1. Fundamentals of Circuits
Chapter 28
Fundamentals of Circuits
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2. Circuits
potentialfield current
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3. Always true! Kirchoff’s rules
KLR: Kirchoff’s loop rule (conservation of energy)
KJR: Kirchoff’s junction rule (conservation of charge)
Always true!
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4. Ohm’s Law --Recall lab: rheostat (resistor), tungsten, carbon
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5. Question
A typical resistance value is 1Ω. A typical copper wire has a radius of 0.5 mm.
How long must the typical copper wire be so that it has a 1Ω resistance?
copper = 1.7 x 10-8 Ωm
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6. Ideal wire: --no potential difference (“no voltage drop”)
--all potential difference across resistors
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7. Circuit elements: real and schematic
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8. Basic circuit + -
I (+) ≈0
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9. Problem A
--Find the magnitude and direction of the current through the 18 resistor. On your way to the solution:
Draw a schematic of this circuit.
Choose a direction of positive current
Indicate the high and low side of the resistor.
Apply Kirchoff’s law
--Draw a graph of the potential as a function of the clockwise distance around the circuit. Start with V=0 at lower left corner.
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10. + - Problem A (ans) I (+) V r Choose a direction of positive current
Indicate the high and low side of the resistor.
Draw a schematic of this circuit.
Apply Kirchoff’s law
I (+)
6 V
3 V V r
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11. Do Workbook 31.6 Iout ? Iin < > = b) R1 ? R2 ? R3
c) E ?
Right
Left
E = 0
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12. Do Workbook 31.9
DV12 = ? 0V 3V
<3V
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13. Resistors-series Currents are the same In general
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14. Problem B Determine the current through R1 and R2?
Determine the potential difference ∆V1 and ∆V2?
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15. Problem B (ans) + I - R1 & R2 in series R1 & R2 in series
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16. Voltage in a circuit
The light bulb in this circuit has a resistance of 1 W.
What are the values of:
DV12
DV23
DV34
Suppose the bulb is removed from its socket. Then what are values of
Answers: 0V 1V 2V 3V
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17. Resistors-parallel Potential differences are the same In general
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18. Problem C Determine the current through R1 and R2?
Determine the potential difference ∆V1 and ∆V2?
c) What fraction of the current goes through R1? What happens to this fraction if the value of R2 is increased?
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19. Problem C (ans) + I - R1 & R2 in parallel R1 & R2 in parallel
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20. Power and energy
For battery
For resistor
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21. Problem D How much power is dissipated by each resistor?
How much power is provided by each battery?
Series
Parallel
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22. Problem D (ans)
Parallel
Series
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23. Real batteries: ideal emf and internal resistance
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24. Problem E
Compared to an ideal battery, by what percentage does the battery’s internal resistance reduce the potential difference across the 30  resistor?
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25. Problem E (ans)
Compared to an ideal battery, by what percentage does the battery’s internal resistance reduce the potential difference across the 30  resistor?
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26. Conceptual 1
In the circuit below, the battery maintains a constant potential difference between its terminals at points 1 and 2 (i.e., the internal resistance of the battery is considered negligible). The three light bulbs, A, B, and C are identical.
How do the brightnesses of the three bulbs compare to each other?
A = B = C
B = C > A
A > B = C
A > B > C
*RTP Lab 3 Homework
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27. Conceptual 2
A wire is connected from the battery terminal at point 1 to point 4
What happens to the potential difference across bulb B? Explain.
What happens to the potential difference across bulb C? Explain.
What happens to the potential difference between points 1 and 5? Explain your reasoning.
What happens to the brightness of each of the three bulbs? Explain.
What happens to the current through point 3? Explain.
*RTP Lab 3 Homework
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28. Resistors series parallel V V1+V2= Veq V1=V2 I I1=I2 I1+I2= Ieq
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29. General relationships
Series
Parallel V
add
same
Q, I
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30. Problem 31.67
Find the current through and potential difference across each resistor. (Hint: Collapse and expand.)
Phys Chapter 31

31. Problem (ans)
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32. Problem: Multi-loop circuit
Find the current (I) and potential difference (V) across each resistor. (Hint: use KLR and KJR.)
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33. Circuit problem strategy
--draw currents (any direction), split at each junction
--use KJR at junction(s)
--using KLR, go around a loop (any direction)
Battery--V increases going (-  +) of battery
--V decreases going (+  -) of battery
Resistor--V increases upstream (against current)
--V decreases downstream (with current)
--solve equations for unknown currents
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34. Problem F
Find the current (I) and potential difference (V) across each resistor. (Hint: use KLR and KJR.)
--draw currents (any direction), split at each junction
--use KJR at junction(s)
--using KLR, go around a loop (any direction)
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35. Problem F (ans) Apply KLR + - I1 + - I3 + - I2 Apply KJR I1
abcea: + - I3 + - I2
abcdea:
Apply KJR
Junction c:
ecde:
Junction e:
5 equations, 3 unknowns
Choose 3, and solve
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36. Grounding: convention/safety
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37. Do Workbook 31.32
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38. Problem 31.34 Determine the potential at points a through d.
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39. Problem 31.34 (ans) Determine the potential at points a through d. + -
9 V
7 V
0 V
4 V
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40. RC circuits: discharge
Before the switch closes
Apply KLR
After the switch is closed
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41. RC circuits: discharge
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42. RC circuits: charging
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43. Problem G
A 20 F capacitor initially charged to 40 C is discharged through a 5.0 k resistor.
How long does it take to reduce the capacitor’s charge to 10 C?
What is the initial current through the resistor?
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44. Problem G (ans) Close switch at t=0, then Find t when Q(t)=20µC
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