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CHPT 6 PRACTICE
ELECTRICAL POWER PRACTICE
MATHEMATICAL MODELS
Suppose you want to know how much of the wind’s energy is converted to electrical energy by
your wind turbine. In order to make that calculation, we need to know how hard the electrons
in the circuit are being pushed (i.e., the voltage) and how much resistance they experience along
the way.
Scientists have discovered several relationships that will help us answer the question.
Relationship #1
An increase in voltage (“electrical pressure”, measured in joules per coulomb, or volts,
V) leads to an increase in electrical current (the rate at which electrons’ energy passes
though the circuit, measured in coulombs per second, or amps, A).
 voltage  current
Mathematically, we say voltage is proportional to current, which we abbreviate
Voltage  Current.
The resistance in circuit allows us to make precise predictions about the relationship
between voltage and current:
𝑉 = 𝑅𝐼
Where 𝑉 = voltage
𝑅 = resistance
𝐼 = current
In other words, resistance is the ratio of voltage to current: 𝑅 = 𝑉/𝐼. The units for
𝐽
𝐶
𝐽𝑠
resistance is 𝐶 / 𝑠 or 𝐶 2 . This unwieldy unit is abbreviated “ohms” and symbolized with
the Greek letter omega, .
Resistors take many forms: some just constrict the flow of energy; others convert
electrical potential into forms of energy we consider more useful: thermal energy (e.g.,
toaster and heaters), radiant energy (e.g., light bulbs), motion (e.g., motors and
compressors), chemical energy (e.g., charging batteries), etc. As you can see from the
list above, resistors play an important role in devices that rely on electricity.
Relationship #2
Voltage tells us how much energy is available per charge.
Current tells us the rate at which electrons’ energy passes through the circuit.
If you multiply voltage and current, the product has units of joules per second, or watts.
𝐽
𝐶
𝐽
Voltage [𝐶] x Current [ 𝑠 ] = Power [𝑠 or W]
𝑉𝐼 = 𝑃
The product of voltage and current is the rate at which electrical energy is converted to
or from a different form of energy, i.e., it is the power.
To organize your work and make your thinking visible, use the GUESS method for each of your
responses: identify what is Given, Unknown, and the Equation. Then Substitute and Solve.
Example:
What voltage will produce a current of 0.10 A if the resistance is 10 ?
G
Given
𝐶
𝐼 = 0.10 𝐴 = 0.10 𝑠
U
E
S
Unknown
Equation
Substitute
S
Solve
𝑅
𝑉
𝑉
𝑉
𝐽𝑠
= 10  = 10 𝐶 2
=?
= 𝐼𝑅
𝐶
𝐽𝑠
= (0.10 𝑠 ) (10 𝐶 2 )
𝐽
𝑉 = 1.0 𝐶 = 1.0 𝑉
1) What is the current traveling through a device that has an electrical pressure (or voltage) of
4.5 V and a resistance of 33 ?
𝐽
G
Given
𝑉 = 4.5 𝑉 = 4.5
𝐶 things you know.
List the
𝐽𝑠
U
E
S
Unknown
Equation
Substitute
S
Solve
𝑅 = 33  = 33 𝐶 2
𝐼 =?
𝑉 = 𝐼𝑅 so 𝐼 =Re-arrange
𝑉/𝑅 the equation to isolate current
𝐽
𝐽𝑠
𝐼 = 4.5 𝐶 / Substitute
33 𝐶 2 known values. Include units.
𝐶
𝐼 = 0.14 𝑠 = 0.14Solve.
𝐴 Include units.
2) What is the resistance of a device if 9 V produces a current of 0.18 A?
𝐶
G
𝐼 = 0.18 𝐴 = 0.18 How else can you write A?
𝑠
𝐽
U
E
S
S
𝑉 = 9 𝑉 = 9 𝐶 How else can you write V?
𝑅 =?
𝑉 = 𝐼𝑅 so 𝑅 Re-arrange
= 𝑉/𝐼 the equation to isolate resistance
𝐽
𝐶
Substitute
𝑅 = (9 𝐶) / (0.18
) known values. Include units.
𝑠
𝐽𝑠
𝑅 = 50 𝐶 2 = 50 Solve. Include units.
3) How quickly is electrical energy produced by a device that has a current of 0.14 A and
an electrical pressure (voltage) of 4.5 V?
𝐶
G
𝐼 = 0.14 𝐴 = 0.14
𝐽
U
E
S
S
𝑠 How else can you write A?
𝑉 = 9 𝑉 = 9 𝐶 How else can you write V?
𝑃 =?
𝑃 = 𝐼𝑉
Re-arrange the equation to isolate resistance
𝐽
𝐶
𝑃 = (9 𝐶)(0.14
) known values. Include units.
Substitute
𝑠
𝐽
𝑃 = 1.26 𝑠 = 1.26 𝑊
Solve. Include units.
Name ___________________________________ Period _____ Date _______________
ELECTRICAL POWER PRACTICE
MATHEMATICAL MODELS
Mathematical modeling is a tremendously powerful tool for understanding and making
predictions about nature. Scientists use the following mathematical model to describe and
understand the relationship.
𝑉 = 𝐼𝑅 and 𝑃 = 𝐼𝑉
Use this mathematical model to make predictions about thermal energy, specific heat, mass, and
temperature change. To organize your work and make your thinking visible, use the GUESS method for
each of your responses: identify what is Given, Unknown, and the Equation. Then Substitute and
Solve.
1) If you look closely at a smart phone charger, you will see that it puts out a voltage of 5 V and a
current of about 0.8 A. Use this information to predict the resistance of the smart phone battery as
it charges.
G
Given
U
Unknown
E
Equation
S
Substitute
S
Solve
2) At what rate does the smart phone charger convert electrical energy into chemical energy? What is
the power?
G
Given
U
Unknown
E
Equation
S
Substitute
S
Solve
3) A computer charger converts electrical energy to chemical energy at a rate of 65 J/s. If the current
is 3.33 A, predict the electrical pressure (voltage).
G
Given
U
Unknown
E
Equation
S
Substitute
S
Solve
4) Suppose your turbine produces 7.2 V across a 33  resistor. What is the current?
G
Given
U
Unknown
E
Equation
S
Substitute
S
Solve
5) Suppose your turbine produces 7.2 V across a 33  resistor. What is the rate at which kinetic
energy in the wind is converted to electrical energy (i.e., what is the power)?
G
Given
U
Unknown
E
Equation
S
Substitute
S
Solve