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Chapter 23
Series and Parallel Circuits
• Series and parallel circuits
• Calculate equivalent resistance
• Calculate current and voltage drops in
series and parallel circuits
• Combination circuits
Explain
• Think about and explain how a
flashlight is set up.
• Explain how the brightness of a
flashlight bulb would change if you
could add more batteries.
Series circuits
• When all the devices are
connected using series
connections, the circuit is referred
to as a series circuit.
• In a series circuit, each device is
connected in a manner such that
there is only one pathway
•
Resistors in Series
In series circuits, the same current
flows through all of the components
• The voltage across the components is
the sum of the voltages across each
component.
• In a series circuit, every device must
function for the circuit to be complete.
Resistors in Series
Resistors connected end to end are said to be in
series.
Resistors in Series
The total resistance of resistors in series is equal to the sum
of their individual resistances:
Example
• Voltage drops in series circuit
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Example
• Mathematical analysis of series circuit
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Example
• Compare circuit X and Y below. Each is powered by a 12-volt battery.
The voltage drop across the 12-ohm resistor in circuit Y is ____ the
voltage drop across the single resistor in X.
• a. smaller than
• b. larger than
• c. the same as
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• A 12-V battery, a 12-ohm resistor and a light bulb are connected as
shown in circuit X below. A 6-ohm resistor is added to the 12-ohm
resistor and bulb to create circuit Y as shown. The bulb will appear
____.
• a. dimmer in circuit X
• b. dimmer in circuit Y
• c. the same brightness in both circuits
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• Page 619, # 1-5 odds
• Page 622, # 7, 10
• Page 623, # 12, 14
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Parallel circuits
When all the devices are connected using parallel connections,
the circuit is referred to as a parallel circuit.
In a parallel circuit,
- each device is placed in its own separate branch.
- there are multiple pathways for charge flow.
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Parallel circuits
Facts
1. In parallel, all components have the same potential difference
(voltage) across their ends.
Vbattery  V1  V2  V3  ...
2. The total current is the sum of the currents through the individual
components. The current outside the branches is the same as
the sum of the current in the individual branches.
Itotal = I1 + I2 + I3 + ...
This is called Kirchhoff's current law (KCL).
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Resistors in Series and Parallel
Resistors can again be
replaced by a single
equivalent resistance:
Resistors in Series and Parallel
Using the facts 1 and 2, we find:
Note that this equation gives you the inverse of the resistance, not the
resistance itself!
Check Your Understanding
• As more and more resistors are added in parallel to a
circuit, the equivalent resistance of the circuit
____________ (increases, decreases) and the total
current of the circuit ____________ (increases,
decreases).
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Check Your Understanding
• Three identical light bulbs are connected to a D-cell as shown
below. P, Q, X, Y and Z represent locations along the circuit.
Which one of the following statements is true?
a. The current at Y is greater than the current at Q.
b. The current at Y is greater than the current at P.
c. The current at Y is greater than the current at Z.
d. The current at P is greater than the current at Q.
e. The current at Q is greater than the current at P.
f. The current is the same at all locations.
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Check Your Understanding
• Mathematical Analysis of Parallel Circuits
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Check Your Understanding
• A 12-V battery , a 12-ohm resistor and a 4-ohm resistor are connected
as shown. The current in the 12-ohm resistor is ____ that in the 4-ohm
resistor.
• a. 1/3
b. 1/2
• c. 2/3
d. the same as
• e. 1.5 times
f. twice
• g. three times
h. four times
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Practice problems
• Page 626, # 15-19, and 24
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Combination circuit
A third type of circuit involves the dual use of
series and parallel connections in a circuit;
such circuits are referred to as compound
circuits or combination circuits.
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Combination circuit
• The basic strategy for the analysis of combination
circuits involves using the meaning of equivalent
resistance for parallel branches to transform the
combination circuit into a series circuit.
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Example
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Example
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Practice problems
• How many different ways can you connect 3
resistors?
Answer – 4 ways
• How about 4 resistors?
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Practice problems
• Page 630, # 25-27,
• Page 637, #67, 77, 81,
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