as electric energy consumed in the circuit. It depends upon the power of the appliance used in the circuit and the time for which the power is maintained.
Electric energy, $W=P.t=VIt={{I}^{2}}Rt$
Unit of electric energy: The S.I Unit of electric energy is Joule
$1\text{Joule}=1Volt\times 1\text{Ampere}\times 1\text{Second=1Watt}\times 1\text{Second}$
The unit ‘Watt’ is very small. So in practical terms a bigger unit is used like kilo-Watt,Mega-Watt.
The commercial unit of electric energy is \[\text{kilowatt-hour}\]. One \[\text{kilowatt-hour}\] is defined as the electrical energy consumed by an appliance of power one kilo-watt in one hour.
\[\begin{align}
  & 1\text{kilowatt-hour} \\
 & =1kilowatt\times \text{1hour} \\
 & =1000watt\times \text{3600s} \\
 & \text{=3,600,000watt}\times \text{second} \\
 & \text{=3,600,000}Joules \\
 & \Rightarrow 1kWh=3.6\times {{10}^{6}}J \\
\end{align}\]

So the commercial unit of electrical energy is \[\text{kilowatt-hour}\].

Additional Information: The potential difference across two ends of a circuit is produced by a battery. A battery consists of one or more electric cells. The chemical action within a cell generates the potential difference across the terminals of the cell, even when no current is drawn from it. When the cell is connected to a circuit, the potential difference produced will drive the electrons from the conductor which in turn produce the electric current through the circuit. In order to maintain the current flowing in a given electric circuit, the cell has to expend its chemical energy stored in it. A part of this energy is used to produce useful work and another part may be used to raise the temperature. This is known as the heating effect of electric current.

Note: One \[\text{kilowatt-hour}\] is also known as a “Board of trade” unit. The electric meters installed in houses measure the electrical energy consumed in\[\text{kilowatt-hour}\]. Another common unit of electric energy is$\text{watt-hour}$. It is the energy consumed by an appliance of power $\text{one-watt}$in one hour.
$\text{1watt-hour=1watt}\times \text{1hour=3}\text{.6}\times \text{1}{{\text{0}}^{3}}J$.