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Question: An electric kettle is rated \(2.5\,kW\) , \(250\,V\) . What is the cost of running the kettle for tw...

An electric kettle is rated 2.5 kW2.5\,kW , 250 V250\,V . What is the cost of running the kettle for two hours at Rs.  5.40Rs.\,\,5.40 per unit?
A. Rs.  17.00Rs.\,\,17.00
B. Rs.  27.00Rs.\,\,27.00
C. Rs.  26.00Rs.\,\,26.00
D. Rs.  16.20Rs.\,\,16.20

Explanation

Solution

The cost of running any electrical appliance depends directly on how much energy is it consuming. This energy is calculated using the specifications of the appliance and then multiplied with the rate of each unit.
The energy consumed is expressed as the product of the power consumed and the time for which the appliance is used. Mathematically this is expressed as E=PtE = Pt where E is the energy consumed, P is the power drawn and t is the time taken.
The relation between energy expressed in units and energy expressed in joules is given as 1 unit=3.6×106 J1\,unit = 3.6 \times {10^6}\,J
Commercially we use units to express the energy to accommodate larger energy consumption.

Formula used: We shall use the formula E=PtE = Pt where E is the energy consumed, P is the power drawn and t is the time taken.

Complete step-by-step answer:
We know that the energy consumed is expressed as the product of the power consumed and the time for which the appliance is used.
This is rewritten as E=PtE = Pt where E is measured in units, P is measured in kW and t is measured in hours.
So, in the above situation it is given that the power consumed by the kettle is 2.5 kW2.5\,kW .
So P=2.5 kWP = 2.5\,kW .
It is also given that the appliance is operated for two hours. Hence t=2 hrt = 2\,hr
Substituting in the formula, we get
E=2.5×2E = 2.5 \times 2
⇒E=5 units\Rightarrow E = 5\,units
Given that the cost of each unit is Rs.  5.40Rs.\,\,5.40 .
Hence the cost of 5 units is  5.40×5\,5.40 \times 5
⇒Rs.  27.00\Rightarrow Rs.\,\,27.00

So, the correct answer is “Option B”.

Note: The ratings on the appliances are always done in the commercial units only. 1 unit can also be described as 1 kW hr and so it is important to keep the units of power in kW and units of time in hr. Note that this convention is applicable only for the commercial application. Use the SI units everywhere to follow the standard.