Chapter 19: Electric Current and Circuits Topics

2. Chapter 19: Electric Current and Circuits Topics Electric current EMF Current & Drift Velocity Resistance & Resistivity Kirchhoff’s Rules Series & Parallel Circuit Elements Applications of Kichhoff’s Rules Power & Energy Ammeters & Voltmeters RC Circuits

3. Electric Current & Circuits Electric Current: steady flow of electric charge. Potential Difference: work done by the electric force to move 1 Coulomb of charge between two points. Convention: current has the direction of the flow of positive charges.

4. Current Direction Direct current (DC): electrons flowing in one direction only. Alternating current (AC): electrons continuously reverse their direction of motion.

5. Definition of I • Current (I) =amount of charge that passes through a cross sectional area of a conductor in one unit of time. Charge Charge Time = ΔQ/Δt I = Unit of measurement: Cross-sectional area Ampere (A)

6. Current defined – Figures 19.1 and 19.2

7. Microscopic View of Current in a Metal • The electrons moving in a wire collide frequently with one another and with the atoms of the wire • This results in the zigzag motion shown • When no electric field is present, the average electron displacement is zero, vdrift = 0. • There is no net movement of charge. • There is no current. Section 19.3

8. Current, cont. • With a battery connected, an electric potential is established • There is an electric field in the wire: E = V / L • The electric field produces a force that gives the electrons a net motion • The velocity of this motion is the drift velocity, vdrift  0. Typically, vdrift < 1 mm/sec Section 19.3

9. Calculate the number of charges (Ne) that pass through the shaded region in a time t: l The current in the wire is:

10. Example : A copper wire of cross-sectional area 1.00 mm2 has a constant current of 2.0 A flowing along its length. What is the drift speed of the conduction electrons? Copper has 1.101029 electrons/m3.

11. Electric Current Example How many electrons flow through a cross sectional area of a conductor in 5s, if it is traveled by a current of 3.2 A 1. Find the total charge: 2. Find the number of electrons N using the charge of an electron e=1.6 x 10-19C

12. Current and Voltage • The current is directed from a region of higher potential to a region of lower potential • Or higher to lower voltage • The direction of I is always from high to low potential, regardless if the current is carried by positive or negative charges • The potential difference may be supplied by a battery Section 19.2

13. Analogy • A ball rolling down a hill High Low Difference of height causes the ball to roll down the hill.

14. Sources High Potential Low Potential The positive electrode is called the anode; the negative electrode is the cathode. In a complete circuit, electrons flow from the negative electrode to the positive one.

15. Batteries (Voltage sources, sources of emf): Purpose is to provide a constant potential difference (voltage) between two points. + - OR V - + Sources The potential difference across the terminals in an open circuit is called electromotive force or “emf” ξ.

16. Voltage A useful meter is a multimeter,which can measure voltage or current, and sometimes resistance. To measure voltage, the meter’s probes are touched to two places in a circuit or across a battery.

17. Measuring current If you want to measure current you must force the current to pass through the meter. Multimeters can measure two types of current: alternating current (AC) and direct current(DC).

18. Construction of a Battery • Alessandro Volta and his contemporaries developed the first batteries • Batteries convert chemical energy to electrical energy • In drawing an electric circuit the terminals of any type of battery are labeled with + and - Section 19.2

19. Thermocouples • Device that produces electric energy due to temperature difference at the junction b/w 2 different metals (Seebeck). • Copper • Iron Can be used to measure the temperature. Ex.:cars, gas furnaces. Hot Cold

20. Photoelectric Cell • Light energy is converted into electric energy. Light Metallic Surface Electrons Emitted electrons can be used in a circuit.

21. Sources • Electromagnetic induction: conversion of electromagnetic energy into electricity. • Piezoelectric: mechanical stress on certain crystals creates a difference of potential.

22. Electric Circuit • Electric Circuit: complete path through which a current can flow. Made of a source of current (battery), connecting wires, and an electricity user. User Wires - + I S

23. Electric Circuits • When drawing a circuit diagram,symbols are used to represent each part of the circuit.

24. Electrical Symbols • Electrical symbolsare quicker and easier to draw than realistic pictures of the components.

25. Resistance Resistance (R): opposition to the flow of the electric current. Caused by collisions b/w electrons and the atoms of the metal. Measured in ohms Ω. Depends upon type of material (resistivity ρ), proportional to length L, inversely proportional to thickness (cross sectional area A). R = ρL/A

26. How thick? How big? What’s it made of? or Resistivity • The resistivity, ρ, depends only on the material used to make the wire • The resistance of a wire of length L and cross-sectional area A is given by The structure of this relation is identical to heat flow through materials … think of a window for an intuitive example Section 19.3

27. Resistance Continuation R is proportional to the temperature. At low temperatures conductors exhibit low resistance (superconductors). Causes electric energy to turn into heat.

28. Simple Electric Circuit Analogy

30. Example Deformation of Wire • A very thin metal wire patterned as shown is bonded to some structure. • As the structure is deformed slightly, this stretches the wire (slightly). • When this happens, the resistance of the wire: (c) stays the same (b) increases (a) decreases Because the wire is slightly longer, is slightly increased. Also, because the overall volume of the wire is ~constant, increasing the length decreases the area A, which also increases the resistance. By carefully measuring the change in resistance, the strain in the structure may be determined.

31. Exercise :Compare Resistances Two cylindrical resistors are made from the same material, and they are equal in length. The first resistor has diameter d, and the second resistor has diameter 2d. Compare the resistance of the two cylinders. a) R1 > R2 b) R1 = R2 c) R1 < R2 Larger cross sectional area decreases the resistance.

33. Determined experimentally the relationship between current and voltage in a circuit. Ohm’s Law

34. Ohm’s Law • I=V/R V A R S Source: provides electric energy. V - voltmeter: measures voltage (parallel) A - ammeter: measures electric current (series)

35. R I I V V slope = R I Ohm’sLaw • Experimental: • Vary applied voltage V. • Measure current I • Ratio remains constant. or V=RI

36. Solving Problems • A toaster oven has a resistance of 12 ohms and is plugged into a 120-volt outlet. • How much current does it draw?

37. Solving Problems • Looking for: • …current in amps • Given • …R = 12 ; V = 120 V • Relationships: • I = V R • Solution • I = 120 V 12  • = 10 A

38. I2 I1 V (c) I1 > I2 (b) I1 = I2 (a) I1 < I2 The resistivity of both resistors is the same (r). Therefore the resistances are related as: The resistors have the same voltage across them; therefore Example Compare Currents • Two cylindrical resistors, R1 and R2, are made of identical material. R2 has twice the length of R1 but half the radius of R1. • These resistors are then connected to a battery V as shown: • What is the relation between I1, the current flowing in R1 , and I2 , the current flowing in R2?

39. Electric Energy • The work done by the electric field to move the charge ΔQ through the potential difference V is a measure of the electric energy expanded in this case. Therefore the electric energy is given by the formula: Since: V=IR, we can also write: W= I2Rt (thermal or Joule effect) Also:

40. Batteries & Resistors Energy expended chemical to electrical to heat Rate is: What’s happening? Assert: Charges per time or you can write it as Potential difference per charge For Resistors: Units okay? Power

41. Electric Power • Electric Power: is the time rate at which electricity does work or provides electric energy. • P=W/t, therefore: Power = Voltage x Current • or P = VI, P= I2R, P= V2/R • Power is measured in Watts. • Watts = Volts x Amperes • 1 kilowatt = 1000 watts. • 1kwh=1000 W x 3600 s= 3,600,000 J

42. Example Higher Resistance • Two appliances operate at the same voltage. Appliance “A” has a higher power rating than “B”. How does the resistance of “A” compare with that of “B”: a) larger b) smaller c) the same P = VI, I = P/V, Since PA > PB it results that IA > IB, and RA< RB

43. Example Numerical A computer monitor has a power requirement of 200 W, whereas a toaster is rated at 1500 W. Find and compare: a) the electric currents flowing through each device, and b) the resistances of the two devices if both are connected at 120 V. P = VI, I = P/V a) Monitor: Im = Pm/V = 200W/120V = 1.67A Toaster: It = Pt/V = 1500W/120V = 12.5A I= V/R, R = V/I b) Monitor: Rm = V/Im = 120V/1.67A = 71.9Ω Toaster: Rt = V/It = 120V/12.5A = 9.6Ω

44. Example Repair A hair dryer is rated @ 1200 W for 115 V operating voltage. A repair done by the owner shortens the wire of the filament by 10%. What will be the power output after the repair? P = V2/R, R = V2/P= (115V)2 / 1200W = 11.02Ω R = ρL/A so R’=0.9 R = .9 x 11.02Ω = 9.92Ω P’= V2/R’= (115V)2 / 9.92Ω =1333.15 W Change + 133W, do not perform the repair!

45. Consumer Electric Energy • Energy = Power x Time; W = P x t = V x I x t • Measured in Kilowatt-hours (kWh). • 1 kilowatt-hour =1kilowatt x 1 hour. • Electric bill: # of kWh x price of 1 kWh. • Electric safety. NO: 1. Wet hands, 2. Wires under carpets, 3. Too many appliances, 4. Worn or frayed wires, 5. Touch electric sockets without protection, 6. Close to wires or power poles.

46. Example Cost • A toaster rated at 1500 W. If you pay $0.10/KWh, how much does it cost to use the appliance for 15 min.? W = Pt = 1500 W x 900s = 1,350,000 J # of kwh = 1,350,000 J/3,600,000 J=0.375 Cost= 0.375 x 0.1= $ 0.0375

47. Review • I=V/R; P=V x I; W=P x t; W = V x I x t • Cost = # of kWh x Price of kWh

48. ConcepTest 17.1 Connect the Battery 4) all are correct 5) none are correct Which is the correct way to light the lightbulb with the battery? 1) 2) 3)

49. ConcepTest 17.1 Connect the Battery 4) all are correct 5) none are correct Which is the correct way to light the lightbulb with the battery? 1) 2) 3) Current can only flow if there is a continuous connection from the negative terminal through the bulb to the positive terminal. This is only the case for Fig. (3).

50. ConcepTest 17.2Ohm’s Law 1) Ohm’s Law is obeyed since the current still increases when V increases 2) Ohm’s Law is not obeyed 3) this has nothing to do with Ohm’s Law You double the voltage across a certain conductor and you observe the current increases three times. What can you conclude?