1 Electrical Power Electronics Copyright © Texas Education Agency, All rights reserved.

Electrical Power Electrical power is the rate of electrical energy consumed by an electrical circuit o Shows how fast energy is used Mechanical power is the rate at which work is done A rate is like a speed o Typical values for speed: mi/hr or m/s 2 Copyright © Texas Education Agency, All rights reserved.

Power and Work Mechanical work has units of force times distance o Something has to move for work to be done o The thing that moves for electrical work is the electron Electron movement is measured by the amount of current The force that makes electrons move is voltage 3 Copyright © Texas Education Agency, All rights reserved.

Watt’s Law 4 P = V I P = Δ V I Copyright © Texas Education Agency, All rights reserved. Electrical power is the product of current times voltage o Use change in voltage only when a portion of the available voltage is used by a circuit or component The unit of electrical power is the watt ( W ) A watt has units of joules per second ( J/s )

Power and Energy Power is a rate of energy usage o Utility companies charge for energy used, not for power used Energy is a product of power and time o For example, if one watt is used for one second, one joule of energy is consumed 5 Copyright © Texas Education Agency, All rights reserved.

Household Energy Use Utility companies use kilowatt hours ( kWh) to measure units of energy in houses How many joules are in one kWh ? o 3,600,000 joules or 3.6 MJ (mega joules) 6 Copyright © Texas Education Agency, All rights reserved.

Other Power Formulas You may alternate between versions of the power formula depending on the known circuit values These two versions result from substituting Ohm’s Law for either voltage or current 7 Copyright © Texas Education Agency, All rights reserved.

8 Abbreviations for Power Power = P Watt = W Kilowatt = kW Kilowatt hours = kWh Copyright © Texas Education Agency, All rights reserved.

9 Summary of Power Formulas When current and voltage are known, use P=IV When current and resistance are known, use P=I 2 R When voltage and resistance are known, use P=V 2 / R Copyright © Texas Education Agency, All rights reserved.

10 Using a Wattmeter To measure power with a wattmeter: 1. Turn off circuit power 2. Connect the current (I) terminals of the wattmeter in series with the circuit load o CAUTION - Observe polarity. The positive lead must be toward the positive side, and the negative lead toward the negative side. Copyright © Texas Education Agency, All rights reserved.

11 Using a Wattmeter (cont’d.) 3. Connect the voltage (V) terminals of wattmeter across the load 4. Turn on circuit power 5. Read and record power value in watts indicated on wattmeter 6. Turn off circuit power and disconnect wattmeter Copyright © Texas Education Agency, All rights reserved.

12 Copyright © Texas Education Agency, All rights reserved.

13 Wattage Rating of Resistors Resistors have ohm values and wattage ratings Resistor size generally indicates wattage rating Wattage rating indicates the maximum amount of power o Wattage rating should be double the expected power level of the circuit Copyright © Texas Education Agency, All rights reserved.

Calculate P T, P 1, and P 2 14 V S = 15 V R 1 = 100 Ω R 2 = 200 Ω Practice Problem 1: Power in a Series Circuit Copyright © Texas Education Agency, All rights reserved.

Calculate P T, P 1, and P 2 o This problem can be solved in several ways 15 V S = 15 V R 1 = 100 Ω R 2 = 200 Ω Practice Problem 1: Power in a Series Circuit Copyright © Texas Education Agency, All rights reserved.

Practice Problem 1: Power in a Series Circuit First, write the equation(s) that solve the problem 16 Copyright © Texas Education Agency, All rights reserved. V S = 15 V R 1 = 100 Ω R 2 = 200 Ω

Practice Problem 1: Power in a Series Circuit First, write the equation(s) that solve the problem 17 Copyright © Texas Education Agency, All rights reserved. V S = 15 V R 1 = 100 Ω R 2 = 200 Ω P = V I so P T = V T I T, P 1 = V 1 I 1, P 2 = V 2 I 2

Practice Problem 1: Power in a Series Circuit First, write the equation(s) that solve the problem Second, look for what you need to solve o The information you need may or may not be given 18 Copyright © Texas Education Agency, All rights reserved. V S = 15 V R 1 = 100 Ω R 2 = 200 Ω P = V I so P T = V T I T, P 1 = V 1 I 1, P 2 = V 2 I 2

Calculate the current o Current is the same everywhere because this is a series circuit 19 V S = 15 V R 1 = 100 Ω R 2 = 200 Ω Practice Problem 1: Power in a Series Circuit Copyright © Texas Education Agency, All rights reserved.

Calculate the current o Current is the same everywhere because this is a series circuit 20 V S = 15 V R 1 = 100 Ω R 2 = 200 Ω Practice Problem 1: Power in a Series Circuit Copyright © Texas Education Agency, All rights reserved.

Now, calculate total power 21 V S = 15 V R 1 = 100 Ω R 2 = 200 Ω Practice Problem 1: Power in a Series Circuit Copyright © Texas Education Agency, All rights reserved.

You don’t have voltage for the individual resistors You do have current and resistance values for the individual resistors o Use an alternate power formula 22 V S = 15 V R 1 = 100 Ω R 2 = 200 Ω P = I 2 R Practice Problem 1: Power in a Series Circuit Copyright © Texas Education Agency, All rights reserved.

Calculate power used by each resistor 23 V S = 15 V R 1 = 100 Ω R 2 = 200 Ω Practice Problem 1: Power in a Series Circuit Copyright © Texas Education Agency, All rights reserved.

Calculate power used by each resistor Combine the power of these resistors to get the total power 24 V S = 15 V R 1 = 100 Ω R 2 = 200 Ω Practice Problem 1: Power in a Series Circuit Copyright © Texas Education Agency, All rights reserved.

Calculate P T, P 1, and P 2 o This problem can be solved in several ways 25 V S = 18 V R 2 = 300 Ω R 1 = 200 Ω Practice Problem 2: Power in a Parallel Circuit Copyright © Texas Education Agency, All rights reserved.

First, write the equation(s) that solve the problem 26 V S = 18 V R 2 = 300 Ω R 1 = 200 Ω P = V I so P T = V T I T, P 1 = V 1 I 1, P 2 = V 2 I 2 Practice Problem 2: Power in a Parallel Circuit Copyright © Texas Education Agency, All rights reserved.

Method 1 To Calculate Power, Solve for Current First, write the equation(s) that solve the problem Current can be calculated using Ohm’s Law Voltage is the same across each parallel path 27 P = V I so P T = V T I T, P 1 = V 1 I 1, P 2 = V 2 I 2 Copyright © Texas Education Agency, All rights reserved. V S = 18 V R 2 = 300 Ω R 1 = 200 Ω

Method 1 28 V S = 18 V R 2 = 300 Ω R 1 = 200 Ω Copyright © Texas Education Agency, All rights reserved.

Method 1 Current adds in a parallel circuit 29 V S = 18 V R 2 = 300 Ω R 1 = 200 Ω I T = I 1 + I 2 = 90 mA + 60 mA = 150 mA Copyright © Texas Education Agency, All rights reserved.

Method 1 First, calculate individual power 30 V S = 18 V R 2 = 300 Ω R 1 = 200 Ω P 1 = V 1 I 1 = 18 V 90 mA = 1.62 W P 2 = V 2 I 2 = 18 V 60 mA = 1.08 W Copyright © Texas Education Agency, All rights reserved.

Method 1 Now, calculate total power o Total power is the sum of the power for each resistor Conclusion: power adds in a parallel circuit 31 V S = 18 V R 2 = 300 Ω R 1 = 200 Ω P T = V T I T = 18 V 150 mA = 2.7 W Copyright © Texas Education Agency, All rights reserved.

Method 2 You have voltage and resistance for this circuit o Use the alternate power formula 32 V S = 18 V R 2 = 300 Ω R 1 = 200 Ω Copyright © Texas Education Agency, All rights reserved.

Method 2 33 V S = 18 V R 2 = 300 Ω R 1 = 200 Ω Copyright © Texas Education Agency, All rights reserved.

Method 2 34 V S = 18 V R 2 = 300 Ω R 1 = 200 Ω Copyright © Texas Education Agency, All rights reserved. Method 1 and Method 2 have the same result

Application of Watt’s Law 35 Copyright © Texas Education Agency, All rights reserved. How much power will be expended to operate the electric toaster?

36 Power Formula Proportions Direct proportion - a change in one quantity produces the same direction of change in another quantity o Example: In the power formula P=VI, if the current remains constant but the voltage is decreased, power is also decreased Inverse proportion - a change in one quantity produces the opposite direction of change in another quantity o Example: In the power formula P= V 2 /R, if voltage remains constant but resistance is increased, power is decreased Copyright © Texas Education Agency, All rights reserved.

37 Terms and Definitions Mechanical power - the rate at which work is being done Electrical power - the rate of electrical energy used by an electrical circuit Watt - the unit of measurement for power; one volt times one amp Kilowatt - 1,000 watts Kilowatt hours - a unit of electrical energy Fuse - a non-resettable electrical device which protects a circuit from excessive current Circuit breaker - a resettable electrical switch which protects a circuit from excessive current Copyright © Texas Education Agency, All rights reserved.

38 Electrical Power Safety Precautions Circuit safety precautions o Never install a fuse or circuit breaker if current rating is higher or if voltage rating is lower than specified for a particular circuit o Never bypass or defeat a fuse or circuit breaker Worker safety precautions with live circuits o Work with well-insulated tools o Avoid completing a circuit through the body Copyright © Texas Education Agency, All rights reserved.

39 Summary Electrical power overview Formulas used to compute electrical power Wattmeter and sequence for power measurement Power calculations and applying Watt’s Law Wattage rating of resistors Electrical power safety precautions Terms and definitions Copyright © Texas Education Agency, All rights reserved.