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Lecture 11. Combinations of Resistors, Kirchhoffs Rules
Outline:
Resistor Circuits. Voltage and Current Sources. Voltmeters and
Ammeters. Kirchhoffs Rules.
Lecture 10: Batteries: the potential energy of charge carriers
is increased by non-electrostatic (non-conservative) forces.
Non-ideal batteries: internal resistance. Potential distribution
around a complete circuit. Energy and power in electric
circuits.
1
=
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More Complex Circuits
8
1 = 13 + 13 + 13 1 = 1 2 = 1 21 + 2 + 13 = 1 2 5 = 1 + 1 = 2 4 2
5 = 1 21 + 2 = 23 3 4 2 5 = 23 + 13 = 1
= 1 3 4 2 5 = 1 11 + 1 = 0.5
3 3 3 1 1
1 2 1/3
1/3 3 3 3
1 1
1 2 1/3
1/3
R1
R2
R3
R4
R5
= 100.5 = 20 = = 200
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Voltage Source
10
The goal: to provide output voltage that is independent of the
load resistance.
An ideal voltage source:
A. has zero internal resistance (zero means that > all
possible values of load ).
= +
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Current Source
12
The goal: to provide output current that is independent of the
load resistance.
An ideal current source:
A. has zero internal resistance (zero means that > all
possible values of load ).
= +
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Voltmeters and Ammeters
13
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Voltmeters
15
The goal: to measure the voltage difference across an element
(ideally, without affecting the circuit due
to the voltmeter connection).
An ideal voltmeter:
Voltmeter: high internal resistance
V
V
A. has = and should be connected in parallel with the circuit
element being measured.
B. has = and should be connected in series with the circuit
element being measured.
C. has = and should be connected in parallel with the circuit
element being measured.
D. has = and should be connected in series with the circuit
element being measured.
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Battery Tester
16
typical Rload
Can we use a voltmeter (very
high r) to test the freshness of a
battery?
The voltmeter will measure provided . But can be as high as 106
107 , and even if ~103 104 , we wont notice the battery
aging.
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Ammeters
18
The goal: to measure the current in a circuit element (ideally,
without affecting the current due to the
ammeter connection).
An ideal ammeter:
Ammeter: low internal resistance
I
I
A. has = and should be connected in parallel with the circuit
element being measured.
B. has = and should be connected in series with the circuit
element being measured.
C. has = and should be connected in parallel with the circuit
element being measured.
D. has = and should be connected in series with the circuit
element being measured.
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Kirchhoffs Junction Rule
19
Junction Rule (for currents): charge conservation
= 0 Currents flowing in + Currents flowing out -
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Kirchhoffs Loop Rule
20
Loop Rule (energy conservation):
= 0
+
= 0 for any closed loop
if we neglect the difference between s and s, and accept the
sign conventions.
:
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Example
21
We dont need to know the actual direction of the current: if we
get the negative value of I, that would mean that the current flows
in the direction opposite to the direction of travel.
+
= 0 4 + 12 7 + 2 + 3 + 4 = 0
= 816 = 0.5
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Example (contd)
22
a reference voltage =0
V
4 7
2 3
4V 12V
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More Examples
25
Problem 26.77: (a) what is the potential difference Vab when the
switch is open? (b) What is the current through the switch when the
switch is closed? (c) What is the equivalent resistance when the
switch is closed?
6
3 6
3 3
= 36 6 4 = 12 (a) = 369 = 4 = 36 3 4 = 24
= 12 24 = 12
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More Examples (contd)
26
Problem 26.77: (b) What is the current through the switch when
the switch is closed?
loop 1: 36 6 1 3 1 3 = 0 loop 2: 6 1 3 3 + 3 2 = 0 loop 3: 3 1 3
+ 6 2 + 3 + 3 3 = 0 1 2
3 + 3 = 2 21
3 1 + 12 3 + 6 2 = 0 (from Eq.2) (from Eq.3) 3 1 + 12 2 24 1 + 6
2 = 0 2 = 32 1 36 6 1 3 1 + 3 2 21 = 36 10.5 1 = 0
1 = 3610.5 3 = 32 1 21 = 0.51 3 = 1810.5 = 1.71 - means that our
initial direction of I3 has to be reversed.
6
3 6
3 3
(b) Choose (arbitrary) directions of currents and travel along
the loops.
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More Examples (contd)
27
Problem 26.77: (a) what is the potential difference Vab when the
switch is open? (b) What is the current through the switch when the
switch is closed? (c) What is the equivalent resistance when the
switch is closed?
1 2
3 + 2 = 32 1 = 1 + 2
1 = 3610.5
6
3 6
3 3
(c) =
8.6 = 368.6 = 4.2
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Conclusion
28
Next time: Lecture 12: RC circuits 26.4
Resistors in Series and Parallel Voltmeters and Ammeters
Kirchhoffs Rules
Lecture 11. Combinations of Resistors, Kirchhoffs RulesIclicker
QuestionIclicker QuestionIclicker QuestionIclicker QuestionIclicker
QuestionIclicker QuestionMore Complex CircuitsVoltage SourceVoltage
SourceCurrent SourceCurrent SourceVoltmeters and
AmmetersVoltmetersVoltmetersBattery
TesterAmmetersAmmetersKirchhoffs Junction RuleKirchhoffs Loop
RuleExampleExample (contd)Iclicker QuestionIclicker QuestionMore
ExamplesMore Examples (contd)More Examples
(contd)ConclusionExample: Built-in Battery TesterMore Complicated
Resistor CircuitsSlide Number 31
