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Combination Electrical Circuits
This workforce solution was funded by a grant awarded by the U.S. Department of Labor's Employment and Training Administration. The solution was created by the grantee and does not necessarily reflect the official position of the U.S. Department of Labor. The Department of Labor makes no guarantees, warranties, or assurances of any kind, express or implied, with respect to such information, including any information on linked sites, and including, but not limited to accuracy of the information or its completeness, timeliness, usefulness, adequacy, continued availability or ownership.
This work is licensed under a Creative Commons CC BY 3.0 Unported License. http://creativecommons.org/licenses/by/3.0/
100V
40Ω
30Ω15Ω
When analyzing combination circuits we must first determine the
Total Values in the circuit. We already know the total EMF, or ET,
which is 100V
1ET = 100V R1
R2 R3
Next
100V
40Ω
30Ω15Ω
2
Here are the parallel resistors in this combination circuit
Rules for adding resistors in parallel circuits: 1/RT = 1/R1+ 1/R2+…+ 1/RN
Where N is the number of resistors in parallel
ET = 100V
Next
100V
40Ω
30Ω15Ω
3
Here are the parallel resistors in this combination circuit
Also, if the resistors are in parallel and are the same value, there is a shortcut rule:
R/N, where R is the common resistor value and N is the number of resistors with that value
ET = 100V
Next
100V
40Ω
30Ω15Ω
4
Here are the parallel resistors in this combination circuit
There is another shortcut rule that can be used if there are only two resistors in parallel:
R1 X R2 where R1 and R2 are the two resistors
R1 + R2 u
ET = 100V
Next
100V
40Ω
30Ω15Ω
5
Here are the parallel resistors in this combination circuit
This last formula is the formula we are going to use for this circuit because we have only two resistors in parallel, and they are not the same.
ET = 100V
Next
100V
40Ω
30Ω15Ω
Because there are only two resistors in parallel, I can use the formula:
R1 x R2
R1 + R2
15 x 30
15 + 30=
450
45= 10
Click Here First
Click Here Next
6ET = 100V
Next
100V
40Ω
30Ω15Ω 10Ω
This gives an equivalent resistance of 10Ω
In order to continue, we redraw the diagram to show the “equivalent
resistor”
7ET = 100V
Next
100V
40Ω8
10Ω
These two resistors, the original 40Ω resistor and our calculated equivalent resistor of 10 Ω, are in series, so we are just going to add them together using
our series formula RT = R1 + R2 + R3 … RN
ET = 100V
Next
100V
6
40Ω + 10Ω = 50Ω
ET = 100V
40Ω
And, as before we redraw the circuit to reflect the “equivalent resistance”
of 50Ω
10Ω50Ω
Next
100V
6
40Ω + 10Ω = 50Ω
ET = 100V
40Ω
And, as before we redraw the circuit to reflect the “equivalent resistance”
of 50Ω
10Ω50Ω
Next
100V
6ET = 100V
Since there is no more multiple resistors to combine, we have now reached the Total Resistance of the
circuit
50Ω
RT = 50Ω
Next
100V
6ET = 100V
Now we need to solve for IT, or Total Current. We use Ohms Law to figure
this out. E = IR
50Ω
RT = 50Ω
Next
100V
6ET = 100V
We will use an excellent tool to remember the formula!
50Ω
RT = 50Ω
Just cover over the letter that represents the value you are solving for … in this case I for
Current.
Therefore our formula is E divided by R
E
I R
Ohms Triangle
Next
100V
6ET = 100V
50Ω
RT = 50Ω
ET = 100V and RT = 50Ω E
I R
Ohms Triangle
Therefore, ET/RT = 100V/50Ω = 2A
IT = 2A
IT = 2A
Next
100V
6ET = 100V
50Ω
RT = 50Ω
BUT WAIT! WE ARE NOT DONE! E
I R
Ohms Triangle
We have to go backward now and solve voltage and amperage for
each of the original resistors
IT = 2A
Next
100V
6ET = 100V
RT = 50Ω
Lets put the values next to the equivalent resistor above
E
I R
Ohms Triangle
Great! Now lets start to work backward and expand to the
original circuit.
IT = 2A50Ω2A
100V
Next
100V
6ET = 100V
40Ω
We have now expanded backward to the previous circuit, and the two
resistors are now split back out into two resistors in series.
10Ω
E
I R
Ohms Triangle
ET = 100V
RT = 50Ω
IT = 2A
R1
Next
100V
6ET = 100V
40Ω
If you remember your lessons, when I have resistors in series, voltage
changes across each resistor, but amperage remains the same.
10Ω
E
I R
Ohms Triangle
ET = 100V
RT = 50Ω
IT = 2A
R1
And we know what the amperage is from the last slide … 2A.
Next
100V
6ET = 100V
40Ω
So, lets put the amperage at each resistor.
10Ω
E
I R
Ohms Triangle
ET = 100V
RT = 50Ω
IT = 2A
R1
Now, using Ohms Triangle, we determine the formula to find E.
2A
2A
We see that to find E we must multiply I times R. Next
100V
6ET = 100V
40Ω
For the resistor at the top, R1, I = 2A, R1 = 40Ω
10Ω
E
I R
Ohms Triangle
ET = 100V
RT = 50Ω
IT = 2A
R1
2A X 40Ω = 80V
2A
2A
For the resistor on the right:
2A X 10Ω = 20V
Note that when I add the voltages together they equal the total voltage.
Next
100V
6ET = 100V
40Ω
Now we put the voltages on each of the resistors
10Ω
E
I R
Ohms Triangle
ET = 100V
RT = 50Ω
IT = 2A
R1
2A
2A80V
20V
Next
2A
2A
100V
6ET = 100V
40Ω
All right. The next step is to expand the resistor on the right to its original
position, which were two parallel resistors
10Ω
E
I R
Ohms Triangle
ET = 100V
RT = 50Ω
IT = 2A
R1
80V
20V
We also need to remove the 10Ω equivalent value and replace it with the two values we had started with
30Ω15Ω
Next
2A
2A
100V
6ET = 100V
40Ω
In a parallel circuit the voltage stays the same and the amperage changes, so we are going to use voltage now to
determine the amperage at each resistor
E
I R
Ohms Triangle
ET = 100V
RT = 50Ω
IT = 2A
R1
80V
20V
We place the voltage that we calculated in the previous calculation (20V) and place it with
each of the parallel resistors and remove the amperage rating.
30Ω15Ω20V 20V
Next
2A
100V
6ET = 100V
40Ω
Again we use Ohms Triangle to determine the formula to find
amperage (I).
E
I R
Ohms Triangle
ET = 100V
RT = 50Ω
IT = 2A
R1
80V
As seen, the formula is E divided by R. For the rightmost resistor this is 20V / 30Ω or .67A and for the leftmost resistor it would be 20V / 15Ω or
1.33A. Note the two add up to 2A
30Ω15Ω20V 20V
Next
2A
100V
6ET = 100V
40Ω
Now place the two amperage values next to their corresponding resistors. E
I R
Ohms Triangle
ET = 100V
RT = 50Ω
IT = 2A
R1
80V
Finally, a list can be made to show the different values on the left side to make identification
easier.
30Ω15Ω20V 20V
.67A1.33AR2 R3E1 = 80V
E2 = 20V
E3 = 20V
I1 = 2A
I2 = 1.33A
I3 = .67A
Next