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Question

Calculate the electric bill at the end of a month of $$30$$ days at $$Rs. 2.00$$ per unit if $$6$$ lamps of $$40\ watt$$ each burn for $$8$$ hours per day, an electric iron of $$1\ kW$$ is used for $$2$$ hours per day and $$4$$ fans of $$50\ watt$$ each are used for $$10$$ hours per day.


Solution

Given:
Rate of one unit $$=Rs. 2.00 \ /unit$$
Also, $$1 \ unit = 1 \ kWh$$

So let us calculate the total energy consumed by all the appliances.
Energy consumed by an appliance in kWh $$=Power \ (in \ kW) \times time \ (in \ hours)$$

Power of a lamp $$P_1=40 \ W=40 \times 10^{-3} \ kW$$
Time for which it is operated per day $$t_1=8 \ hrs$$
Energy consumed by 6 lamps per day $$E_1=6 \times P_1 \times t_1$$
                                                                      $$=6 \times (40 \times 10^{-3}) \times 8$$
                                                                      $$=1.92 \ kWh$$
Power of an electric iron $$P_2= 1 \ kW$$
Time for which it is operated per day $$t_2=2 \ hrs$$
Energy consumed by the iron per day $$E_2=P_2 \times t_2$$
                                                                      $$=1 \times 2$$
                                                                      $$=2 \ kWh$$
Power of a fan $$P_3=50 \ W=50 \times 10^{-3} \ kW$$
Time for which it is operated per day $$t_3=10 \ hrs$$
Energy consumed by 4 fans per day $$E_3=4 \times P_3 \times t_3$$
                                                                    $$=4 \times (50 \times 10^{-3}) \times 10$$
                                                                    $$=2 \ kWh$$
Total energy consumed per day $$E_{total}=E_1+E_2+E_3$$
                                                                 $$=1.92+2+2=5.92 \ kWh$$
Total energy consumed per month $$E_{month}=30 \times E_{total}$$
                                                                       $$= 30 \times 5.92 $$
                                                                       $$=177.60 \ kWh$$ or $$177.60 \ units$$

Bill for one month $$=Rate/unit \times units=(Rs.2.00 / unit) \times (177.60 \ units)$$
                                                                       $$=Rs. 355.20$$

So the electric bill at the end of a month will be $$Rs. 355.20$$

Physics

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