Question

$1kWh=$
A. 3.6 J
B. 3.6 KJ
C. 3.6 MJ
D. 3.6 GJ

Answer 1

Hint: Define kilowatt-hour. obtain the units of the physical quantities and try to break them to fundamental quantities. kW is a unit of power and kWh is a unit of energy. So, we can convert kWh into joule. The formula we will use will be $\text{Energ}{{\text{y}}_{\text{J}}}=\text{Powe}{{\text{r}}_{\text{W}}}\times \text{Tim}{{\text{e}}_{\text{S}}}$

Complete step-by-step answer:
The watt-hour is a unit of energy. It can be symbolised as Wh. One watt-hour is a unit of energy representing 1 Watt of power expended for 1 hour of time.
One kilowatt-hour can be defined as the 1000 watt of power expended for 1 hour of time.
We can’t directly convert Watt to Joules as the units define different quantities. Watt is the unit of power and Joule is the unit of energy.
Power in watt(W) can be converted to energy in joules(J) by multiplying power in watt by time in second(s)
So,
$\text{Energ}{{\text{y}}_{\text{J}}}=\text{Powe}{{\text{r}}_{\text{W}}}\times \text{Tim}{{\text{e}}_{\text{S}}}$ --- (1)
${{E}_{J}}={{P}_{W}}\times {{T}_{s}}$
Converting into units we can write the equation as,
$\text{joule}=\text{watt}\times \text{second}$
To convert one watt-hour to joules we need to convert the time from hour to second.
\[\text{1 hour}=60\text{ minute}\]
$\text{1 minute = 60 seconds}$
$1\text{ hour }=\text{ }60\times 60\text{ seconds}$
$\text{1 hour }=\text{ 3600 seconds}$
Hence from equation (1), we get,
${{E}_{J}}=\text{1 kW }\times \text{ 1 hour}$
${{E}_{J}}=\text{1000 watt }\times \text{ 3600 seconds}$
${{E}_{J}}=3600000\text{joules}$
${{E}_{J}}=3.6\times {{10}^{6}}\text{joules}$
Hence, the correct answer is ${{E}_{J}}=3.6\times {{10}^{6}}\text{joules}$ or 3.6 MJ
Correct answer is Option (C).
Additional information: Watt-hour is a unit of energy defined as 1 watt of power expended for 1 hour of time. It is not a standard unit in any formal system but it is used widely in electrical appliances. One should remember watt and watt-hour is a completely different unit. Watt is a unit of power and watt-hour is the power used for an hour.

Note: Remember all the fundamental quantities and first try to express the derived quantities in terms of the fundamental quantities.
Power can be defined as work done per unit time (or energy per unit time). So, we can write energy as a product of power and time.
Dimension of energy is given as, $\left[ M{{L}^{2}}{{T}^{-2}} \right]$
We can use different units of energy. Some of them are joule, watt-hour, kilowatt-hour etc.