Question

A 2 kW heater, a 200 W TV and three 100 W lamps are all switched on from 6 p.m. to 10 p.m. What is the total cost at Rs. 5.50 per kWh?

Answer 1

In order to solve this question, we should know the power formula and the total energy consumed by the heater, TV and lamps. We should note here they have given that the number of lamps is taken as n.

Complete step by step answer: Let us take heater:
Given: P = 2kW, t = 4h
We have power formula is given by,
$P = \dfrac{E}{t}$
$E = P\times t\\\ \Rightarrow E = 2 x 4\\\ \Rightarrow E = 8kWh$
Let us take TV:
Given, P = 200W = 0.2kW, t = 4h
$E = P \times t\\\ \Rightarrow E = 0.2 x 4\\\ \Rightarrow E = 0.8 kWh$
Let us take Lamps:
Given: P = 100W = 0.1 kW, t= 4h, n= 3
$E = n \times P \times t\\\ \Rightarrow E = 3 \times 0.1 \times 4\\\ \Rightarrow E = 1.2 kWh$
Total energy consumed = 8 + 0.8 + 1.2 = 10 kWh
Cost of 1 kWh = 5.50 Rs
Cost of 10 kWh = 5.50 $\times$ 10 = 55 Rs

Note: An electric power measure of the rate of electrical energy transfer by an electric circuit per unit time. Denoted by P and measured using the SI unit of power is the watt or one joule per second. Electric power is commonly supplied by sources such as electric batteries and produced by electric generators.The power in watts which is equal when the energy consumed in kilowatt-hours (kWh) per day which is the number consumed in hours per day that is time which is divided by 1000 watts per kilowatt.
$E = P \times t / 1000$