# Class 8. Resistivity and Resistance Circuits. Physics 106. Winter Press CTRL-L to view as a slide show. Class 8. Physics 106.

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1 and Circuits and Winter 2018 Press CTRL-L to view as a slide show.

2 Last time we learned about Capacitance Problems Parallel-Plate Capacitors Capacitors in Circuits Current Ohm s Law and

3 Today we will learn about Resitivity How resistivity (and resistance) changes with temperature parallel circuits with resistors Kirchoff s Laws and

4 Virtual Lbb and Try this lab, it will help you get a better feeling how resistor circuits work. Go to the "Resources" tab and click on "Click here for instructions" under "Virtual Labs" Then click on "Resistor Network"

5 and

6 and Length and is proportional to the energy lost in a conductor. The longer a wire, the greater the resistance of the wire.

7 and Drift Speed Earlier we found: I = nev d A Hence: v d = I/(neA) If the cross sectional area is big, the electrons go more slowly. If the electrons go more slowly, they lose less energy in collisions. If the electrons lose less energy, the resistance is smaller. and

8 In summary: R = ρ L A and ρ is the resistivity of the material

9 and and

10 Variation of For most metals, resistance increases with increasing temperature With a higher temperature, the metal s atoms vibrate with increasing amplitude The electrons lose more energy in collisions to the faster-moving atoms and

11 Variation of and Approximately linear: R = A + BT where A and B are constants.

12 Variation of We usually rewrite the constants in a more convenient form: R = R 0 [1 + α(t T 0 )] R is the resistance at temperature T R 0 is the resistance at the reference temperature T 0 (often T 0 = 20 C) α is the temperature coefficient of resistivity and

13 Variation of and Since R = ρl/a : ρ = ρ 0 [1 + α(t T 0 )]

14 and

15 Electrical A battery converts chemical potential energy to electrical energy Pushing charges on the wire increases potential energy, much like compressing a spring. As charge moves through a resistor, it loses this potential energy during collisions with atoms in the resistor and

16 A Simple Circuit and A battery is connected to a resistor in series.

17 A Simple Circuit The ground sets the voltage on the lower wire to zero. No current flows to or from ground, or a large charge would build up in the circuit. and

18 A Simple Circuit and The voltage everywhere on the lower wire is zero. The upper wire is at the battery s voltage.

19 Energy Transfer in the Circuit and Imagine a quantity of positive charge, Q, moving around the circuit from point A back to point A

20 Energy Transfer in the Circuit Point A is V = 0. The battery raises the voltage of the charge to V battery. This adds energy V Q to the charge. and

21 Energy Transfer in the Circuit Points B and C are at V = V battery. Collisions of charges with atoms in the resistor reduce the energy of the charges. The voltage at D is V = 0. and

22 Energy Transfer in the Circuit and As charge Q flows through the resistor, the resistor s thermal energy increases by V Q.

23 Electrical The rate at which the energy is lost is the power P = V Q t = IV From Ohm s Law, alternate forms of power are P = V 2 R = I2 R and

24 Electrical and The SI unit of power is Watt (W) Energy = P t The unit of energy used by electric companies is the kilowatt-hour 1 kwh = J = 3.60 MJ

25 and

26 in a Circuit Ammeter and An ammeter is used to measure current An ammeter is connected in series, so the current passing through the bulb also passes through the meter.

27 in a Circuit Voltmeter and A voltmeter is used to measure voltage A voltmeter is connected in parallel, to measure the potential difference between the two points to which it is connected.

28 and

29 and Recall that R = ρ L A

30 and Recall that R = ρ L A If we double the length of a resistor, the resistance doubles.

31 and Recall that R = ρ L A If we double the length of a resistor, the resistance doubles. If we double the cross-sectional area of a resistor, the resistance halves.

32 Identical Resistors in Series When we combine two identical resistors in series, it is like making one resistor twice as long. and

33 Identical Resistors in Series R eq = 2R and

34 Identical Resistors in Parallel When we combine two identical resistors in parallel, it is like making one resistor with twice the area. and

35 Identical Resistors in Parallel R eq = 1 2 R and

36 and

37 Heating a Graphite Resistor Graphite has a negative temperature coefficient of resistivity, alpha R = R 0 [1 + α(t T 0 )] As the temperature rises, the resistance drops. and

38 Heating a Graphite Resistor A pure graphite resistor has a length of 1.00 cm and a diameter of 3.50 mm. What is the resistance of this resistor at 20 C and at 100 C? (ρ = Ωm and α = / C) and

39 Heating a Graphite Resistor A pure graphite resistor has a length of 1.00 cm and a diameter of 3.50 mm. What is the resistance of this resistor at 20 C and at 100 C? (ρ = Ωm and α = / C) At 20 C: R = ρ L A = ( Ωm) 0.01m π ( m) 2 = 36.4mΩ At 100 C: R = R 0 [1 + α(t T 0 ) = 36.4mΩ[ / C 80 C] = 34.9mΩ and

40 Heating a Graphite Resistor When connected to a 12 V power supply, what is the power dissipated by the resistor at 20 C? P = IV But we don t know I. Since I = V /R P = V 2 R = (12 V) Ω = 3.96kW and

41 and

42 Sources of emf and The voltage source in a circuit is called the emf (electromotive force) Batteries and generators are typical emfs

43 Simple Resistive Circuits and We ll first study simple circuits that contain only emfs and resistors

44 Resistors in Series and The current is the same in all resistors in series because any charge that flows through one resistor flows through the others. The sum of the voltages across the resistors is equal to the total voltage across the combination.

45 Resistors in Series and Or more simply... Current is equal Voltage adds

46 Equivalent Series V eq = V 1 + V 2 Since V = IR for each resistor and

47 Equivalent Series V eq = V 1 + V 2 Since V = IR for each resistor and IR eq = IR 1 + IR 2

48 Equivalent Series and R eq = R 1 + R 2 + R 3 + The equivalent resistance of a series combination of resistors is the sum of the individual resistances It is always greater than any of the individual resistors

49 Equivalent Series: An Example and You need to replace these four resistors with one equivalent resistor. What value must it have?

50 Resistors in Parallel and The voltage is the same across all resistors in parallel. The sum of the currents through the resistors is equal to the total current through the combination.

51 Resistors in Parallel and Or more simply... Voltages are equal Currents adds

52 Equivalent Parallel I eq = I 1 + I 2 and

53 Equivalent Parallel I eq = I 1 + I 2 Since I = V /R for each resistor V 1 R eq = V 1 R 1 +V 1 R 2 and

54 and

55 emf and and A real battery has some internal resistance A 12 V battery has an emf of 12 V when no current flows

56 emf and and When current flows, the terminal voltage of the battery is less than 12 V.

57 The internal resistance is like a resistor rconnected in series with a "perfect" emf The terminal voltage is V = V b V a V =ɛ Ir and

58 and emf The emf ɛ is equal to the terminal voltage when the current is zero R is called the load resistance The current depends on both the load resistance and the internal resistance The internal resistance is usually small enough we can ignore it and

59 and Kirchoff s Rules

60 Gustav Kirchhoff and Invented spectroscopy with Robert Bunsen Formulated rules about radiation

61 Why Do We Need? and Sometimes series-parallel reduction does not work can be always be used to solve circuit lead to several equations in several unknowns, so they can be hard to solve.

62 Junction Rule The sum of the currents entering any junction must equal the sum of the currents leaving that junction and

63 Junction Rule The sum of the currents entering any junction must equal the sum of the currents leaving that junction Loop Rule The sum of the potential differences across all the elements around any closed circuit loop must be zero and

64 The Junction Rule and I in = I out This comes from conservation of charge This is similar to water flow in pipes

65 The Loop Rule and The total change in voltage from point c back to point c in the circuit is zero.

66 The Loop Rule and Let s start with the voltage at c.

67 The Loop Rule As charge passes through the battery, the voltage increases. and

68 The Loop Rule The voltage drops when charge passes through the first resistor. and

69 The Loop Rule And it drops again when it passes through the second resistor. and

70 The Loop Rule So the voltage returns to where we started when we return to point c. and

71 and

72 and Answer the following six questions to see if you understand what series and parallel mean.

73 1. Resistors A and B are in and A.series B.parallel C.neither

74 2. Resistors A and B are in and A.series B.parallel C.neither

75 3. Resistors A and B are in and A.series B.parallel C.neither

76 4. Resistors A and B are in and A.series B.parallel C.neither

77 5. Resistors A and B are in and A.series B.parallel C.neither

78 6. Resistors A and B are in and A.series B.parallel C.neither

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