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1/81
Circuit Examples
Identify and describe series and parallel circuits.
Simplify those circuits.
Calculate the current and/or voltage of each part of a circuit.
By observing and participating in this lesson, you will be able to:
2/81
Series and Parallel Circuits
Electrical components can be connected in various ways. This drastically changes the properties of the circuit.
3/81
Series Circuits
One simple way to arrange components in an electrical circuit is to create one large continuous loop with the components:
2 batteries
switch
Light bulb
resistor
This is similar to a TV series where one episode follows another.
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Parallel Circuits
Another way to connect a circuit is in parallel. In this arrangement, each component is connected separately in its own “loop”.
2 batteries
3 resistors in parallel
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Resistors in Parallel
To find the equivalent resistance of resistors added in parallel:
...R
1
R
1
R
1
R
1
321P
Parallel or total combined
resistance, ΩIndividual
resistors, Ω
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Parallel Resistor Example
Calculate the total effective resistance of two 10 Ohm resistors connected in parallel.
21P R
1
R
1
R
1
10Ω
1
10Ω
1
R
1
P
10Ω
2
R
1
P
5ΩRP
Take the reciprocal of each side of
equation
Combine, use common
denominator if needed
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Parallel Resistor Observations
5 Ohms. Notice that the total overall resistance is lower than either one of them individually!
This occurs because there are multiple paths for the electrons to take, lowering their resistance.
8/81
Circuit Problems
This section will detail how to calculate the various electrical quantities in a circuit.
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Series Circuit
Calculate the current and electric potential difference for each component of the circuit shown.
R2=
10Ω
R1=5Ω
5V
A good first step is to simplify the circuit.
10/81
Circuit Simplification
R2=
10Ω
R1=5Ω
5V
Because this is a series circuit, to combine the resistors and simplify the circuit, they are merely added together.
5V
Rs=
15Ω
...RRRR 321S
15Ω10Ω5ΩRS
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Current in a Series Circuit
5V
Rs=
15Ω
Use the voltage of the power supply and the total resistance of the circuit to find the total current flowing through the circuit.
Because the electron flow has no where else to go, this amount is also the current flowing through both resistors. I1 and I2 is that same .33 Amperes.
IRV
R
VI
.33A15Ω
5VI
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Voltage in a Series Circuit
R2=
10Ω
R1=5Ω
5V
Since we know the current flowing through each resistor, we can use Ohm’s law to find the potential difference for each of those resistors.
IRV1
) (.33A)(5ΩV1
1.67VV1 Notice how the sum of the two voltages adds up to the power supply for the circuit.
IRV2
) (.33A)(10ΩV23.33VV2
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Parallel Circuit
Calculate the current and electric potential difference for each component of the circuit shown.
5V
R1=5Ω R2=10Ω
Notice how this parallel circuit contains the exact same components as the series circuit, they are just arranged differently.
Again, a good first step is to simplify the circuit.
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Circuit Simplification
21P R
1
R
1
R
1
5V
R1=5Ω R2=10Ω
10Ω
1
5Ω
1
R
1
P
10Ω
1
10Ω
2
R
1
P
10Ω
3
R
1
P
3.3ΩΩ3
10RP
Notice this parallel resistance is less than either one individually.
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Shortcut Formula
An equivalent formula can be used for two resistors, R1 and R2, connected in parallel. Sometimes this formula is easier to manipulate.
21
21P RR
RRR
It may be easier to remember this formula as the product over the sum for the two resistors.
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Voltage in a Parallel Circuit
5V
R1=5Ω R2=10Ω
The easy part about any parallel circuit is the voltage applied to each item.
Since each item has its own independent connection to the battery or power supply, each item receives that potential.
In this case, V1 and V2 are each 5V.
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Current in a Parallel Circuit
5V
R1=5Ω R2=10Ω
Once you realize that the electric potential for each resistor is 5V, finding the current is easy using Ohm’s law, V=IR.
1
11 R
VI
2
22 R
VI
1A5Ω
5VI1 .5A
10Ω
5VI2
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Current Observations
5V
R1=5Ω R2=10Ω
Notice the two currents add up to the same value as the total current in the circuit. This is a good way to check your work.
1.5A3.3Ω
5V
R
VI
TT
1.5A.5A1AIII 21T
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Conclusion
You should now be able to describe series and parallel circuits with words and numbers!
Questions???
Homework:
Check with your instructor