Physics 122C Electricity and Magnetism

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Physics 122C Electricity and Magnetism
Lecture 14 DC Circuits and Power April 27, 2007

• Martin Savage

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Lecture 14 Announcements

• Lecture HW Assignment 5 has been posted on the
  Tycho system and is due Wednesday at 10 PM.
• Remember that Midterm 2 is next friday

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Circuit Elements Diagrams
These are some of the symbols we will use to
represent objects in circuit diagrams.
Variable elements are indicated by adding an
arrow. Other symbols inductance,
transformer, diode, transistor, ammeter, etc.
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A Circuit Diagram
Actual Circuit
Circuit Diagram
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Kirchhoffs Laws
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Basic Circuit
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Plumbers Analogy
The plumbers analogy of this circuit is a
pump (battery) pumping water in a closed loop of
pipe that includes a constriction (resistor).
The pressure (V1) is the upper part of the loop
is higher than in the lower part (V2). There is
a pressure drop (V1-V2) across the constriction
and a pressure rise across the pump. The water
flow I is the same at all points around the loop.
Pump Battery Constriction Resistor Pressure
PotentialWater Flow Current
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ExampleA Single-Resistor Circuit
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ExampleA More Complex Circuit (1)

• Analyze the circuit shown, to
• Find the current in and potential difference
  across each resistor.
• Graph the potentials around the circuit

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ExampleA More Complex Circuit (2)
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Question
What is the DV across the indicated circuit
element in the direction of the current, I?

1. -4 V (b) -2 V (c) 0 V (d) 2 V (e) 4 V

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Applying KirchhoffsLoop Law to Many Loops
i1 i3

1. Define a minimum set of current loops. Label all
   elements.
2. Write a loop equation for each loop. (Battery or
   0 SDV).
3. Solve equations for currents
4. Calculate other variables of interest.

R1
i3
R2
i1
Vbat
R4
R3
R5
Loop equations
i2
i1 i2
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Solving for the loop currents

• -8 -6 I1 V
• -8 32 -24 I2 0
• -6 -24 54 I3 0

• -8 -6 I1 V
• -1 4 -3 I2 0
• -1 -4 9 I3 0

Gaussian Elimination
0 0 36 I1 V -1 0 3 I2
0 0 2 -3 I3 0
I1 2 A , I2 1 A , I3 2/3 A
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Applying Kirchhoffs JunctionLaw to Many
Junctions

1. Define a minimum set of junction potentials. You
   can select one ground point. Label all elements.
2. Write a junction equation for each unknown
   junction .
3. Solve these equations for the unknown junction
   potentials.
4. Calculate the other variables of interest.

J1
R1
R5
Vbat
V1
R3
R2
R4
Junction equations
J2
V2
V0
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Energy and Power (1)
Example A 90 W load resistance is connected
across a 120 V battery. How much power is
delivered by the battery?
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Energy and Power (2)
The energy delivered by the battery is dissipated
by the resistor.
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Example The Power of Light
How much current is drawn by a 100 W light
bulb connected to a constant 120 V outlet?
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Example The Power of Sound
Most loudspeakers are designed to have a
resistance of 8 W. If such a loudspeaker is
connected to a stereo amplifier with a rating of
100 W, what is the maximum possible current in
the loudspeaker?
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Example A Dim Bulb
How much power is used by a 60 W light bulb
rated at 120 V if it is operated using a dimmer
switch at 100 V? (Assume the resistance is
constant.)
(Actually, the resistance at this lower operating
potential will be less than the R-value
calculated above because the temperature will be
lower, so the actual power used will be somewhat
higher.)
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End of Lecture 14

• Before the next lecture, read Knight, sections
  31.5 through 31.8.
• Lecture HW Assignment 5 has been posted on the
  Tycho system and is due next Wednesday at 10 PM.
  
• Remember that next Friday we will have Exam 2.