# Current Electricity continual movement of sustained charges. Potential (Voltage), Current, Resistance

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1 Current Electricity continual movement of sustained charges Potential (Voltage), Current, Resistance 1

2 Electric Current the flow of charge Two types of Current Where does the charge that moves come from? 2

3 Resistance (R) a quantity measuring the difficulty of charge movement. Factors that effect Resistance 3

4 OHM s Law Ohmic vs Non Ohmic Materials Graph 4

5 1.) What do the following units represent (a) J/C (b) C/s (c) V/m (d) N/C 2.) A lightening bolt delivers 35 coulombs of charge to the ground in 1/1000 of a second. (a) How many electrons are transferred, (b) What is the current of the lightening bolt. 3.) 9mC of charge passes through a cross section of wire in 3.5 seconds. (a) What is the current (b) How many electrons move through this section in 10 seconds (c) if the charge was doubled, what would the new current be 5

6 4.) A 10 m wire consists of 5m of copper followed by 5 m of aluminum of equal 1mm diameter. A potential difference of 80 V is placed across the composite wire (a) What is the total resistance (b) current flow throughout and (c) potential difference across aluminum and copper parts respectively. 6

7 Electric Power and Energy 7

8 Light Bulbs 8

9 Electric Energy 9

10 5.) A 12 V battery pushed a current of 0.50 A through a resistor. What is the resistance of the resistor and how many joules of energy does the battery loose in 1 minute 10

11 6.) A 150 W light bulb operates with a 120 V potential difference. (a) How much energy does it used in 2 hrs. (b) at a rate of \$.08/ kw hr how much does it cost to operate the bulb for 2 hrs (c) If this bulb was connected to a 240 V source of potential difference, at what rate would it dissipate energy. 11

12 Electric Circuits 12

13 Open / Closed / Short Circuit 13

14 Types of circuits Series vs Parallel 14

15 Christmas Light Strings 15

16 Circuit Rules (potential, current, resistance) Series Parallel Currents Potential (voltage) Resistance 16

17 V = I x R S T E T P E T R 17

18 Conservation of Charge in a circuit Which is correct 18

19 Using Meters To Measure Current and Voltage Ammeter 19

20 Voltmeter 20

21 Circuit Problems A) A 4 Ω, 8 Ω and 12 Ω resistor are connected in series to a 24 V Battery. a) Draw the schematic, b) find all the currents and "potential drops" across each resistor 21

22 B) An 18 Ω, 9 Ω and 6 Ω resistor are connected in parallel. a) determine the equivalent resistance of the connected resistors b) the current in the 9 Ω resistor is 4 A, determine the currents and potentials in the other resistors. 22

23 Problem Pack 23

24 24

25 25

26 Combined Circuit 4) 26

27 5) 27

28 6) 28

29 7) 29

30 8) 30

31 31

32 REDRAWING CIRCUITS R1 R2 R3 R4 R2 R1 R3 R4 R5 32

33 R2 R4 R1 R3 R5 R1 R4 R3 R2 R5 R7 R6 33

34 R3 R5 R4 R2 R6 R1 R5 R6 R4 R3 R2 R1 34

35 R1 R2 R3 R4 R8 R5 R6 R7 35

36 9) 1Ω 5Ω 2Ω 3Ω 10 V 1Ω 36

37 10) 37

38 Fuses and Circuit Breakers 38

39 Will either fuse burn out? Prove it 39

40 Circuits w/ power An electric heater is rated at 1200 W, a toaster is rated at 1100 W, and an electric grill is rated at 1300 W. The three appliances are connected in parallel to a common 120 V circuit. (a) How much current does each appliance draw? (b) Is a 28.0 A circuit breaker sufficient in this situation? Explain. 40

41 Light Bulbs and Brightness Determined By? Recall how bulbs relate to voltage (100 W bulb) If hooked up in series original (single 100 W) series connection (50 / 100 W) Adding bulbs in series Removing bulbs in series 41

42 Parallel Bulbs Add / Remove a Bulb 42

43 Complex bulb connections How does the reading on Ammeter A change How do bulbs a, b, c brightness change Compare brightness of each bulb in new orientation 43

44 How does the reading on Ammeter A change Compare brightness of each bulb 44

45 Bulb X How does the reading on Ammeter A change How do bulbs a, b, c brightness change Compare brightness of each bulb in new orientation 45

46 Bulb X How does the reading on Ammeter A change How do bulbs a, b, c brightness change Compare brightness of each bulb in new orientation 46

47 Bulb X How does the reading on Ammeter A change How do bulbs a, b, c brightness change Compare brightness of each bulb in new orientation 47

48 EMF and Terminal Voltage 48

49 How to include EMF in a problem If not indicated If EMF given 49

50 Graph 50

51 EMF EXAMPLE. A 20 V emf battery with an internal resistance of 1 ohm is connected in series to two 5 ohm resistors. (a) Determine the terminal voltage of the battery. (b) Determine the energy dissipated by the external circuit in 1 minuts 51

52 Massive All Inclusion Circuit Question (w/o Kirchhoff rules) A student is provided with a 12.0 V battery of negligible internal resistance and four resistors with the following resistances: 100 Ω, 30 Ω, 20 Ω, and 10 Ω. The student also has plenty of wire of negligible resistance available to make connections as desired. a.) Using all of these components, draw a circuit diagram in which each resistor has nonzero current flowing through it, but in which the current from the battery is as small as possible. b.) Using all of these components, draw a circuit diagram in which each resistor has nonzero current flowing through it, but in which the current from the battery is as large as possible (without short circuiting the battery). The battery and resistors are now connected in the circuit shown c.) Determine the following for this circuit. i.) The current in the 10 Ω resistor ii.) The total power consumption of the circuit d.) Assuming that the current remains constant, how long will it take to provide a total of 10 kj of electrical energy to the circuit? The battery is replaced with a different battery of the same EMF but having internal resistance of 1 ohm e.) How will the power consumption of the external circuit be affected f.) What is the terminal voltage of this battery when connected in the circuit shown g.) The resistance free battery is returned to the circuit and the resistors are replaced with equal sized light bulbs B1, B2, B3 and B4, rank the brightness of each in order of increasing magnitude (Use = signs if bulbs have the same brightness) h.) If only Bulb B4 was removed, how would the brightness of the other bulbs be affected i.) If only Bulb B2 was removed, how would the brightness of the other bulbs be affected 52

53 Complex Combined Circuits and Kirchoff s Laws 1) The junction rule (charge conservation rule) 2) The loop rule (energy conservation rule) 53

54 Find Unknowns 54

55 2) Find I total 55

56 3) For the circuit shown: The current through resistor R 2 is 0.33 A as shown. The batteries have emfs of ε 1 = 9.0 V and ε 2 = 12.0 V and the resistors have values of R 1 = 15Ω, R 2 = 20Ω, and R 3 = 32 Ω. 15 Ω y a) Determine the magnitudes and directions of the currents through each resistor 9V 20 Ω x 12V I 2 = 0.33 A 32 Ω b) Determine the potential difference from x > y 56

57 4) Random use of loop rule In the circuit shown above, what is the resistance R? 5) In the circuit shown above, the current in each battery is 0.04 ampere. a) What is the potential difference between the points x and y? b) Which point is at a higher potential, X or Y 57

58 Terminal Voltage > EMF??? 6) A 12 volt storage battery, with an internal resistance of 2 Ω, is being charged by a current of 2 amperes as shown in the diagram above. Under these circumstances, a voltmeter connected across the terminals of the battery will read (show wrong answer first) 58

59 Advanced Kirchoff Problem see handout on next page 7) Determine the magnitudes and directions of the currents through each resistor shown. The batteries have emfs of ε 1 = 9.0 V and ε 2 = 12.0 V and the resistors have values of R 1 = 15Ω, R 2 = 20Ω, and R 3 = 32 Ω. 9V 15 Ω y 20 Ω x 12V 32 Ω 59

60 60

61 Capacitors in Circuits 61

62 Capacitors in series when connected to a battery EQ. Capacitance (C EQ ) Charge (Q) Potential (voltage) (V) 62

63 Example 1.) A 0.40 μf and a 0.50 μf capacitor are connected in series to a 9 V emf source. Calculate the potential across each capacitor 63

64 Capacitors hooked to each other 64

65 EX 2.) A 1µF capacitor is connected to a 12 V battery an allowed to charge. It is then disconnected from the battery an attached to a 2 µf uncharged capacitor. (a) Determine the charge stored on the capacitor while connected to the battery (b) Determine the charge stored on each capacitor after being connected to one another 65

66 Capacitors in parallel with a battery vs Equivalent Capacitance (C EQ ) Voltage (V) Charge (Q) 66

67 Circuit Rules Summary Chart VIR VIR Resistors STET PETR Capacitors STER PETT 67

68 3.) 12.5 μ F cap C 1 is connected in series to a 6.25 μf cap C 2 and these are then connected in parallel to a 12.5 μf cap C 3. The whole combination is connected in parallel to 45 V emf source. a) How much charge is stored on each capacitor. b) How much total charge is stored 68

69 Inserting material between capacitors 1) Dielectrics 2) Conductors 69

70 Quick Summary Rules for changing Parallel Plates dimensions Capacitance C, is physical and changed based on C= ε o A / d 1) Isolated: NOT connected to battery Charge Q Potential V E Field 2) Connected to battery Charge Q Potential V E Field 70

71 RC circuits Series How to Treat the capacitor 1) At first 2) as time goes on 3) When fully charged 71

72 Parallel 1) At first 2) as time goes on 3) When fully charged 72

73 Combined Parallel and Series RC behavior depends on the configuration 4) (a) Determine the current flowing in the circuit when the switch is first flipped (b) Determine the current flowing in the circuit after a long time (c) Determine the energy and charge stored in the capacitor 73

74 5.) Two resistors and two uncharged capacitors are arranged as shown in Fig ( R = 8.8, C = 0.24 µf) with a potential difference of 24 V across the combination. (a) What is the potential at point a? (Let V = 0 at the negative terminal of the source.) (Potential at a = the potential difference from a to c) (b) What is the potential at point b (Potential at b = potential diff b to c) (c) Find the energy in each cap 74

75 6) (a) Determine the current flowing in the circuit when the switch is first flipped on (b) Determine the current flowing in the circuit after a long time (c) Determine the energy and charge stored in the capacitor 75

76 7.) 2000B B3. Three identical resistors, each with resistance R, and a capacitor of F are connected to a 30 V battery with negligible internal resistance, as shown in the circuit diagram above. Switches I and S S 2 are initially closed, and switch 3 Sis initially open. A voltmeter is connected as shown. a. Determine the reading on the voltmeter. Switches S l and S 2 are now opened, and then switch S 3 is closed. b. Determine the charge Q on the capacitor after S 3 has been closed for a very long time. After the capacitor is fully charged, switches S 1 and S 2 remain open, switch S 3 remains closed, the plates are held fixed, and a conducting copper block is inserted midway between the plates, as shown below. The plates of the capacitor are separated by a distance of 1.0 mm, and the copper block has a thickness of 0.5 mm. c. i. What is the potential difference between the plates? ii. What is the electric field inside the copper block? iii. On the diagram above, draw arrows to clearly indicate the direction of the electric field between the plates. iv. Determine the magnitude of the electric field in each of the spaces between the plates and the copper block. 76

77 8) Into which circuit should the battery be connected to obtain the greatest steady power dissipation? (A) A (B) B (C) C (D) D (E) E Which circuit will retain stored energy if the battery is connected to it and then disconnected? (A) A (B) B (C) C (D) D (E) E 77

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