Question

Cost of a $1$ unit of electricity in our city is (say) $Rs. 5$. Then, the cost of using a \[40\;W\] bulb, eight hours per day for one month is:
A. $Rs. 48$
B. $Rs. 50$
C. $Rs. 108$
D. $Rs. 92$

Answer 1

Hint: By using simple unitary method and application of basic mathematics the cost of the electricity that is used for one month can be calculated. The total power consumed must be obtained before calculating the cost. The cost is calculated in a step by step process, that is, the cost is first calculated for one day and then for the entire month.

Complete step by step answer:
The above problem asks us to find the total cost for electricity that has been used in the city, that is, the electricity bill for a period of month is being asked. In order to find this let us first look into the concept of power.

We know that all households use electrical appliances for which an electricity supply is required to be given for it to work and this electricity is nothing but the voltage supply or the current provided to the appliances. Electricity is said to be the flow of charges or electrons which is basically the source of production of current. The amount of electricity used up by the appliances is measured in terms of the power dissipated by the electrical appliances.

When there is a certain amount of current that passes through these appliances there will be a heat that is dissipated and this is known by a term called as power. Power is defined as the rate at which the work is done by a source of emf or voltage supply in maintaining an electric current throughout the circuit. The power is a measure of the heat that is dissipated due to the production of current when there is a voltage supply connected across its circuit elements.

Here, the electrical appliance that is taken into consideration is an electrical bulb. The power that is consumed by it is given to be \[40\;W\]. The energy that is consumed by these electrical appliances is measured by its power and hence we must first calculate the total power that is consumed by the bulb every day, that is, for the entire day. We are also given that the bulb is being used for $8$ hours daily. This means that we apply the unitary method over here. Thus, we get:

Since, the bulb is used for $8$ hours per day, the total power consumed for a single day will be:
$Power = 40 \times 8$
$ \Rightarrow Power = 320\;W$
Hence, this is the power consumed by the bulb for a single day. The power is usually measured in the unit of kilowatt and hence we must convert the power in Watts to kilowatts. Hence this is given by the relation:
$1kW = {10^3}W$

By using unitary method we get:
$ \Rightarrow 320W = 320 \times {10^{ - 3}}kW$
$ \Rightarrow Power = 0.32\;kW$
But we are asked to calculate for a period of one month. We know that a month has either $30$ or $31$ days in it neglecting February since on an average most of the months have either $30$ or $31$ days. We can approximately take the number of days in a month to be $30$.

We know the power for each day so for $30$ days the power consumed can be found out using the unitary method.
Since, $1\;month = 30\;days$
We know that, $1\;day = 0.32\;kW$
Hence, by applying unitary method again we get:
$ \Rightarrow 30\,days = 30 \times 0.32$
$ \Rightarrow \text{Power} = 9.6\;kW$
Hence, the total power consumed for one month will be $9.6\;kW$. Now, we come to the cost of the bulb and the power consumed by it. It is given that the cost of the electricity measured per unit is$Rs. 5$. We have also calculated the energy or the power consumed by the bulb in one month.
Hence, we can say that the energy consumed by the bulb in one month is $9.6\;units$. We know that: Cost of electricity measured per unit is $Rs. 5$. Hence, the cost of electricity for one month can be determined by using the unitary method once again.
$ \Rightarrow 1\;unit = Rs. 5$
Then, $9.6\;units = ?$
The question mark indicates what we must find out, that is, the cost for the bulb that uses $9.6\;units$ of electrical energy for one month.
Thus, \[\text{Cost} = 9.6 \times 5\]
$ \Rightarrow \text{Cost} = Rs. 48$
Hence, the total cost of electricity for one month is $Rs. 48$.

Therefore, the correct answer is option A.

Note: The common error which is seen in the above problem is that the power is not converted into kilowatt. The power is often measured in this unit itself because since the quantity of power is said to be large in amount or large in quantity the measurement is usually in kilowatt and hence this unit must be considered in order to select the correct option.