Lesson 4 Circuits and Resistance

1. Lesson 4Circuits and Resistance

2. Today we will: • learn about current, voltage, and power in circuits. • learn about resistance of materials and how resistance depends on geometry and temperature. • introduce Ohm’s law. Class 9

3. Current, Voltage, and Power in Simple Circuits

4. Current • Benjamin Franklin didn’t know if current was caused by positive charges moving or negative charges moving, so he took a guess… and got it wrong. Current • Current was defined as the direction positive charge in a wire would travel.

5. Current • In reality, negative charges are moving in the opposite direction to the current. Current • However, we usually ignore that and talk about “positive charge carriers” in a wire that move in the direction of the current.

6. Current • Current is the charge that moves past a point in the wire per unit time.

7. Current • Units of current are amperes or amps. • Car batteries deliver several hundred amperes. • Most electronic circuits run on a few mA.

8. Voltage • Voltage is electric potential in circuits. • Voltage is provided by batteries or generators. • A battery pushes electrons out the negative terminal and sucks electrons into the positive terminal.

9. Voltage • If we attach a wire to the positive terminal, a few go into the battery, leaving a positive charge on the surface of the wire. • The electrons stop moving when the surface charge on the wire pulls the electrons in the wire with the same force as the positive charge on the battery. + + + + + + + + + + + + +

10. Circuits • If we connect a wire from the positive to the negative terminal of the battery, current will continue to flow through the circuit. – – – – + + + + – – – + + – – – – + ++ + + +

11. Circuits • Charge remains on the surface of the wire. The surface charge is positive near the positive terninal and negative near the negative terminal. • The charge density is greatest near the terminals of the battery. • Current flows uniformly through the entire cross-section of the wire. – – – – + + + + – – – + + – – – – + ++ + + +

12. Circuits • A 10V battery gives 10eV of energy to each electron that passes through it. • Collisions with atoms in the wire cause each electron to lose 10eV of energy every time it goes around the circuit. – – – – + + + + – – – + + – – – – + ++ + + +

13. + Ground • The ground acts like a huge conductor. • Current can flow into the ground or out of the ground without any limits. • The two circuits below are equivalent. +

14. Circuits • Definitions: • An open circuit is one where there is an open switch or a broken wire so that no current flows. • A closed circuit is one in which there is a continuous path for current to flow from positive to negative. • A short circuit is one where there is an unintentional current path to ground. Currents, sometimes large, flow where they should not, leading to shock and fire hazards.

15. Circuits • What good does flowing charge do? • Produces heat, light. • Produces magnetic fields – used in motors, vibrators, etc. to give mechanical power. • Produces electromagnetic radiation – radio waves for communication. • Electronics: amplification, logic, light detection, radiation detection, cathode-ray tubes, etc.

16. Power • Each time an electron goes through a battery, it gains energy. The total energy gained per second is: P=iV

17. Where does the energy go? • Electrons collide with other electrons in atoms and quickly reach terminal velocity – so they don’t keep gaining kinetic energy.

18. Where does the energy go? P=iV • In a wire, it goes to heat. • In other devices it can go to light, mechanical energy, energy of radiation fields, etc.

19. Resistance

20. Resistance in a Wire • Definition: • In general R is a function of I, and V. • For many materials R is nearly a constant. • When R is a constant, we call the material “ohmic.”

21. Resistors • Devices to increase the resistance in part of a circuit. • Made of graphite chunks, wire wound around a core, etc. • Used to • Produce heat or light • Adjust current flow and voltages in circuits.

22. Resistors • Even if we don’t want the resistance, we often need to account for resistance in cables, electronic devices, etc.

23. Ohm’s Law We assume resistors have constant V. Resistance has units of ohms, written as an upper case omega. Typical resistances range from a few ohms to several megohms.

24. Graphite Resistors • Resistance is color coded. 0 1 2 3 4 5 6 7 8 9 5% 10% 20% 5 6 2 10% second digit # of zeros tolerance first digit R=5600 Ω (+/-10%)

25. What Affects Resistance? • Material • Length • Cross-sectional area • Temperature

26. Resistance and Geometry • One block has V, I, R.

27. Resistance and Geometry • Take two blocks with I going through each. • Voltage is Current is • Resistance is

28. Resistance and Geometry • Take two blocks with I going through each. • Voltage is Current is • Resistance is

29. Resistance and Resistivity • ρ is the resistivity. It depends on the material from which the resistor is made. The units of resistivity are Ωm. • σ = 1/ ρ is the conductivity

30. Resistance and Temperature We assume that resistance varies linearly with temperature.

31. Resistance and Temperature If T = T0, then R =R0.

32. Resistance and Temperature • α is the temperature coefficient of resistivity (resistance). • α is usually positive. • α is negative for graphite.

33. Today we will: • learn how to determine if two resistors are in series or parallel. • find out how resistors combine when connected in series and parallel. • work examples of series-parallel reduction to find current, voltage and power in resistance networks. Class 10

34. Resistors in SeriesHave the Same Current • Take two resistors with I going through each. • Voltage is Current is • Resistance is

35. Resistors in Series

36. Resistors in ParallelHave the Same Voltage • Take two blocks with I going through each. • Voltage is Current is • Resistance is

37. Resistors in ParallelHave the Same Voltage

38. Look at the wire connecting the two resistors. Is there any junction between the resistors? yes no The resistors are connected in series. The resistors are NOT connected in series. A Test for Resistors in Series

39. A Test for Resistors in Parallel Look at the wire connecting one end of the first resistor to one end of the second resistor. Is there a circuit element (a junction is OK and usually there are junctions) along this wire? yes no The resistors are NOT connected in parallel. Look at the wire connecting the other end of the first resistor to the other end of the second resistor. Is there a circuit element along this wire? no yes The resistors are connected n parallel. The resistors are NOT connected n parallel.

40. Series-Parallel QuizAnswer the following six questions to see if you understand what series and parallel mean.

41. Resistors A and B are in • series • parallel • neither

42. Resistors A and B are in • series • parallel • neither

43. Resistors A and B are in • series • parallel • neither

44. Resistors A and B are in • series • parallel • neither

45. Resistors A and B are in • series • parallel • neither

46. Resistors A and B are in • series • parallel • neither

47. Quiz Answers1. series2. neither3. neither4. parallel5. series 6. parallel

48. Series- Parallel Reduction • Find a combination in series or parallel. • Combine resistors into a single equivalent resistor. • Repeat until there is only one resistor. • The voltage across the resistor is the same as the voltage across the battery.

49. Series- Parallel Reduction • Find V, I, R, P for the last step. • Bootstrap your way back to the beginning, diagram by diagram. • What if there are resistors that aren’t in series or parallel? • --- You’ll need to use Kirchoff’s Laws which we’ll learn later.

50. Now we’ll work some examples…