Question

What is the meaning of the symbol\[KWh\]? What quantity does it represent? How much electric energy in \[KWh\] is consumed by an electrical appliance of \[1000\text{ }Watts\] when it is switched on for 60 minutes?

Answer 1

Hint: We have to define about the\[KWh\] term as well as write the quantity that the term\[KWh\]contain in terms of Joule and calculate the energy consumed by an appliance of \[1000\text{ }Watts\]in 60 minutes which is the mathematical form of the term \[KWh\].


$Energy,E=P\times t$
Where, $P$is the power consumed by an appliance and its unit is Watt or ‘$W$’. Whereas, $t$ is the time in which the power is consumed and its unit is sec or ‘$s$’.
While,$E$is the energy and its unit is joule or ‘$J$’.

Complete step-by-step solution:
\[KWh\] means the kilowatt-hour, which is called the commercial unit for the measurement of electrical energy. Also, One-kilowatt-hour is defined as the amount of electrical energy consumed when an electrical appliance has power that is rated to 1 kilowatt which is used for 1 hour.
Now, the amount of electric energy in \[KWh\] that is consumed by an electrical appliance of 1000 watts when it is switched on for 60 minutes is as follow :-
\[Power,P=1000\text{ }Watts\]
\[P=\text{ 1KW}\]
\[time,t=60\text{ }min\]
\[t=1\text{ }hr\]
$Energy,E=Power\times time$
So, $P=1000Watts\times 60\min $
$P=1000\dfrac{Joule(J)}{\sec }\times 60\times 60\sec $
$P=36\times 100000\times Joule$
$P=3.6\times {{10}^{6}}J$
Therefore, the commercial unit of energy that is \[1~kWh\] represents the \[~~3.6\times {{10}^{6}}J\]of energy.
Also,$E=1KW\times 1hr$
So,
Energy consumed is$E=1KWh$
Which is the Mathematically derivation of the term\[KWh\].

Additional information: Energy is defined as the capacity for doing work. It exists in many forms like potential, kinetic, thermal, chemical, electrical, etc. Therefore, Electrical energy refers to the energy that is converted from the electric potential energy. This energy is supplied by the combination of electric current and electric potential that is delivered by an electric circuit provided by an electric power utility. Thus, all electrical energy is potential energy before it is delivered to the end of use. Once it converts from potential energy, it becomes electrical energy which is called another form of energy.

Note:\[KWh\] is only the commercial term for electrical energy not the S.I term as the S.I term of electrical energy is Joule represented by the symbol ‘$J$’ because electrical energy is also one of the forms of energy.