A student in a town in India, where the price per unit ( $1$ unit $=1 \,kWh$ ) of electricity is $₹ 5.00$, purchases a $1 \,kVA$ $UPS$ (uninterrupted power supply) battery. A day before the exam, $10$ friends arrive to 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 $3 \,A$ fuse.
$III.$ If all the $10$ friends use the laptop for $5 \,h$, then the cost of the consumed electricity is about $₹ 22.50.$
Select the correct option with the true statements.
KVPY 2019, Advanced
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(c)
Power requirement for $1$ laptop, $P_1=90 \,W$
So, power requirement for $10$ laptops,
$P=10 \times P_1=10 \times 90$
$=900 W =0.9 \,kW$
In 5h, electrical energy used by all laptops,
$E=P \times t=0.9 \times 5$
$=4.5 \,kWh$
Cost of electrical energy used is
$\text { Cost }=E \times \text { Unit cost }$
$=4.5 \times 5$
$=₹ 22.50$
So, statement $III$ is correct.
For laptop charger, input voltage is $220 \,V .$
So, current when all $10$ laptops are connected through an extension,
$I=\frac{P}{V}=\frac{900}{220} \approx 4.1 \,A$
As, line current exceeds current rating of fuse, therefore $3 A$ fuse cannot be used. So, statement $II$ is incorrect.
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