Question

An electric heater of power $3kW$ is used for $10h$ . How much energy does it consume? Express your answer in (i) $kWh$ (ii) Joule

Answer 1

Hint: We will first find out the energy consumed by the heater. Then we will convert the answer into the required units.
Formulae Used: \[E = P \times t\]
Where, $P$ is the power rating of the appliance, $t$ is the time of use and $E$ is the energy consumed by the appliance.

Step By Step Solution
Here,
Given,
\[P = 3kW\]
\[t = 10h\]
Thus,
The energy consumed by the heater is, \[E = {\text{ }}\left( {3 \times 10} \right)kWh = 30kWh\]
Now,
We know the standard unit of power is $W$ and that of time is $s$.
Also, we know that the standard unit of energy is $J$.
Thus,
We can say that
\[Joule\left( J \right) = Watt\left( W \right) \times Second\left( s \right)\]
Now,
To convert from \[kWh\] to \[J\]
\[1kWh = {10^3}W \times 3.6 \times {10^3}s\]
Thus, we can say that
\[1kWh = 3.6 \times {10^6}Ws = 3.6 \times {10^6}J\]
Thus,
\[E = 30kWh = 3 \times 10 \times 3.6 \times {10^6}J = 10.8 \times {10^7}J = 1.08 \times {10^8}J\]

Hence,
The answers are:
\[E = 30kWh\]
\[E = 1.08 \times {10^8}J\]

Additional Information: The value of energy we calculated for the first question is the unit on which the electricity boards apply charges on.
In other words,
Let us say the electricity board of a state charges \[10paise\] per \[1kWh\] of energy used.
Thus,
For \[30kWh\] of energy used, we will be charged an amount of \[10 \times 30 = 300paise = Rs.3\]
Also,
The unit actually signifies that we have used an appliance rated \[30kW\] for an hour.
Thus, the rating is also presumed by just evaluating the value and the unit connected with each other for the situation.

Note: We converted the answer to the required unit by finding its conversion for the units when the value of either is unity. We can then interchange the both for any other given situation.