Download Combination Circuits

Combination Circuits
Simplifying Resistors in
Combination Circuits
3Ω
11Ω
4Ω
18 Ω
18 Ω
4Ω
12V
12V
12V
4
4
4
3
3
3
6
2
2
4
12
6
12V
Combo
Circuits
Quiz
12V
4
2
6
Now we can analyze other aspects of a circuit…in order to do this
we must first simplify.
R1 = 1 Ω
R2 = 8 Ω
100 V
0V
R3 = 8 Ω
1= 1 + 1
R2,3 R2
R3
1= 1
R2,3
R1 = 1 Ω
100 V
+
1
8Ω 8Ω
=
2
=
4Ω
8Ω
R2,3 = 4 Ω
0V
Next simplified the circuit down to one resistor.
R1 = 1 Ω
R2,3 = 4 Ω
100 V
0V
Series = RT = R1 + R2,3
RT = 1 Ω + 4 Ω
RT = 5 Ω
RT = 5 Ω
100 V
0V
We went from
R2 = 8 Ω
R1 = 1 Ω
100 V
0V
R3 = 8 Ω
to
R1 = 1 Ω
R2,3 = 4 Ω
100 V
0V
to
RT = 5 Ω
100 V
0V
Next find the total current flowing through the simplified circuit.
RT = 5 Ω
100 V
0V
IT = VT
RT
IT = 100 V
5Ω
IT = 20 A
Now we can go back
and un-simplify the
circuit and find the
current and voltage
through specific
resistors…
Find the current and voltage through R1.
Hint: Always find current first, then voltage.
RT = 5 Ω
100 V
0V
R1 = 1 Ω
100 V
R2,3 = 4 Ω
0V
We already found the current through RT and since
this is a series circuit IT = I1 = I2,3 so I1 = 20 A.
Next find voltage…
R1 = 1 Ω
R2,3 = 4 Ω
100 V
0V
I1 = 20 A
I2,3 = 20 A
In a series circuit VT = V1 + V2,3 so the voltages across
both of these resistors will add up to 100 V.
V1 = I1R1
V2,3 = I2,3R2,3
V1 = (20A)(1 Ω)
V2,3 = (20A)(4 Ω)
V1 = 20 V
V2,3 = 80 V
Let’s check to see if the voltages make sense: VT = V1 + V2,3
100 V = 20 V + 80 V
Now we can find the separate currents and
voltages through R2 and R3.
R1 = 1 Ω
R2,3 = 4 Ω
100 V
0V
I1 = 20 A
R1 = 1 Ω
I2,3 = 20 A
R2 = 8 Ω
I2,3 = 20 A
100 V
I1 = 20 A
R3 = 8 Ω
0V
V2,3 = 80 V
R1 = 1 Ω
R2 = 8 Ω
I2,3 = 20 A
100 V
I1 = 20 A
V1 = 20 V
R3 = 8 Ω
R2 and R3 are in parallel so we know that
V2,3 = V2 = V3 therefore
V2 and V3 are 80 V.
Now we can find I2 and I3.
I2 = V2,3
R2
I3 = V2,3
R3
I2 = 80 V
8Ω
I3 = 80 V
8Ω
I2 = 10 A
I3 = 10 A
0V
Let’s try another one…
R1 = 4 Ω
R2 = 2 Ω
100 V
0V
R3 = 6 Ω
Resistors R1 and R2 are in series so R1,2 = R1 + R2
R1,2 = R1 + R2
R1,2 = 4 Ω + 2 Ω = 6 Ω
100 V
R1,2 = 6 Ω
R3 = 6 Ω
0V
R1,2 = 6 Ω
100 V
0V
R3 = 6 Ω
1=
RT
1=
RT
1 + 1
R1,2 R3
1
+
1
6Ω 6Ω
=
2
=
3Ω
6Ω
RT = 3 Ω
100 V
0V
R1 = 4 Ω
R2 = 2 Ω
100 V
0V
R3 = 6 Ω
R1,2 = 6 Ω
100 V
0V
R3 = 6 Ω
RT = 3 Ω
100 V
0V
What do we do next?
RT = 3 Ω
100 V
0V
IT = VT
RT
IT = 100 V
3Ω
IT = 33.33 A
Next we un-simplify
the circuit and find
the rest…
R1,2 = 6 Ω
100 V
IT = 33.33 A
0V
R3 = 6 Ω
Since R1,2 and R3 are in parallel they
have voltage in common: VT = V1,2 = V3 therefore
V1,2 and V3 are both 100 V. We can now find each
resistors individual current flow, IT = I1,2 + I3.
I1,2 = V1,2
R1,2
I3 = V3
R3
I1,2 = 100 V
6Ω
I3 = 100 V
6Ω
I1,2 = 16.67 A
I3 = 16.67 A
Now let’s separate R1 and R2…
R1,2 = 6 Ω
100 V
0V
R3 = 6 Ω
I1,2 = 16.67 A
R1 = 4 Ω R2 = 2 Ω
100 V
0V
R3 = 6 Ω
I3 = 16.67 A
I1,2 = 16.67 A
R1 = 4 Ω R2 = 2 Ω
100 V
0V
R3 = 6 Ω
I3 = 16.67 A
R1 and R2 are in series with each other so they have
the same amount of current flowing through them: I1,2 = I1 = I2
therefore the current flowing through both of them is 16.67 A
which will help us find the voltage drop across each resistor.
V1 = I1,2R1
V2 = I1,2R2
V1 = (16.67A)(4 Ω)
V2 = (16.67A)(2 Ω)
V1 = 66.68 V
V2 = 33.34 V
Let’s try another…
R1 = 2 Ω
R2 = 4 Ω
21 V
R4 = 3 Ω
0V
R3 = 4 Ω
Remember the steps:
1. Simplify the circuit so that there is only 1 resistor.
2. Find the total current of the simplified resistor.
3. Work backward, un-simplifying the circuit, finding the
current and voltage of each resistor along the way.
4. Be sure to do this using the correct equations that
go with that section of the circuit.
1. Simplify the circuit so that there is only 1 resistor.
R1 = 2 Ω
R2 = 4 Ω
R4 = 3 Ω
21 V
0V
R3 = 4 Ω
R1 = 2 Ω
R2,3 = 2 Ω
R4 = 3 Ω
21 V
0V
RT = 7 Ω
21 V
0V
2. Find the total current of the simplified resistor.
RT = 7 Ω
21 V
0V
IT = VT
RT
IT = 21 V
7Ω
IT = 3 A
3. Work backward, un-simplifying the circuit, finding the
current and voltage of each resistor along the way.
RT = 7 Ω
21 V
0V
R1 = 2 Ω
R2,3 = 2 Ω
R4 = 3 Ω
21 V
0V
I1 = 3 A
I2,3 = 3 A
I4 = 3 A
V1 = I1R1
V2,3 = I2,3R2,3
V4 = I4R4
V1 = (3 A)(2 Ω)
V2,3 = (3 A)(2 Ω)
V4 = (3 A)(3 Ω)
V1 = 6 V
V2,3 = 6 V
V4 = 9 V
R1 = 2 Ω
R2,3 = 2 Ω
R4 = 3 Ω
21 V
0V
I1 = 3 A
V1 = 6 V
R1 = 2 Ω
I2,3 = 3 A
V2,3 = 6 V
V2 = 6 V
R2 = 4 Ω
I4 = 3 A
V4 = 9 V
R4 = 3 Ω
I2,3 = 3 A
21 V
I2 = V2
R2
R3 = 4 Ω
V3 = 6 V
0V
I3 = V3
R3
I2 = 6 V
4Ω
I3 = 6 V
4Ω
I2 = 1.5 A
I3 = 1.5 A
Let’s try another…
R1 = 1 Ω
R2 = 3 Ω R3 = 3 Ω
30 V
R5 = 1 Ω
0V
R4 = 6 Ω
Remember the steps:
1. Simplify the circuit so that there is only 1 resistor.
2. Find the total current of the simplified resistor.
3. Work backward, un-simplifying the circuit, finding the
current and voltage of each resistor along the way.
4. Be sure to do this using the correct equations that
go with that section of the circuit.
R1 = 1 Ω
R2 = 3 Ω R3 = 3 Ω
R5 = 1 Ω
30 V
0V
R1 = 1 Ω
R4 = 6 Ω
R2,3 = 6 Ω
R5 = 1 Ω
30 V
0V
R4 = 6 Ω
R1 = 1 Ω
R2,3,4 = 3 Ω
R5 = 3 Ω
30 V
0V
RT = 5 Ω
30 V
0V
More practice…
a)Which letter shows the graph of voltage vs. current for the smallest resistance?
b) Which letter shows the graph of voltage vs. current for the largest resistance?
a) What is the total resistance of this circuit?
b) What is the total current of this circuit?
c) What is the amount of current running through each resistor?
a) What is the total resistance of this circuit?
b) What is the total current of this circuit?
a) Find the equivalent resistance.
b) Find the current (IT) going through this circuit.
c) Find potential drop across R1 & R2
a) Find combined resistance (RT).
b) Find the current in R1.
c) Find I3.
d) Find R2.
e) Find value of the second resistor.
a) If the voltage drop across the 3 ohm resistor is 4 volts, then
what would the voltage drop be across the 6 ohm resistor?
b) Find the total voltage in this series circuit.
c) Find combined resistance in this circuit.
d) Find the total current in this circuit.
a) Current in this circuit?
b) Potential difference in 20 ohm resistor?
c) Equivalent resistance in the circuit?
Find R2.