Question

In what unit does the electric meter in a house measure the electrical energy consumed? What is its value in the SI unit?
$\text{A}\text{. }Wh\text{, }1Wh=3.6\times {{10}^{6}}J$
$\text{B}\text{. }kWh\text{, }1kWh=3.6\times {{10}^{5}}J$
$\text{C}\text{. }W\text{, }1W=3.6\times {{10}^{6}}J$
$\text{D}\text{. }kWh\text{, }1kWh=3.6\times {{10}^{6}}J$

Answer 1

Hint: The energy that is consumed in our houses is a very large amount. As a result, the unit of joules becomes a very small quantity compared to the total energy consumed. That is why we introduce a larger unit for energy.

Complete step-by-step solution:
We know that most of our appliances in our house operate on electricity. However, this electricity is not free and we have to pay for it every month.
But when we see the bill, we do not find the energy consumption in the units of Joules. Whereas we have studied that the unit of energy is Joules.
Actually, the energy that is consumed in our houses is a very large amount. As a result, the unit of joules becomes a very small quantity compared to the total energy consumed. That is why we introduce a larger unit for energy called kilowatt-hour (kWh).
The electrical energy consumption in our houses is measured in the units of kWh.
1 kWh is equal to the energy consumed by an appliance with the power of 1kW.
i.e. $1kWh={{10}^{3}}W\times 1hr$ …. (i).
We know that the SI unit of energy is Joules (J).
Let us find the value of 1kWh in the unit of joules.
1W is equal to 1$J{{s}^{-1}}$.
1hr = 3600s
Substitute the values of 1W and 1hr in equation (i).
 $\Rightarrow 1kWh={{10}^{3}}\left( 1J{{s}^{-1}} \right)\times 3600s$
\[\Rightarrow 1kWh=3.6\times {{10}^{6}}J\].
Hence, the correct option is D.

Note: Many times students get confused between the units watt and kilowatt-hour.
Therefore, understand that a watt is a unit of power. Power is the rate of energy consumed in one unit of time. Therefore, 1watt means that 1 joule of energy is consumed every second.
Whereas, a kilowatt-hour is a unit of energy.