Combination Electrical Circuits

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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

Congratulations!