1. This Class Resistors in series: Current through is same.
Voltage drop across is IRi
Resistors in series:
Voltage drop across is same.
Current through is V/Ri
Resistors in parallel:
Solve Circuits V R1 R2 R4 R3

2. Kirchhoff’s First Rule (“Loop Rule” or “Kirchhoff’s Voltage Law”)
The algebraic sum of the changes in potential encountered in a complete traversal of any loop of circuit must be zero. e1 R1 R2 I e
Move around circuit:
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3. Rules e1 e - + e - + e R1 R2 I Voltage Gains enter with a + sign.
Voltage Drops enter with a - sign. - + e a b - + e b a I a b I b a
Note: e always points from negative to positve
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4. Loop Example a d b e c f R1 I R2 R3 R4 e1 e
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5. Internal Resistance of an emf Device
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6. Resistors in Series
*When a potential difference, V, is applied across resistances in series, the resistances have identical current.
* Resistances in series can be replaced with an equivalent resistance, REQ, that has the same current I and the same total potential difference V as the actual resistances. I e1 R2 R3 R1
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7. Another (intuitive) way
Consider two cylindrical resistors with lengths L1 and L2 V R1 R2 L2 L1
Put them together, end to end to make a longer one...
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8. Kirchhoff’s Second Rule (Junction Rule or “Kirchhoff’s Current Law”)
The sum of the current entering any junction must be equal to the sum of the currents leaving that junction.
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9. How to use Kirchhoff’s Law: e R3 R2 R1 a b c d
Analyze the circuit & identify all circuit nodes:
Identify all independent loops & use Kirchhoff’s Voltage Law:
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10. Resistors in Parallel e R1 R3 R2 R3 R2 R1
*In parallel, the resistances all have the same potential differences.
* Resistances in parallel can be replaced with an equivalent resistance, REQ, that has the same potential difference, V, and the same total current, I, as the actual resistances.
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11. Another (intuitive) way
Consider two cylindrical resistors with cross-sectional areas A1 and A2 V R1 R2 A1 A2
Put them together, side by side … to make one “fatter”one,
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12. Example 1 Consider the ideal circuit shown:
What is the relation between Va -Vd and Va -Vc ?
12V I1 I2 a b d c
50
20
80
(a) (Va -Vd) > (Va -Vc)
(b) (Va -Vd) = (Va -Vc)
(c) (Va -Vd) < (Va -Vc)
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13. Example 2 Consider the ideal circuit shown:
12V I1 I2 a b d c
50
20
80
What is the relationship between I1 and I2?
(a) I1 > I2
(b) I1 = I2
(c) I1 < I2
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14. Summary of Resistor & Capacitor Combinations
Resistors Capacitors
Series
Parallel
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15. Summary of Simple Circuits
Resistors in series:
Current through is same; Voltage drop across is IRi
Resistors in parallel:
Voltage drop across is same; Current thru is V /Ri
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16. Problem Solving Tips
When you are given a circuit, you must first carefully analyze circuit topology.
find the nodes and distinct branches and pick Linearly Independent subsets of each.
assign branch currents
Use Kirchhoff’s First Rule for all independent loops in the circuit.
Use Kirchhoff’s Second Rule for all independent nodes in circuit.
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17. QUIZ 11: September 24, 2013
Three resistors are connected to a battery with emf V as shown. The resistances of the resistors are all the same, i.e. R1 = R2 = R3. Compare the current through R2 to the current through R3.
I2 < I3
I2 = I3
I2 > I3
Current is the same

18. QUIZ lecture 11
Three resistors are connected to a battery with emf V as shown. The resistances of the resistors are all the same, i.e. R1 = R2 = R3. Compare the current through R2 to the current through R1.
I2 < I1
I2 = I1
I2 > I1
Current is the same

19. Example 25-16
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20. Cramer’s Rule If
then
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21. = New Circuit How Can We Solve This One? THE ANSWER: Kirchhoff’s Rules

22. QUIZ lecture 11
In the following circuit, consider the loop abc. The direction of the current through each resistor is indicated by black arrows. If we are to write Kirchoff's voltage equation for this loop in the clockwise direction starting from point a, what is the correct order of voltage gains/drops that we will encounter for resistors R1, R2 and R3?
drop, drop, drop
gain, gain, gain
drop, gain, gain
gain, drop, drop
drop, drop, gain

23. QUIZ lecture 11
You are to connect resistors R1 and R2 (with R1>R2) to a battery, first individually, then in series and then in parallel. Rank those arrangements according to the amount of current through the battery, greatest first.
Series, R1, R2, Parallel
R2, Series, Parallel, R1
R1, Series, R2, Parallel
Parallel, R2, R1, Series
R1, Parallel, R2, Series
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24. DEMO 5B-06
For the same EMF source, the bulbs will burn equally bright when connected in
Parallel
Series
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25. DEMO 5B-06
If the middle bulb is replaced with a 90 Watt bulb (15 Ohms), and connected to two 34 Watt (45 Ohms) in parallel, which bulb or bulbs will burn brightest?
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26. Ammeter & Voltmeter I I Ammeter, A, inserted into the circuit.
Voltmeter, V, across the circuit element. I
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27. Galvanometer Ig Rg =
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28. Make a 1.0 Ampere full scale deflection ammeter
small parallel resistor (shunt)
If Rg = 100  and Ig = 50 A, then
To change the scale, change RP .
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29. Voltmeter
Assume Rg = 100  and Ig = 50 A for full scale deflection (typical). Make a 100 V full scale deflection voltmeter.
100  negligible
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30. Ohmmeter
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