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W10D2 DC Circuits

W10D2 DC Circuits. Today ’ s Reading Assignment W10D2 DC Circuits & Kirchhoff ’ s Loop Rules Course Notes: Sections 7.1-7.5. 1. PS 8 due Week 11 Tuesday at 9 pm in boxes outside 32-082 or 26-152 Next Reading Assignment W10D3 PS07: PhET: Building a Circuit 7.1-7.5, 7.10

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W10D2 DC Circuits

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  1. W10D2DC Circuits Today’s Reading Assignment W10D2 DC Circuits & Kirchhoff’s Loop Rules Course Notes: Sections 7.1-7.5 1

  2. PS 8 due Week 11 Tuesday at 9 pm in boxes outside 32-082 or 26-152 Next Reading Assignment W10D3 PS07: PhET: Building a Circuit 7.1-7.5, 7.10 Exam 3 Thursday April 18 7:30 pm –9:30 pm Announcements

  3. Outline DC Circuits Kirchoff’s Laws Electrical Power Measuring Voltage and Current

  4. DC Circuits

  5. Examples of Circuits

  6. Symbols for Circuit Elements

  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

  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

  9. Concept Question • The electric field inside the battery points to • The left • The Right

  10. Concept Question Answer • The electric field inside the battery points to • The left • Goes from positive to negative charge

  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

  12. Concept Question • The electric field inside the resistor points to • The left • The Right

  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!

  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

  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)

  16. Series vs. Parallel Series Parallel

  17. Resistors In Series The same current I must flow through both resistors

  18. Current Conservation Sum of currents entering any junction in a circuit must equal sum of currents leaving that junction.

  19. Resistors In Parallel Voltage drop across the resistors must be the same

  20. Concept Q: Resistors In Parallel • Suppose that . Then the equivalent resistance • 2. • 3. • 4.

  21. Concept Q: Resistors In Parallel Answer 1. When Then the equivalent resistance is the smaller resistance. This is an important circuit design principle.

  22. 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. Group Problem: Four Resistors

  23. Measuring Voltage & Current

  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

  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

  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.

  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 .

  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)

  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

  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.

  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

  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.

  33. Electrical Power Power is change in energy per unit time So power to move current through circuit elements:

  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

  35. Power – Resistor (Joule Heating) Moving across a resistor in the direction of current decreases your potential. Resistors alwaysdissipate power

  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

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

  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

  39. Concept Question Answer: Power 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. Answer: 5. Is 1/4 as bright

  40. Kirchhoff’s Loop Rules

  41. Recall: Current Conservation Sum of currents entering any junction in a circuit must equal sum of currents leaving that junction.

  42. Sum of Potential Differences Around a Closed Path Sum of potential differences across all elements around any closed circuit loop must be zero.

  43. Sum of Potential Differences Around a Closed Path Sum of potential differences across all elements around any closed circuit loop must be zero.

  44. Demonstration:Five Different Types of Resistance F13 http://tsgphysics.mit.edu/front/?page=demo.php&letnum=F 13&show=0

  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

  46. Worked Example: Circuit What is current through each branch of the circuit shown in the figure below?

  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

  48. Demonstration:Wheatstone Bridge F14 http://tsgphysics.mit.edu/front/?page=demo.php&letnum=F 14&show=0

  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 Rvaris adjusted to 12 ohms, there is zero current through the ammeter. What is the unknown resistance Ru?

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