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Chapter 23
Circuits
Topics:
• Circuits containing
•
•
•
multiple elements
Series and parallel
combinations
Complex Multi-loop
Circuits
RC circuits
Sample question:
An electric eel can develop a potential difference of over 600 V. How
do the cells of the electric eel’s body generate such a large potential
difference?
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Slide 23-1
Series and Parallel
Series
• Circuit elements in a chain between 2 points
• Same current flows through circuit elements
I1 = I2
• Electric Potentials add => Delta Vtotal = Delta V1 + Delta V2
Parallel
• Circuit elements on multiple paths connecting the same
points
• Since paths connect the same points,
Delta V’s are the same
• Currents Add => Itotal = I1 + I2
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Slide 22-25
QuickCheck
The battery current I is
A. 3 A
B. 2 A
C. 1 A
D. 2/3 A
E. 1/2 A
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QuickCheck
The battery current I is
A. 3 A
B. 2 A
C. 1 A
D. 2/3 A
E. 1/2 A
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QuickCheck
The diagram below shows a circuit with two
batteries and three resistors. What is the potential
difference across the 200 Ω resistor?
A. 2.0 V
B. 3.0 V
C. 4.5 V
D. 7.5 V
E. There is not enough
information to decide.
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QuickCheck
The diagram below shows a circuit with two
batteries and three resistors. What is the potential
difference across the 200 Ω resistor?
A. 2.0 V
B. 3.0 V
C. 4.5 V
D. 7.5 V
E. There is not enough
information to decide.
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QuickCheck 23.7
The current through the 3 ohm resistor is
A. 9 A
B. 6 A
C. 5 A
D. 3 A
E. 1 A
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Why is one bulb Brighter, 40 W vs. 100 W
Why is one bulb brighter?
Which has the greatest resistance?
In parallel, which carries the greatest current?
Voltage Divider
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Slide 22-35
Kirchhoff’s Laws
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Slide 23-11
Series and Parallel
• There are two
possible ways that you
Circuits
can connect the circuit.
• Series and parallel circuits have very
different properties.
• We say two bulbs are connected in
series if they are connected directly to
each other with no junction in between.
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Calculating Equivalent Resistance
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Slide 22-35
Example Problem
A resistor connected to a power supply works as a
heater. Which of the following two circuits will provide
more power?
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Equivalent Resistance Examples
1. By using only two resistors singly, in series, or in parallel you are
able to obtain resistances of 18.0, 24.0, 72, and 96 . What are
the two resistances? (Make sure your answer is consistent.)
2. Find the equivalent resistance of the following circuit: Be sure to
show each step.
3. Find the heat energy generated by the 3 Ohm and the 12 Ohm
resistors in the circuit in problem 2
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Slide 22-35
Circuit Analysis with Equivalent Resistance
For the following circuit, calculate the equivalent resistance for
this system of resistors:
Now find the Equivalent resistance for this system for the
following case: R1 = R2 = R3= R4 = R5 = 10 Ohms
Find Delta V, I, and Power dissipated by R1
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Slide 22-35
QuickCheck 23.13
The battery current I is
•
3A
•
2A
•
1A
•
2/3 A
•
1/2 A
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QuickCheck 23.13
The battery current I is
• 3A
• 2A
• 1A
• 2/3 A
• 1/2 A
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QuickCheck 23.5
•
Which is the correct circuit
diagram for the circuit shown?
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QuickCheck 23.5
•
Which is the correct circuit
diagram for the circuit shown?
A
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Circuit Analysis using Kirchoff’s rules (Loop +
Junction)
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Slide 23-11
Circuit Analysis using Kirchoff’s rules (Loop +
Junction)
Circuit from End of Circuit Activity 1
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Slide 22-35
Circuit Analysis using Kirchoff’s rules (Loop +
Junction)
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Slide 22-35
Capacitors in Parallel and Series
•
Parallel or series capacitors can be
represented by a single equivalent
capacitance.
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Capacitor Combinations
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Slide 19-24
QuickCheck
• Which of the following combinations of
capacitors has the highest capacitance?
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Equivalent Capacitance
 = RC
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Slide 23-29
RC Circuits
•
•
•
RC circuits are circuits containing resistors
and capacitors.
In RC circuits, the current varies with time.
The values of the resistance and the
capacitance in an RC circuit determine the
time it takes the capacitor to charge or
discharge.
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RC Circuit Demonstrations
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RC Circuits
The figure shows an RC circuit consisting of a charged
capacitor, an open switch, and a resistor before the
switch closes. The switch will close at t = 0.
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RC Circuits
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RC Circuits
• The initial potential difference is (ΔV ) = Q /C.
• The initial current—the initial rate at which the
C 0
capacitor begins to discharge—is
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0
RC Circuits
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RC Circuits
•
•
•
After some time, both the charge on the
capacitor (and thus the potential difference)
and the current in the circuit have decreased.
When the capacitor voltage has decreased to
ΔVC, the current has decreased to
The current and the voltage decrease until the
capacitor is fully discharged and the current is
zero.
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RC Circuits
• The current and the
capacitor voltage
decay to zero after
the switch closes,
but not linearly.
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RC Circuits
The decays of the voltage and the current
are exponential decays:
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RC Circuits
• The current and voltage in a circuit do
not drop to zero after one time constant.
Each increase in time by one time
constant causes the voltage and current
to decrease by a factor of e−1 = 0.37.
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RC Circuits
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RC Circuits
• The time constant has the form τ = RC.
• A large resistance opposes the flow of charge, so
increasing R increases the decay time.
• A larger capacitance stores more charge, so
increasing C also increases the decay time.
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QuickCheck
• The following circuits contain capacitors
that are charged to 5.0 V. All of the
switches are closed at the same time.
After 1 second has passed, which
capacitor is charged to the highest
voltage?
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Charging a Capacitor
•
•
•
In a circuit that charges a
capacitor, once the switch is
closed, the potential difference
of the battery causes a current
in the circuit, and the capacitor
begins to charge.
As the capacitor charges, it develops a
potential difference that opposes the current,
so the current decreases, and so does the rate
of charging.
The capacitor charges until ΔVC = ℇ.
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Charging a Capacitor
• The equations that describe the capacitor
voltage and the current as a function of
time are
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QuickCheck 23.26
• The red curve shows how the capacitor
charges after the switch is closed at t =
0. Which curve shows the capacitor
charging if the value of the resistor is B
reduced?
Smaller time constant.
Same ultimate amount
of charge.
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Example Problem
1. In the circuit shown below, rank in order, from most to least
bright, the brightness of bulbs A–E. Explain.
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Slide 23-42
Example Problem
2. In the circuit shown below:
A. Rank in order, from most to least bright, the brightness of
bulbs A–D. Explain.
B. Describe what, if anything, happens to the brightness of
bulbs A, B, and D if bulb C is removed from its socket.
Explain.
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Slide 23-41
Example Problem
1. In the circuit shown below, use Kirchhoff's rules to write
equations to find the currents.
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Slide 23-42
Capacitor Combinations
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Slide 19-24
Equivalent Capacitance
 = RC
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Slide 23-29
Equivalent Capacitance
 = RC
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Slide 23-29
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Slide 23-29
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Slide 23-29
RC Circuits
 = RC
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Slide 23-29
RC Circuits
 = RC
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Slide 23-29
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Slide 23-29
 = RC
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Slide 23-29
Clicker Question 2
The following circuits contain capacitors that are charged to 5.0 V.
All of the switches are closed at the same time. After 1 second has
passed, which capacitor is charged to the highest voltage?
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Slide 23-30
Answer
The following circuits contain capacitors that are charged to 5.0 V.
All of the switches are closed at the same time. After 1 second has
passed, which capacitor is charged to the highest voltage?
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Slide 23-31
Additional Clicker Questions
2. In the circuit shown below, the switch is initially closed and the
bulb glows brightly. When the switch is opened, what happens
to the brightness of the bulb?
A. The brightness of the bulb is not affected.
B. The bulb gets dimmer.
C. The bulb gets brighter.
D. The bulb initially brightens, then dims.
E. The bulb initially dims, then brightens.
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Slide 23-39
Answer
2. In the circuit shown below, the switch is initially closed and the
bulb glows brightly. When the switch is opened, what happens
to the brightness of the bulb?
B. The bulb gets dimmer.
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Slide 23-40