```Electrical Power
Electronics
1
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
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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
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Watt’s Law

Electrical power is the product of current
times voltage P = V • I
o
Use change in voltage only when a portion of the
available voltage is used by a circuit or component
P = ΔV • I

The unit of electrical power is the watt (W)

A watt has units of joules per second (J/s)
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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
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Household Energy Use

Utility companies use kilowatt hours (kW•h)
to measure units of energy in houses

How many joules are in one kW•h?
o
3,600,000 joules or 3.6 MJ (mega joules)
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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
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Abbreviations for Power

Power = P

Watt = W

Kilowatt = kW

Kilowatt hours = kW•h
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Summary of Power Formulas

When current and voltage are known, use
P=IV

When current and resistance are known, use
P=I2R

When voltage and resistance are known, use
P=V2 / R
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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
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Using a Wattmeter (cont’d.)
3. Connect the voltage (V)
terminals of wattmeter
4. Turn on circuit power
5. Read and record power value
in watts indicated on
wattmeter
6. Turn off circuit power and
disconnect wattmeter
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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
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Practice Problem 1:
Power in a Series Circuit
R1 = 100 Ω
VS =
15 V

R2 =
200 Ω
Calculate PT, P1, and P2
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Practice Problem 1:
Power in a Series Circuit
R1 = 100 Ω
VS =
15 V

R2 =
200 Ω
Calculate PT, P1, and P2
o
This problem can be solved in several ways
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Practice Problem 1:
Power in a Series Circuit
R1 = 100 Ω
VS =
15 V

R2 =
200 Ω
First, write the equation(s) that solve the problem
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Practice Problem 1:
Power in a Series Circuit
R1 = 100 Ω
VS =
15 V

R2 =
200 Ω
First, write the equation(s) that solve the problem
P = V • I so PT = VT • IT, P1 = V1 • I1, P2 = V2 • I2
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Practice Problem 1:
Power in a Series Circuit
R1 = 100 Ω
VS =
15 V

R2 =
200 Ω
First, write the equation(s) that solve the problem
P = V • I so PT = VT • IT, P1 = V1 • I1, P2 = V2 • I2

Second, look for what you need to solve
o
The information you need may or may not be given
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Practice Problem 1:
Power in a Series Circuit
R1 = 100 Ω
VS =
15 V

R2 =
200 Ω
Calculate the current
o
Current is the same everywhere because this is a
series circuit
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Practice Problem 1:
Power in a Series Circuit
R1 = 100 Ω
VS =
15 V

R2 =
200 Ω
Calculate the current
o
Current is the same everywhere because this is a
series circuit
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Practice Problem 1:
Power in a Series Circuit
R1 = 100 Ω
VS =
15 V

R2 =
200 Ω
Now, calculate total power
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Practice Problem 1:
Power in a Series Circuit
R1 = 100 Ω
VS =
15 V
R2 =
200 Ω

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 P = I2 • R
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Practice Problem 1:
Power in a Series Circuit
R1 = 100 Ω
VS =
15 V

R2 =
200 Ω
Calculate power used by each resistor
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Practice Problem 1:
Power in a Series Circuit
R1 = 100 Ω
VS =
15 V
R2 =
200 Ω

Calculate power used by each resistor

Combine the power of these resistors to get the
total power
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Practice Problem 2:
Power in a Parallel Circuit
VS =
18 V

R1 =
200 Ω
R2 =
300 Ω
Calculate PT, P1, and P2
o
This problem can be solved in several ways
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Practice Problem 2:
Power in a Parallel Circuit
VS =
18 V

R1 =
200 Ω
R2 =
300 Ω
First, write the equation(s) that solve the problem
P = V • I so PT = VT • IT, P1 = V1 • I1, P2 = V2 • I2
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Method 1
To Calculate Power, Solve for Current
VS =
18 V

R1 =
200 Ω
R2 =
300 Ω
First, write the equation(s) that solve the problem
P = V • I so PT = VT • IT, P1 = V1 • I1, P2 = V2 • I2

Current can be calculated using Ohm’s Law

Voltage is the same across each parallel path
I= V R
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Method 1
VS =
18 V
R1 =
200 Ω
R2 =
300 Ω
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Method 1
VS =
18 V

R1 =
200 Ω
R2 =
300 Ω
Current adds in a parallel circuit
IT = I1 + I2 = 90 mA + 60 mA = 150 mA
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Method 1
VS =
18 V

R1 =
200 Ω
R2 =
300 Ω
First, calculate individual power
P1 = V1 • I1 = 18 V • 90 mA = 1.62 W
P2 = V2 • I2 = 18 V • 60 mA = 1.08 W
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Method 1
VS =
18 V

R2 =
300 Ω
Now, calculate total power
o

R1 =
200 Ω
Total power is the sum of the power for each resistor
PT = VT • IT = 18 V • 150 mA = 2.7 W
Conclusion: power adds in a parallel circuit
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Method 2
VS =
18 V

R1 =
200 Ω
R2 =
300 Ω
You have voltage and resistance for this circuit
o
Use the alternate power formula
2
V
P=
R
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Method 2
VS =
18 V
R1 =
200 Ω
R2 =
300 Ω
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Method 2
VS =
18 V

R1 =
200 Ω
R2 =
300 Ω
Method 1 and Method 2 have the same result
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Application of Watt’s Law
How much power will be expended to operate
the electric toaster?
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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= V2/R, if voltage
remains constant but resistance is increased,
power is decreased
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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
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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
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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
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