12.7 power and efficiency

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Electricity

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2

Power (it’s Electric!)

 _Power_{: Rate at which work is done. OR Rate}

at which energy is transformed

 _{Electric Power}_{: The rate at which charge}

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Electrical Energy Consumption:

Power and Energy

12.7

Power

 _{Electrical power}_{is the rate at which electrical energy is}

produced or consumed during a given period of time.

_{Power is measured in watts (W).}

Energy

_{Energy is measured in joules (J).}

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Calculating Power

 _{Power (P) is measured in watts (W)}

 _{Energy (E) is measured in joules (J)}

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Calculating Power

 _{From the definition we can determine the}

formula for power to be:

Power = Energy P = E

time t

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Given: t = 1.30 h

x 3600 t = 4700s

E = 210 000 J Required: P = ?

Analysis: P = E / t

Solution: P = 210 000 J / 4700 s P = 45 W

Paraphrase/Statement: Therefore, the iPod’s power is 45 watts.

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Electrical POWER

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POWER

It is interesting to see how certain electrical

variables can be used to get POWER. Let’s take Voltage and Current for example.

V = E

Q

So what happens when we put these triangles together?

Q

I

t

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POWER

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POWER

variables can be used to get POWER. Let’s take Voltage and Current for example.

V x I

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POWER

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POWER

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Electric Power

SO: Electric power can be calculated using the current and voltage.

Power = Current x Voltage

unit watt, W

J 1 W = 1



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Other useful power formulas

These formulas can also be used! They are simply

derivations of the

POWER formula with different versions of

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Complete Worksheet

•_Power

•_{Mixed word problems}

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Electrical Energy Use in the

Home

In an electric meter in your home, the electrical energy is measured in kilowatt

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 _{There are 3 600 000J in one kW x h, therefore it}

is much more practical to use kilowatt hours.

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 _{A kilowatt hour refers}

to 1000 watts being used over an hour, therefore a 100W

bulb would have to be on for 10 hours to

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 _{The electrical meter in}

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Household Appliances

 _{Federal law in Canada, under Canada’s Energy}

Efficiency Regulations, requires that the EnerGuide label be placed on all new electrical appliances

manufactured in or imported into Canada and that the label indicate the amount of electricity used by that appliance. This information is determined by

standardized test procedures. A third-party agency verifies that an appliance meets Canada’s minimum energy performance levels.

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Electrical Energy Consumption:

Efficiency

_{Many major appliances have energy usage stickers (EnerGuide labels)}

that indicate how much electrical energy the device uses during one year. The kilowatt•hour ratings on EnerGuide labels are based on the average Canadian household use.

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The Black and White

EnerGuide Label

1. Average annual energy consumption of the appliance in kilowatt hours (kWh)

2. Energy efficiency of the appliance

relative to similar models

3. Annual energy consumption range for

models of this type and size

4. Type and size of the model

5. Model number

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Electrical Energy Consumption:

Efficiency

_{Some electrical devices use less electrical energy to do}

a task than other devices.

_The_efficiency_{of a device is a measure of how much}

useful energy the device produces compared with the amount of energy that the device uses.

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Electrical Efficiency

 _{You can find out}

how efficient an electrical device is by comparing how much energy is put in to how much

energy is put out.

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Calculating the Efficiency of a

Device

 _{You can calculate the percent efficiency of a}

device using the equation:

percent efficiency = energy out x 100% energy in

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SAMPLE PROBLEM 1

 _{A light bulb uses 100 J of electrical energy and}

produces 35 J of light energy. Calculate the percent efficiency of the light bulb.

Given: E _out = 35 J E _in = 100 J

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Analysis: % efficiency = E _out x 100% E _in

Solution: % efficiency = 35 J x 100% 100J

% efficiency = 0.35 x 100% % efficiency = 40%

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SAMPLE PROBLEM 2

 _{A toaster oven uses 1200 J of energy to produce 850 J of thermal}

energy. Calculate the percent efficiency of the toaster oven.

Given:

E _in = 1200 J E _out = 850 J

Required:

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Analysis:

% efficiency = E _out x 100% E _in

Solution:

% efficiency = 850 J x 100% 1200 J

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Cost of Electricity

 _{In order to calculate the cost of electrical energy}

used in your home you can use the following formula:

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SAMPLE PROBLEM 1

A laptop computer uses a 75 W adapter when it is plugged in. Electricity costs 5.6 ¢/kW.h. Calculate how much it would cost to operate the laptop for 1 year for 24 hours per day.

Given: power = 75 W (converted to kW = 75 W x 1 kW = 0.075 kW) 1000 W

time = 24 hours per day for 365 days = 8760 hours cost of electricity = 5.6 ¢/kW.h

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Solution:

Cost to operate = 0.075 kW x 8760 h x 5.6 ¢ kW.h

Cost to operate = 3679 ¢ or 3700 ¢

Statement:

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SAMPLE PROBLEM 2

 _{Calculate the cost of operating a 1500 W hair}

dryer to dry your hair for 6 minutes per day for 3 days. The cost of electricity is 5.6 ¢/kW.h.

Given:

power = 1500 W (converted to kW = 1500 W x 1 kW = 1.5 kW) 1000 W

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Required:

cost to operate

Analysis:

cost to operate = power used x time x cost of electricity

Solution:

Cost to operate = 1.5 kW x 0.3 h x 5.6 ¢ kW.h

Cost to operate = 2.52 ¢ or 3 ¢

Statement:

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Appliances Average

power W Monthly Energy Use kW x h

Approximate Costs $

Air

conditioner 750 90 - 540 7.20 – 43.30

Clothes

Dryer 5000 50 - 150 4.01 – 12.03

Television 80 5 - 15 0.41 – 1.20

Lighting –

60W bulb 60 5 - 30 0.40 – 2.41

Microwave

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Example A

 _{Calculate the cost of the electricity needed to}

operate a refrigerator/freezer (500W) for a day if the rate charged for electricity is $0.08/ kW x h

First convert watts to kW 500W x 1kW/1000w = 0.500kW

Cost = p x t x rate

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Second Formula for power

Since E = V x I x t And P = E

t

Then P = V x I x t t

What happens to the t ?

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Electric Power

Electric power can be calculated using the current and voltage.

Power = Potential Difference x Current

P = V x I

unit watt, W

J 1 W = 1

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Text book work and worksheet

 _{Text p 336}

#2,3,5

 _{Power calculations}

worksheet

 _{Text p 339}

 _#1-6

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ENERGY

 _{Energy is the ability to do work. In electricity}

the energy is transferred to the load in a circuit by moving electrons.

 _{We can calculate the Energy with the formula}

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Charge and current

 _{We have already determined that we can}

calculate Q = I x t

 _{This can be fit into the formula for Energy}

E = V x Q

E = V x(I x t)

So the second formula for Energy is