Question

How much $1 kWh$ = _ _ _ _ _ _ _ J.
A. $3.6\times {{10}^{6}}$
B. $36\times {{10}^{6}}$
C. $36\times {{10}^{7}}$
D. $3.6\times {{10}^{5}}$

Answer 1

Hint: 1 kWh is equal to the amount of work done or energy consumed by an electrical appliance running at a power of 1 kW, in a time interval of 1 hour. Use the formula for power in terms of energy consumed in a time interval and calculate the value of 1 kWh in terms of joules.

Complete answer:
Kilowatt-hour (kWh) is a unit of energy. 1 kWh is equal to the amount of work done or energy consumed by an electrical appliance running at a power of 1 kW, in a time interval of 1 hour. Now, let us write the values of 1 kWh in terms of SI unit energy, which is joules (J).For this we will use the definition of power. Power is equal to the total energy consumed divided by the total time taken to consume that amount of energy.

Therefore, $P=\dfrac{E}{t}$,
where P is the power, E is the energy consumed and t is the time interval.
$E=Pt$ .….. (i)
We know that 1 kWh is equal to energy consumed for 1 hour at power of 1 kW.
Therefore, substitute $P=1kW$, $E=1kWh$ and $t=1h$ in equation (i).
$1kWh=(1kW)(1h)$ ….. (ii).
We know that $1kW={{10}^{3}}W$ and $1h=3600s$.
Now, substitute the values of 1 kW and 1 h in equation (ii).
$1kWh=({{10}^{3}}W)(3600s)$
$\Rightarrow 1kWh=3.6\times {{10}^{6}}Ws$
And $1Ws=1J$.
Then,
$\therefore 1kWh=3.6\times {{10}^{6}}J$
This means that values of 1 kWh in terms of joules is equal to $3.6\times {{10}^{6}}J$.

Hence, the correct option is A.

Note: One may think that if we have a SI unit of energy (joules), then why to use another unit of energy. The unit kWh is used for commercial purposes. When we use electricity on a large scale (like using electricity at home or industry), we require a large amount of energy. Therefore, we need a unit with greater magnitude so that the numerical values are small and easy to measure. Kilowatt-hour (kWh) is also called units. $1kWh=1unit$.