1. Week 04, Day 2
W10D2 DC Circuits
Today’s Reading Assignment W10D2 DC Circuits & Kirchhoff’s Loop Rules Course Notes: Sections 1
Class 09 1

2. Announcements
PS 8 due Week 11 Tuesday at 9 pm in boxes outside or
Next Reading Assignment W10D3 PS07: PhET: Building a Circuit , 7.10
Exam 3 Thursday April :30 pm –9:30 pm
Class 12

3. Outline DC Circuits Kirchoff’s Laws Electrical Power
Measuring Voltage and Current
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4. DC Circuits
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5. Examples of Circuits
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6. Symbols for Circuit Elements
Battery
Resistor
Capacitor
Switch
Equipotential
Junction
Branch
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7. Electromotive Force (EMF)
The work per unit charge around a closed path done is called electromotive force EMF. This is a bad name because it is not a force. Let denote the force per unit charge, then the EMF is
If a conducting closed path is present then
Class 22

8. Ideal Battery
Inside Battery: chemical force , non-zero inside battery (zero outside), moves charges through a region in which static electric field opposes motion
2) Ideal battery: net force on charges is zero
3) Potential difference between its terminals
4) Extend path through external circuit where
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9. Concept Question The electric field inside the battery points to
The left
The Right
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10. Concept Question Answer
The electric field inside the battery points to
The left
Goes from positive to negative charge
Class 12

11. Sign Conventions - Battery
Moving from the negative to positive terminal of a battery increases your potential
Moving from the positive to negative terminal of a battery decreases your potential
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12. Concept Question The electric field inside the resistor points to
The left
The Right
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13. Concept Question Answer
The electric field inside the resistor points to
The right
Electric field pushes charge in the same direction, so current in direction of E
This is cause and effect!
Class 12

14. Sign Conventions - Resistor
Moving across a resistor in the direction of current decreases your potential
Direction of current
Is the same as direction of electric field which points to lower electric potential
Moving across a resistor in the direction of current decreases your potential
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15. Internal Resistance
Real batteries have an internal resistance, r, which is small but non-zero
Terminal voltage:
(Even if you short the leads you don’t get infinite current)
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16. Series vs. Parallel
Series
Parallel
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17. Resistors In Series
The same current I must flow through both resistors
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18. Current Conservation
Sum of currents entering any junction in a circuit must equal sum of currents leaving that junction.
Class 14

19. Resistors In Parallel
Voltage drop across the resistors must be the same
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20. Concept Q: Resistors In Parallel
Suppose that Then the equivalent resistance 2. 3. 4.
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21. Concept Q: Resistors In Parallel
Answer 1. When
Then the equivalent resistance is the smaller resistance. This is an important circuit design principle.
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22. Group Problem: Four Resistors
Four resistors are connected to a battery
as shown in the figure. The current in the battery is I,
the battery emf is ε, and the resistor values are R1 = R, R2 = 2R, R3 = 4R, R4 = 3R.
Determine the current in
each resistor in terms of I.
Class 14

23. Measuring Voltage & Current
Class 14

24. Measuring Potential Difference
A voltmeter must be hooked in parallel across the element you want to measure the potential difference across
Voltmeters have a very large resistance, so that they don’t affect the circuit too much
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25. Measuring Current
An ammeter must be hooked in series with the element you want to measure the current through
Ammeters have a very low resistance, so that they don’t affect the circuit too much
Class 14

26. Concept Question: Measuring Current
If R1 > R2, compare the currents measured by the three ammeters:
I1 > I2 > I3
I2 > I1 > I3
I3 > I1 > I2
I3 > I2 > I1
I3 > I1 = I2
None of the above
Not enough information is given.
Class 14

27. Concept Question Answer: Measuring Current
Answer: 4. I3 > I2 > I1
The total current must add to the two individual currents, so I3 must be largest. Most current prefers to go through the smaller resistor so I2 > I1 .
Class 14

28. Measuring Resistance
An ohmmeter must be hooked in parallel across the element you want to measure the resistance of
Here we are measuring R1
Ohmmeters apply a voltage and measure the current that flows. They typically won’t work if the resistor is powered (connected to a battery)
Class 14

29. Concept Question: Bulbs & Batteries
An ideal battery is hooked to a light bulb with wires. A second identical light bulb is connected in parallel to the first light bulb. After the second light bulb is connected, the current from the battery compared to when only one bulb was connected.
Is Higher
Is Lower
Is The Same
Don’t know
Class 12

30. Concept Question Answer: Bulbs & Batteries
Answer: 1. More current flows from the battery
There are several ways to see this:
(A) The equivalent resistance of the two light bulbs in parallel is half that of one of the bulbs, and since the resistance is lower the current is higher, for a given voltage.
(B) The battery must keep two resistances at the same potential  I doubles.
Class 12

31. Concept Question: Bulbs & Batteries
An ideal battery is hooked to a light bulb with wires. A second identical light bulb is connected in series with the first light bulb. After the second light bulb is connected, the current from the battery compared to when only one bulb was connected.
Is Higher
Is Lower
Is The Same
Class 12

32. Concept Question Answer: Bulbs & Batteries
Answer: 2. Less current flows from the battery
The equivalent resistance of the two light bulbs in series is twice that of one of the bulbs, and since the resistance is higher the current is lower, for the given voltage.
Class 12

33. Electrical Power Power is change in energy per unit time
So power to move current through circuit elements:
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34. Power - Battery
Moving from the negative to positive terminal of a battery increases your potential. If current flows in that direction the battery supplies power I
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35. Power – Resistor (Joule Heating)
Moving across a resistor in the direction of current decreases your potential. Resistors always dissipate power
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36. Concept Question: Power
An ideal battery is hooked to a light bulb with wires. A second identical light bulb is connected in parallel to the first light bulb. After the second light bulb is connected, the power output from the battery (compared to when only one bulb was connected)
Is four times higher
Is twice as high
Is the same
Is half as much
Is ¼ as much
Class 14

37. Concept Question Answer: Power
Answer: 2. Is twice as high
The current from the battery must double (it must raise two light bulbs to the same voltage difference) and
Class 14

38. Concept Question: Power
An ideal battery is hooked to a light bulb with wires. A second identical light bulb is connected in series with the first light bulb. After the second light bulb is connected, the light (power) from the first bulb (compared to when only one bulb was connected)
Is four times higher
Is twice as high
Is the same
Is half as much
Is ¼ as much
Class 14

39. Concept Question Answer: Power
Answer: 5. Is 1/4 as bright
R doubles  current is cut in half. So power delivered by the battery is half what it was. But that power is further divided between two bulbs now.
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40. Kirchhoff’s Loop Rules
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41. Recall: Current Conservation
Sum of currents entering any junction in a circuit must equal sum of currents leaving that junction.
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42. Sum of Potential Differences Around a Closed Path
Sum of potential differences across all elements around any closed circuit loop must be zero.
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43. Sum of Potential Differences Around a Closed Path
Sum of potential differences across all elements around any closed circuit loop must be zero.
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44. Demonstration: Five Different Types of Resistance F13
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45. Steps of Solving Circuit Problem
1. Straighten out circuit (make squares)
2. Simplify resistors in series/parallel
3. Assign current loops (arbitrary)
4. Write loop equations (1 per loop)
5. Solve
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46. Worked Example: Circuit
What is current through each branch of the circuit shown in the figure below?
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47. Worked Example: Simple Circuit
Current conservation at a:
Lower Loop: Start at a and circulate clockwise. Then
Upper Loop: Start at a and circulate counterclockwise. Then
Solve for I2:
and
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48. Demonstration: Wheatstone Bridge F14
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49. Group Problem: Wheatstone Bridge
A circuit consisting of two resistors with R1=6.0 ohms and R2=1.5 ohms, a variable resistor, with resistance Rvar, a resistor of unknown value Ru, and 9.0 volt battery, are connected as shown in the figure. When Rvar is adjusted to 12 ohms, there is zero current through the ammeter. What is the unknown resistance Ru?
Class 14