Question

A student in town in India, where the price per unit $\left( {1\,unit = 1kW - hr} \right)$ of electricity is $Rs.5.00$, purchases a $1kVA$ UPS ( uninterrupted power supply) battery. A day before the exam $10$ friends arrive at the student’s home with their laptops and all connect their laptops to the Ups. Assume that each laptop has a constant power requirement of $90\,W$. Consider the following statements:
I. All the $10$ laptops can be powered by the UPS if connected directly.
II. All the $10$ laptops can be powered if connected using an extension box with a $3A$ fuse.
III. If all the $10$ friends use the laptop for $5hours$, then the cost of the consumed electricity is about $Rs.22.50$.
Select the correct option with the true statements.
A. I only
B. I and II only
C. I and III only
D. II and III only

Answer 1

Hint: We will first convert the power supplied by the battery from kilowatt to watt. Then we have calculated the electricity consumed by $10$ laptops in terms of watt per second. With the help of these quantities we can calculate the cost of the power consumed by $10$ laptops at a time.

Complete step by step answer:
Here, the power supplied by the battery of UPS is, $ = 1kVA = 1000W$
It is given in the question that the laptop consumes a constant power of $90\,W$.
Therefore, when all the laptops will get connected together directly, therefore, the power consumed by the $10$ laptops is given below
${P_T} = 90W \times 10$
$ \Rightarrow \,{P_T} = 900\,W$
And the electricity consumed by the $10$ laptops is, $1kW \times 3600\,\sec = 3600000\,Ws$.
Also, it is given in the question that the price per unit of the electricity consumed is $Rs.5.00$ therefore, the electricity is given below;
$1\,unit = 1kW - hr = Rs.5.00$
Therefore, the cost of the electricity consumed per second is, $ = 5 \times 3600$
Now, if the $10$ laptops are used at one time, therefore, the power consumed by the $10$ laptops is given by
$1\,unit = \dfrac{{900 \times 5 \times 3600}}{{3600000}}$
$ \Rightarrow \,1\,unit = 4.5$
Therefore, the cost of the power consumed by the $10$ laptops in 5 hours is,
$5\,hours = 4.5 \times 5 = 22.5\,rupees$
Also, we can say that all the $10$ laptops can be powered by the UPS if connected directly because a $3A$ bulb cannot provide the power that $10$ laptops need.

Therefore, option C is the correct option.

Note:For solving these types of questions, it is not necessary to convert the units into their smaller units. In this question, you can also solve the question by not converting the power into watts per second. In order to calculate the power you can only divide $1000$ to the power consumed by the $10$ laptops for $5\,hours$.