To calculate the cost of using an electrical device, it is necessary to know its power and its usage time to establish the quantity of electrical energy consumed by the device.
The power is usually listed on the data sheet of the electrical appliance. It also includes other characteristics:
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the voltage required and supported by the device;
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the current intensity;
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the type of current (direct or alternating); in the case of alternating current, the frequency of current required;
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the internal resistance of the device.
Hydro-Québec's rate for the use of electricity is given for consumption in kilowatt-hours |\text {(kWh)}|. The cost therefore depends on the device’s power in kilowatts |\text {(kW)}| and its usage time in hours |\text {(h)}|.
Here are Hydro-Québec's rates for domestic electricity consumption effective since April 1, 2018.
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Subscription fee: |\$ 0.4064 \: \text {per day}|
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Price for the first |36| kWh per day: |\$ 0.0591 \: \text { per kWh}|
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Rate for excess kWh: |\$ 0.0912 \: \text {per kWh}|
A dryer operates under a voltage of |\text {240 V}| and the current intensity flowing through it is |\text {20 A}.| Knowing that the drying time for a load of clothes is approximately |\text {75 minutes},| what will it cost to use this dryer in a week when five loads of clothes are dried? ||\begin{align}V &= \text {240 V} &I = \text {20 A} \\ \triangle t &= \text {75 minutes per load, 5 loads per week} \end{align} || Since the cost depends on the power, it must be determined from the current and the voltage. ||\begin{align}P = V \times I \quad \Rightarrow \quad P &= {\text {240 V}}\times {\text {20 A}} \\ &= \text {4 800 W} \end{align}||
Since the rate is indicated based on a quantity of energy measured in kilowatt-hours, the power must be converted into kilowatts.||\text {4 800 W} \div 1\ 000 = \text {4.8 kW}||The cost also depends on the time of usage in hours. Since there are |\text {60 minutes}| in an hour, the |\text {75 minutes}| will have to be converted to hours and the five loads done during the week will have to be taken into account. ||\triangle t = \text {75 minutes} \div 60 = \text {1.25 h} \times 5 \text { loads} = \text {6.25 h}|| The next step is to find out how much electrical energy is consumed.|| \begin{align}E &= \text {?} &P = \text {4.8 kW} \\ \triangle t &= \text {6.25 h} \\ \end{align}|| ||\begin{align}E = P \times \triangle t \quad \Rightarrow \quad E &= {\text {4.8 kW}}\times {\text {6.25 h}} \\ &= \text {30 kWh} \end{align}||
The dryer will have consumed |\text {30 kWh}| during the week. As of April 1, 2018, the cost posted by Hydro-Québec for each kilowatt-hour was |$0.0591.| To calculate the cost of using the dryer, simply multiply the amount of energy consumed by the cost per kilowatt hour.||30 \text {kWh} \times $0.0591 \text {/kWh} = $1.77||
The cost for using the dryer for one week will be |$1.77.|
How much will it cost to heat a house equipped with |12| electric heaters with a consumption of |\text {1 500 W}| each if they operate eight hours a day for a month of |31| days? ||\begin{align}P &= \text {1 500 W} &\text {Number of operating electric heaters} = \text {12} \\ \triangle t &= \text {8 h per day, 31 per month} \\ \end{align}||
We must take into account the total power, that is the power of all the electric heaters, and then convert this power into kilowatts. ||P_{\text {total}} = \text {1 500 W }\times 12 = \text {18 000 W } \div 1\ 000 = \text {18 kW}||
The total time of use of the electric heater must then be calculated.||\text {8 h/day} \times \text {31 days} = \text {248 h}|| The electrical energy consumed is determined by multiplying the power by the time of use.
||\begin{align}E = P \times \triangle t \quad \Rightarrow \quad E &= {\text {18 kW}}\times {\text {248 h}} \\ &= \text {4 464 kWh} \end{align}|| The first |36| kilowatt-hours are sold daily at a base price, while energy consumed above that level is sold at a higher price.
To begin with, it is necessary to determine how much energy will be sold at a regular price. ||\text {31 days} \times \text {36 kWh} = \text {1 116 kWh}|| The remaining energy will be sold at a higher cost. Therefore, to determine the amount of energy sold at the highest rate, the amount of energy consumed at low cost must be subtracted from the total energy consumed. ||\text {4 464 kWh} – \text{1 116 kWh} = \text {3 348 kWh}||
Therefore, two costs are to be determined, namely the cost of the first |36| kilowatt-hours, and the cost of excess energy.
Cost of the first |36| kilowatt-hours: |\text {1 116 kWh} \times \$ 0.0591 \text {/kWh}= \$ 65.96.|
Cost of excess energy: |\text {3 348 kWh} \times \$ 0.0912 \text {/kWh} = $305.34.|
Total cost: |\$ 65.96 + \$ 305.34 = \$ 371.30.|
To use the twelve electric heaters during |31| days, the price to be paid will be |\$ 371.30.|
Hydro-Québec provides a tool on its website to help better understand how to read the bill that it sends to Québec users.