Transcript Ch. 20

18 Overview
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resistor & capacitor circuits
Kirchoff’s Rules
voltmeters & ammeters
household circuits & safety
• Homework:
• 17, 27, 31, 33, 55, 67, 71, 85
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Connection Types
______
______l
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junctions & loops
• Current value ______________ at
__________________.
• Ex. Point b is a junction
• A closed path is called a ___________
• Ex. bcdeb
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Equivalent Resistance
• The ______________ of a network of resistors
is called the _____________________.
• The equivalent circuit is the circuit made by
replacing the network with an equivalent
resistance valued resistor.
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Resistors in Series
Req  R1  R2  
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Resistors in Parallel

1
1
1
2

Req  R  R  
1
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What happens to the equivalent resistance
of a series network as more resistors are
added to it?
1.
2.
3.
4.
increases
decreases
stays same
cannot be determined
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What happens to the equivalent resistance
of a parallel network as more resistors are
added to it?
1.
2.
3.
4.
increases
decreases
stays same
cannot be determined
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Ex. Find a) equivalent resistance of the circuit. B) the current in and
voltage across each resistor , c) the power dissipated by each resistor.
Req  R1  R2  4  6  10
I eq  V Req  12V / 10  1.2 A
I 4  I 6  I eq  1.2 A
V4  I 4 R  (1.2 A)(4)  4.8V
V6  I 6 R  (1.2 A)(6)  7.2V
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P4  ( I 4 ) R  (1.2 A) (4)  5.76W
P6  ( I 6 ) R  (1.2 A) (6)  8.64W
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Ex. Find a) equivalent resistance of the circuit, b) the current in and
voltage across each resistor , c) the power dissipated by each resistor.

1
1
  4
1 1
2
Req  R  R
1
6

1 1
 2.4
I eq  V Req  12V / 2.4  5.0 A
V4  V6  12V
I 4  V4 R  12V / 4  3.0 A
I 6  V6 R  12V / 6  2.0 A
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2
P4  ( I 4 ) R  (3.0 A) (4)  36W
2
2
P6  ( I 6 ) R  (2.0 A) (6)  24W
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Calculate the equivalent resistance:
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Kirchoff’s 1st Rule
• 1) current into junction = current out
• Ex. I = I1+I2 __________________
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Kirchoff’s 2nd Rule
• 2) voltage change around any loop is ____
• Ex. -I2(6)+I1(4) = 0
• _________________________
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Measuring Devices
• become __________of the circuit being
measured
• each device has ________________
• (ideally) the meter’s resistance should
____________ the resistance of the circuit
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Voltmeters
• used in ____________ with a circuit
element (circled V in diagram)
• (ideally) the voltmeter should have
____________ internal resistance
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Ammeters
• used in __________ (circled A in diagram)
• (ideally) the ammeter should have ______
internal resistance
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RC Circuits
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any circuit with a resistor and a capacitor
Time constant = RC
s = ·F
Ex. 50ohm, 2F
RC = 100s
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Charging a Capacitor
VC  V (1  e
 t / RC
)
V
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Ex. R=100, C=0.5, V = 6.0
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How long for capacitor to get to 4.0 volts?
RC = (100)(0.5) = 50 seconds
 t / 50
Equation: VC  6.0(1  e
)
solve for t: 4.0  6.0(1  e t / 50 )
0.67  1  e
e
t / 50
 t / 50
 0.33
t / 50  1.1
t  50(1.1)  55s
ln( e t / 50 )  ln( 0.33)
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Discharging a Capacitor
VC  Vo e
 t / RC
Vo t / RC
I e
R
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Ex. R=80, C=1.0, Vo = 5.0
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How long for capacitor to get to 3.5 volts?
RC = (80)(1) = 80 seconds
Equation: VC  Vo e  t / RC  5.0e  t / 80
 t / 80
solve for t: 3.5  5.0e
 t / 80
3.5  5.0e
t / 80
e
 3.5 / 5.0  0.7
t / 80  0.36
t  80(0.36)  28.8s
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Household Circuits
• US: _________ @ _____________
• Europe, etc.: 220 @ ______ hertz
• ground wires allow excess current to go
into the ground (safety feature).
• circuit breakers & fuses stop the current
flow if it passes a certain value (safety).
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Summary
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series & parallel circuit analysis
junctions, loops & Kirchoff’s Rules
RC circuits
voltmeters & ammeters
household circuits & safety
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