Question

How much energy in kilowatt hour is consumed in operating ten $50{\rm{ Watt}}$ bulbs for $10$ hours per day in a month (30 days)?
A. 1500
B. 5000
C. 15
D. 150

Answer 1

We have to obtain the amount of energy consumption in kilowatt hour so in the solution we will be using the expression of energy which gives us the relation between energy consumed by the apparatus, time period of operation and power of the apparatus.

Complete step by step answer:
Let us assume the number of bulbs operating is repressed as N, power consumed by each bulb is represented by P and time of operation of bulbs in a month is represented by T.

N = 10\\\ P = 50{\rm{ Watt}} \end{array}$$ It is given that bulbs are operating for a period of 10 hours per day in a month. So the time period of operation for entire month will be given as: $$\begin{array}{c} T = 30 \times 10{\rm{ hr}}\\\ = 300{\rm{ hr}} \end{array}$$ To calculate the amount of energy consumed in a kilowatt hour by a bulb, we will be using the expression for energy given in terms of power and time. $${E_1} = P \times T$$ But, we are required to calculate the energy consumed in a kilowatt hour by N number of bulbs. $$E = N \times P \times T$$ Substitute 10 for N, $$300{\rm{ hr}}$$ for T and $$50{\rm{ Watt}}$$ for P in the above expression of energy. $$\begin{array}{c} E = 10 \times \left( {50{\rm{ Watt}}} \right) \times \left( {300{\rm{ hr}}} \right)\\\ = 150,000{\rm{ Watt}} \cdot {\rm{hr}} \end{array}$$ Now we will divide the obtained value of energy in Watt hour by $$1000$$ to convert it into kilowatt hour. $$E = 150{\rm{ kWatt}} \cdot {\rm{hr}}$$ Therefore, the amount of energy consumed by ten $$50{\rm{ Watt}}$$ bulbs for ten hours per day in a month of 30 days is $$150{\rm{ kWatt}} \cdot {\rm{hr}}$$ and the option (D) is correct. **Note:** Do not forget to convert the obtained energy consumption from Watt hour to kilowatt hour as the final answer is asked in kilowatt hour. Also, take care of the value of time period because it has to be substituted for the entire month, not just for a single day.