# Chapter 17 Electric Current and Resistance Pearson Education, Inc.c

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1 Chapter 17 Electric Current and Resistance 2010 Pearson Education, Inc.c 1

2 Units of Chapter 17 Batteries and Direct Current Current and Drift Velocity Resistance and Ohm s Law Electric Power 2010 Pearson Education, Inc.c 2

3 17.1 Batteries and Direct Current Electric current is the flow of electric charge. A battery is a source of electric energy it converts chemical energy into electric energy Pearson Education, Inc.c 3

4 17.1 Batteries and Direct Current In a complete circuit, electrons flow from the negative electrode to the positive one. The positive electrode is called the anode; the negative electrode is the cathode. A battery provides a constant source of voltage it maintains a constant potential difference between its terminals Pearson Education, Inc.c 4

5 Question 17.1 Which is the correct way to light the lightbulb with the battery? Connect the Battery d) all are correct e) none are correct a) b) c) 5

6 Question 17.1 Which is the correct way to light the lightbulb with the battery? Connect the Battery d) all are correct e) none are correct a) b) c) Current can flow only if there is a continuous connection from the negative terminal through the bulb to the positive terminal. This is the case for only Fig. (3). 6

7 17.1 Batteries and Direct Current The potential difference between the battery terminals when the battery is not connected to anything is called the electromotive force, emf Pearson Education, Inc.c 7

8 17.1 Batteries and Direct Current The actual terminal voltage of the battery is always less than the emf, due to internal resistance. Usually the difference is very small Pearson Education, Inc.c 8

9 17.1 Batteries and Direct Current When batteries are connected in series, the total voltage is the sum of the individual voltages Pearson Education, Inc.c 9

10 17.1 Batteries and Direct Current When batteries of equal voltage are connected in parallel, the total voltage does not change; each battery supplies part of the total current Pearson Education, Inc.c 10

11 17.1 Batteries and Direct Current 2010 Pearson Education, Inc.c 11

12 17.2 Current and Drift Velocity Current is the time rate of flow of charge. SI unit of current: the ampere, A 2010 Pearson Education, Inc.c 12

13 17.2 Current and Drift Velocity Historically, the direction of current has been taken to be from positive to negative; this is opposite to the way electrons flow. However, this seldom matters Pearson Education, Inc.c 13

14 How long would it take for a net charge of 2.7 C to pass a location in a wire if it is to carry a steady current of 4.0 ma? 14

15 17.2 Current and Drift Velocity Electrons do not flow like water in a pipe. In the absence of voltage, they move randomly at high speeds, due to their temperature. When a voltage is applied, a very small drift velocity is added to the thermal motion, typically around 1 mm/s; this is enough to yield the observed current Pearson Education, Inc.c 15

16 17.3 Resistance and Ohm s Law If there is a potential difference across a conductor, how much current flows? The ratio between the voltage and the current is called the resistance. SI unit of resistance: the ohm, Ω 2010 Pearson Education, Inc.c 16

17 17.3 Resistance and Ohm s Law An ohmic material is one whose resistance is constant Pearson Education, Inc.c 17

18 17.3 Resistance and Ohm s Law Ohm s law is valid only for ohmic materials: The resistance of a particular object depends on its length, crosssectional area, material, and temperature Pearson Education, Inc.c 18

19 17.3 Resistance and Ohm s Law As expected, the resistance is proportional to the length and inversely proportional to the cross-sectional area: The constant ρ is called the resistivity, and is characteristic of the material Pearson Education, Inc.c 19

20 Question 17.2 Ohm s Law You double the voltage across a certain conductor and you observe the current increases three times. What can you conclude? a) Ohm s law is obeyed since the current still increases when V increases b) Ohm s law is not obeyed c) this has nothing to do with Ohm s law 20

21 Question 17.2 Ohm s Law You double the voltage across a certain conductor and you observe the current increases three times. What can you conclude? a) Ohm s law is obeyed since the current still increases when V increases b) Ohm s law is not obeyed c) this has nothing to do with Ohm s law Ohm s law, V = IR, states that the relationship between voltage and current is linear. Thus, for a conductor that obeys Ohm s law, the current must double when you double the voltage. 21

22 Question 17.3a Two wires, A and B, are made of the same metal and have equal length, but the resistance of wire A is four times the resistance of wire B. How do their diameters compare? Wires I a) d A = 4d B b) d A = 2d B c) d A = d B d) d A = 1/2d B e) d A = 1/4d B 22

23 Question 17.3a Two wires, A and B, are made of the same metal and have equal length, but the resistance of wire A is four times the resistance of wire B. How do their diameters compare? Wires I a) d A = 4d B b) d A = 2d B c) d A = d B d) d A = 1/2d B e) d A = 1/4d B The resistance of wire A is greater because its area is less than wire B. Since area is related to radius (or diameter) squared, the diameter of A must be two times less than the diameter of B., R ρ A 23

24 Question 17.3b Wires II A wire of resistance R is stretched uniformly (keeping its volume constant) until it is twice its original length. What happens to the resistance? a) it decreases by a factor of 4 b) it decreases by a factor of 2 c) it stays the same d) it increases by a factor of 2 e) it increases by a factor of 4 24

25 Question 17.3b Wires II A wire of resistance R is stretched uniformly (keeping its volume constant) until it is twice its original length. What happens to the resistance? a) it decreases by a factor of 4 b) it decreases by a factor of 2 c) it stays the same d) it increases by a factor of 2 e) it increases by a factor of 4 Keeping the volume (= area x length) constant means that if the length is doubled, the area is halved., Since R, this increases the resistance by a A factor of 4. 25

26 17.3 Resistance and Ohm s Law In this table, you can easily see the differences between the resistivities of conductors, semiconductors, and insulators Pearson Education, Inc.c 26

27 17.3 Resistance and Ohm s Law For many materials, the temperature dependence of the resistivity is approximately linear, as long as the temperature change is not too large. The constant α is called the temperature coefficient of resistivity. Some values of α are listed in the table on the previous page Pearson Education, Inc.c 27

28 17.3 Resistance and Ohm s Law Some materials exhibit a curious phenomenon: at a very low temperature called the critical temperature, their resistivity drops abruptly to zero. These are called superconductors; they have a number of unique properties. They are impractical for everyday home use, however, as they must be cooled to cryogenic temperatures Pearson Education, Inc.c 28

29 17.4 Electric Power Power, as usual, is the rate at which work is done. For work done by electricity: Rewriting, For ohmic materials, we can write: 2010 Pearson Education, Inc.c 29

30 17.4 Electric Power So, where does this power go? It is changed to heat in resistive materials Pearson Education, Inc.c 30

31 Question 17.4 When you rotate the knob of a light dimmer, what is being changed in the electric circuit? Dimmer a) the power b) the current c) the voltage d) both a) and b) e) both b) and c) 31

32 Question 17.4 When you rotate the knob of a light dimmer, what is being changed in the electric circuit? Dimmer a) the power b) the current c) the voltage d) both a) and b) e) both b) and c) The voltage is provided at 120 V from the outside. The light dimmer increases the resistance and therefore decreases the current that flows through the lightbulb. 32

33 17.4 Electric Power Electric appliances are rated in watts, assuming standard household voltage Pearson Education, Inc.c 33

34 Question 17.5a Two lightbulbs operate at 120 V, but one has a power rating of 25 W while the other has a power rating of 100 W. Which one has the greater resistance? Lightbulbs a) the 25 W bulb b) the 100 W bulb c) both have the same d) this has nothing to do with resistance 34

35 Question 17.5a Two lightbulbs operate at 120 V, but one has a power rating of 25 W while the other has a power rating of 100 W. Which one has the greater resistance? Lightbulbs a) the 25 W bulb b) the 100 W bulb c) both have the same d) this has nothing to do with resistance Since P = V 2 / R, the bulb with the lower power rating has to have the higher resistance. Follow-up: Which one carries the greater current? 35

36 17.4 Electric Power 2010 Pearson Education, Inc.c 36

37 17.4 Electric Power The electric company typically bills us for kilowatt-hours (kwh), a unit of energy. We can reduce our energy usage by buying efficient appliances Pearson Education, Inc.c 37

38 Question 17.5b Two space heaters in your living room are operated at 120 V. Heater 1 has twice the resistance of heater 2. Which one will give off more heat? Space Heaters a) heater 1 b) heater 2 c) both equally 38

39 Question 17.5b Two space heaters in your living room are operated at 120 V. Heater 1 has twice the resistance of heater 2. Which one will give off more heat? Space Heaters a) heater 1 b) heater 2 c) both equally Using P = V 2 / R, the heater with the smaller resistance will have the larger power output. Thus, heater 2 will give off more heat. Follow-up: Which one carries the greater current? 39

40 Review of Chapter 17 A battery produces emf; positive terminal is the anode, negative is the cathode. emf is measured in volts; it is the number of joules the battery supplies per coulomb of charge. An electric current can exist only in a complete circuit. Resistance: 2010 Pearson Education, Inc.c 40

41 Review of Chapter 17 Ohm s law is obeyed if the resistance is constant: The resistance of an object depends on its length, cross-sectional area, and resistivity Pearson Education, Inc.c 41

42 Review of Chapter 17 Power is the rate at which work is done Pearson Education, Inc.c 42

43 To move 5.0 C of charge from one electrode to the other, a 12-V battery must do how much work? 60 W 5.0 C 12 J 60 J 12 V 43

44 A car's starter motor draws 59 A from the car's battery during startup. If the startup time is 2.1 s, how many electrons pass a given location in the circuit during that time? 44

45 How long does it take for a charge of 4.70 C to pass through the crosssectional area of a wire that is carrying a current of 0.47 A? 45

46 In a dental X-ray machine, the accelerated electrons move to the east. The conventional current in the machine is in what direction? west east you can't tell from the data given 46

47 Imagine that some protons are moving to the left at the same time that some electrons are moving to the right past the same location. Part A: Will the net current be to the right, to the left, zero, or none of the preceding? A, to the right. B to the left. C. Zero. D. None of the preceding Part B. In 4.0 S, 6.9 C of electrons flow to the right at the same time that 5.2 C of protons flow to the left. What are the direction of the current due to the protons? to the left to the right Part C. What are the magnitude of the current due to the protons? 47

48 What is the emf of a battery with a 0.19 Ω internal resistance if the battery delivers 1.5 A to an externally connected 6.0 Ω resistor? 48

49 If you double the voltage across a resistor while at the same time cutting its resistance to onefourth its original value, what happens to the current in the resistor? it increases by 8 times it increases by four times it doubles you can't tell from the data given 49

50 A battery acquires and stores A, energy. B, charge & potential but not energy. C, energy, charge, & potential. D, potential. E, charge. 50

51 If you connect two identical storage batteries together in series ("+" to "-"), and place them in a circuit, the combination will provide A, twice the voltage, and the same current will flow through each. B, zero volts. C, the same voltage and the same current will flow through each. D, twice the voltage, and different currents will flow through each. 51

52 The resistivity of most common metals A, remains constant over wide temperature ranges. B, increases as the temperature increases. C, varies randomly as the temperature increases. D, decreases as the temperature increases. 52

53 When charging a battery, the terminal voltage is the battery emf. A, zero, as is B, less than C, more than D, equal to 53

54 During a research experiment on the conduction of current in the human body, a medical technician attaches one electrode to the wrist and a second to the shoulder of a patient. If 120 mv is applied across the two electrodes and the resulting current is 14.0 ma, what is the overall resistance of the patient's arm? 54

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