Question

The electricity tariff is Rs.3.00 per unit. Calculate the cost of running an 80W fan for 10h a day for the month of June.
A. Rs.12.00
B. Rs.52.00
C. Rs.72.00
D. Rs.92.00

Answer 1

Hint:One unit is equal to one kilowatt-hour. Use the relation between kilowatt-hour (kWh) and joules to find the amount of energy that is equal to one unit. Then calculate the total energy consumed by the fan in one month and find the number of units consumed in that month. Once you get the units, you can calculate the cost.

Formula used:
$E=Pt$
where P is the power and t is the time for which the appliance works.

Complete answer:
The other word for ‘unit’ is kilowatt-hour, denoted as kWh. One unit is equal to one kilowatt-hour. 1 kWh is equal to the energy consumed by an electrical appliance working with a power of 1kW, consumes energy for 1 hour. Therefore, this means that,
$1kWh=1kW\times 1hr\\
\Rightarrow 1kWh =1000W\times 3600s\\
\Rightarrow 1kWh =3.6\times {{10}^{6}}J$
$\Rightarrow 1kWh=1unit=3.6\times {{10}^{6}}J$
(The SI unit of energy is joules (J)).

Now, let us calculate the energy consumed by the fan. It is said that the fan is working with a power of 80W for 10h per day. We know that the energy consumed is equal to $E=Pt$, where P is the power and t is the time for which the appliance works.Therefore, the energy consumed by the fan in a day is,
$E=80W\times 10h\\
\Rightarrow E =80W\times 10\times 3600s\\
\Rightarrow E =2.88\times {{10}^{6}}J$.
Let us consider that the month has 30 day. Therefore, the total energy consumed by the fan in a month is
$E=80W\times 10h\\
\Rightarrow E =2.88\times {{10}^{6}}\times 30\\
\Rightarrow E =86.4\times {{10}^{6}}J$.
Therefore, the units consumed in a month is $\dfrac{86.4\times {{10}^{6}}}{3.6\times {{10}^{6}}}=24units$. And it is given that the cost is Rs.300 per unit. This means that the cost for 24 units is $24\times 3=Rs.72.00$.

Hence, the correct option is C.

Note:Here, unit is a unit of energy. This means that it indicates a specific amount of energy consumed by the electric appliances. For commercial purposes, the unit ‘unit’ is used for measuring energy. You may have seen in your house electricity that the fees are calculated with respect to the total units consumed.