Chapter 22
Current and Resistance
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Topics:
•  Current
•  Conservation of current
•  Batteries
•  Resistance and resistivity
•  Simple circuits
Sample question:
How can the measurement of an electric current passed through a
person s body allow a determination of the percentage body fat?
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Slide 22-1
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 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
QuickCheck
The battery current I is A.  3 A
B.  2 A
C.  1 A
D.  2/3 A
E.  1/2 A Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
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. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
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. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
• The current through the 3 !
resistor is QuickCheck 23.7
• 9 A
• 6 A
• 5 A
• 3 A
• 1 A
© 2015
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• The current through the 3 !
resistor is QuickCheck 23.7
• 9 A
• 6 A
• 5 A
• 3 A
• 1 A
© 2015
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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 Circuits
• There are two possible ways that you 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 •  3 A
•  2 A
•  1 A
•  2/3 A
•  1/2 A Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
QuickCheck 23.13
The battery current I is • 3 A
• 2 A
• 1 A
• 2/3 A
• 1/2 A Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
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. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
Capacitor Combinations
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Slide 19-24
QuickCheck
• Which of the following combinations of
capacitors has the highest capacitance? Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
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. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
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 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
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 ΔV ,
the current has decreased to C
•  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. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
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. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
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? Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
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 ΔV
C
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= ℇ.
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
B
the value of the resistor is reduced?
Smaller time constant.
Same ultimate amount
of charge.
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