Transcript Series and Parallel Circuits PowerPoint

Series and Parallel Circuits
When devices are connected in an electric circuits, they can
be connected in “series” or in “parallel” with other devices.
Series Connection
When devices are series, any current that goes through one
device must also go through the other devices. For example:
A
1
2
B
The devices, numbered “1” and “2” in the diagram above, are
connected in series. If an electron (or even conventional
positive current) needs to move from point A to point B, it
must go through both device 1 and device 2. Everything that
goes through one must also go through the other.
Series and Parallel Circuits
When devices are connected in an electric circuits, they can
be connected in “series” or in “parallel” with other devices.
Parallel Connection
When devices are parallel, the current goes through one
device only. For example:
1
A
2
B
The devices, numbered “1” and “2” in the diagram above, are
connected in parallel. If an electron (or even conventional
positive current) needs to move from point A to point B, it
must go through only one device, not both. Some current goes
through one, some through the other.
Resistors in Series
2
1
A
B
If devices 1 and 2 are resistors, think of the series connection
as a longer resistor. Longer resistors have greater resistance.
The total resistance of a combination of resistors in series is
greater than any of the individual resistances.
Resistors in Parallel
1
A
2
B
If devices 1 and 2 are resistors, think of the parallel
connection as a wider resistor. Wider resistors have lower
resistance. The total resistance of a combination of resistors in
paralle is smaller than any of the individual resistances.
Series Circuits
R1
The schematic circuit diagram
to the right shows three resistors
(R) connected in series with a
source of potential difference
(V).
V
Rules for a simple series circuit…. (in sentence form)
R2
R3
1) The total equivalent resistance of resistors in series is equal to the sum of
the individual resistances.
2) The sum of the voltage drops across each of the resistors is equal to the
total voltage of the power supply.
3) The same amount of current flows through all the resistors.
4) The total power converted by the three resistors is equal to the sum of the
individual powers
Series Circuits
R1
The schematic circuit diagram
to the right shows three resistors
(R) connected in series with a
source of potential difference
(V).
V
R2
R3
Rules for a simple series circuit…. (in equation form)
Req = R1 + R2 + R3 +...
V = V1 + V2 + V3 + ...
I = I1 = I2 = I3 = ...
P = P1 + P2 + P3 + ...
Parallel Circuits
The schematic circuit diagram
to the right shows three resistors
(R) connected in parallel with a
source of potential difference
(V).
V
R1
R2
R3
Rules for a simple parallel circuit…. (in sentence form)
1) The reciprocal of the total equivalent resistance of resistors in series is
equal to the sum of the reciprocals of the individual resistances.
2) All of the resistors have the same voltage drop across them.
3) The sum of the currents through all the parallel resistors is equal to the
total current supplied by the voltage source.
4) The total power converted by the three resistors is equal to the sum of the
individual powers.
Parallel Circuits
The schematic circuit diagram
to the right shows three resistors
(R) connected in parallel with a
source of potential difference
(V).
V
R1
Rules for a simple parallel circuit…. (in equation form)
1
1
1
1
=
+
+
+ ....
R eq R1 R 2 R 3
V = V1 = V2 = V3 = ….
I = I1 + I2 + I3 +….
P = P1 + P2 + P3 + ….
R2
R3
Series Circuits: Example Problem
R1 = 2 W
Req = R1 + R2 + R3 +…
V = V1 + V 2 + V 3 + …
V = 24 V
R2 = 4 W
I = I1 = I 2 = I 3 = …
P = P1 + P2 + P3 + ...
Fill in Given
R3 = 6 W
Use Req = R1 + R2 + R3 +… to find the
total equivalent resistance.
Use V = IR to find the total current
I = I1 = I 2 = I 3 = …
V
I
R
P
1
4
2
2
8
2
8
2
4
16
Use V = IR to find the individual voltages
3 12 2
6 24
Use P = VI to find all the powers
T 24
12 48
2
Parallel Circuits: Example Problem
1
1
1
1
=
+
+
+ ....
R eq R1 R 2 R 3
V = V1 = V2 = V3 = ...
V = 50 V
R1 =
20 W
I = I1 + I2 + I3 + ...
R2 =
25 W
R3 =
100 W
P = P1 + P2 + P3 = ...
Fill in Given
V = V1 = V2 = V3 = ...
1
1
1
1
=
+
+
+ ....
Use R eq R1 R 2 R 3
to find
the total equivalent resistance.
Use V = IR to find the individual currents
Use P = VI to find all the powers
V
I
R
P
1
50 2.5 20 125
2
50
2
25 100
3 50 0.5 100 25
T 50 5
10 250
Combination Circuits
R1
The circuit to the right is a complicated
combination circuit. The resistors aren’t
all in series or all in parallel.
V
R3
R6
To analyze a combination circuit, first
look for pairs (or more) of resistors
which are in series or parallel. In this
example R3 and R4 are in series, while R5
and R6 are in parallel. Use the series and
parallel rules to replace the pairs with
“equivalent” resistors.
Now R2 is in parallel with R4, 3.
R2
R4
R5
R1
V
R1,2,2 2,3, 3,4
4, 5, 6
R4, 3
Now R2, 3, 4 is in series with R1
and R5, 6.
R5, 6
Combination Circuits
Example: Find the equivalent
resistance of the six resistors
in the circuit at right.
R1 = 19 W
V = 120 V
1/R5,6 = 1/R5 + 1/R6 = 1/30W + 1/6 W
R5,6 = 5 W
R3,4 = R3 + R4 = 12 W + 12 W
R3,4 = 24 W
1/R2,3,4 = 1/R2 + 1/R3,4 = 1/48W + 1/24W
R2,3,4 = 16 W
R1,2,3,4,5,6 = R1 + R2,3,4 + R5,6
R1,2,3,4,5,6 = 19 W + 16 W + 5 W
R1,2,3,4,5,6 = 40 W
R2 =
R6 = 30 W
R5 = 6 W
48 W
R3 =
12 W
R4 =
12 W
Combination Circuits: Finding Equivalent Resistance
R2
R1
R3
R1
R5
R4
R6
R7
R8
R3
R8
R4
R5
R3
R2,6
R7
R8
R1
R3
R1
R8
R4
R2,5,6
R7
R1
R3
R4
R2,5,6,7
R8
R1,2,3,4,5,6,7
R8
R2,4,5,6,7
R3
R8
R1,2,3,4,5,6,7,8
R1,2,4,5,6,7
Combination Circuits: Hints
When the current reaches point A, it must split to
the right or the left. If R1 has a bigger resistance
than R2, most of the current will go through R2.
If R1 = 2 x R2, then twice as much current will go
through R2 as compared to R1.
A
R1
R2
I1 + I2 = I
2 x I1 = I2
B
I1 = (1/3)I
I2 = (2/3)I
Answer:
Example Problem:
How much of the
30 A of current
R2= 10 W
goes through each
resistor in the
diagram at right?
I = 30 A
A
R1 = 50 W
If R1 = 5 x R2, then five times as much current
will go through R2 as compared to R1.
I1 + I2 = 30 A
5 x I1 = I2
B
I1 = (1/6)(30 A) = 5 A
I2 = (5/6)(30 A) = 25 A
Combination Circuits
Example Problem:
The circuit to the right represents a battery and four
identical light bulbs connected in a combination circuit.
R1
R3
R4
Q: Put them in order from brightest to dimmest:
Brightest:R4 (all current goes through it)
2nd
R1 (gets 2/3 of total current)
3rd & 4th R2 and R3 (get 1/3 of total current)
R2
Combination Circuits
Now the bulb represented by R3 is unscrewed from its
socket.
Q: What happens to the brightness of the other three
bulbs?
R2 goes out (no current through that branch)
R4 gets dimmer (fewer current paths = more total
resistance in circuit = less total current = less
through R4)
R1 gets brighter (current through R4 decreases,
voltage across R4 decreases, voltage across R1
increases = it gets less bright)
R1
R2
R3
R4
Combination Circuits
R1
The circuit to the right consists of
ten identical resistors. Put the
resistors in order from the greatest
amount of current to the least
current.
Answer:
V
R2
R10
R6
R3
R4
R9
R8
R7
R5
Most current: R1 (only resistor which all the current passes through)
2nd: R2 (gets 2/3 of the total current)
3rd: R5 and R6 (get 1/2 of the total current)
4th: R3 and R4 (get 1/3 of the total current)
Last: R7, R8, R9, R10 (get 1/4 of total current)