PHYS 1442 – Section 004 Lecture #10+Review

1. PHYS 1442 – Section 004 Lecture #10+Review Monday February 17 2014 Dr. Andrew Brandt • CH 18 • Alternating Current • Short review for test on ch 16-19 PHYS 1442-004, Dr. Andrew Brandt

2. Does the direction of the flow of current change when a battery is connected to a circuit? • No. Why? • Because its source of potential difference is constant. • This kind of current is called the Direct Current (DC • How would DC look as a function of time? • A horizontal line • Electric generators at electric power plant produce alternating current (AC) • AC reverses direction many times a second • AC is sinusoidal as a function of time Alternating Current • Most currents supplied to homes and business are AC. PHYS 1442-004, Dr. Andrew Brandt

3. Alternating Current • The voltage produced by an AC electric generator is sinusoidal • This is why the current is sinusoidal • Voltage produced can be written as • What are the maximum and minimum voltages? • V0 and –V0 • The potential oscillates between +V0 and –V0, the peak voltages or amplitude • What is f ? • The frequency, the number of complete oscillations made per second. What is the unit of f ? What is the normal size of f in the US? • f = 60 Hz in the US and Canada. • Many European countries have f = 50Hz. • w=2pf PHYS 1442-004, Dr. Andrew Brandt

4. What is this? Alternating Current • Since V=IR, if a voltage V exists across a resistance R, the current I is • What are the maximum and minimum currents? • I0 and –I0 • The current oscillates between +I0 and –I0, the peak currents or amplitude. The current is positive when electron flows in one direction and negative when they flow in the opposite direction. • What is the average current? • Zero. So there is no power and no heat produced in a heater? • Wrong! The electrons actually flow back and forth, so power is delivered. PHYS 1442-004, Dr. Andrew Brandt

5. Power Delivered by Alternating Current • AC power delivered to a resistance is: • Since the current is squared, the power is always positive • The average power delivered is • Since the power is also P=V2/R, we can obtain • The average of the square of current and voltage are important in calculating power: Average power PHYS 1442-004, Dr. Andrew Brandt

6. Power Delivered by Alternating Current • The square root of each of these are called root-mean-square, or rms: • rms values are sometimes called effective values • These are useful quantities since they can substitute current and voltage directly in power equations, as if they were DC values • In other words, an AC of peak voltage V0 or peak current I0 produces as much power as DC voltage of Vrms or DC current Irms. • So normally, rms values in AC are specified or measured. • US uses 115 to 120 V rms voltage. What is the peak voltage? • Europe uses 240V PHYS 1442-004, Dr. Andrew Brandt

7. Electric Hazards: Leakage Currents • How does one feel an electric shock? • Electric current stimulates nerves and muscles, and we feel a shock • The severity of the shock depends on the amount of current, how long it acts and through what part of the body it passes • Electric current heats tissues and can cause burns • Currents above 70mA on a torso for a second or more is fatal, causing heart to function irregularly, “ventricular fibrillation” • Dry skin has a resistance of 104 to 106W. • When wet, it could be 103W. • A person in good contact with the ground who touches 120V DC line with wet hands can receive a fatal current PHYS 1442-004, Dr. Andrew Brandt

8. Superconductivity • At temperatures near absolute 0K, the resistivity of certain materials approaches 0. • This state is called the “superconducting” state. • Observed in 1911 by H. K. Onnes when he cooled mercury to 4.2K (-269oC). • Resistance of mercury suddenly dropped to 0. • In general superconducting materials become superconducting below a transition temperature. • The highest temperature superconductor so far is 160K • First observation above the boiling temperature of liquid nitrogen is in 1987 at 90K observed from a compound of yttrium, barium, copper and oxygen. • Since a much smaller amount of material can carry just as much current more efficiently, superconductivity can make electric cars more practical, computers faster, and capacitors store higher energy (not to mention LHC magnets) PHYS 1442-004, Dr. Andrew Brandt

9. Quick Review • Test Weds on CH 16-19 • Multiple choice, bring a 50 problem Scantron form PHYS 1442-004, Dr. Andrew Brandt

10. Electric Charge and Conservation • Two types of electric charge • Like charges repel while unlike charges attract • The net amount of electric charge produced in any process is ZERO!! • When a positively charged metal object is brought close to an uncharged metal object • If the objects touch each other, the free charges flow until an equilibrium state is reached (charges flow in a conductor.) • If the objects are close, the free electrons in the neutral object still move within the metal toward the charged object leaving the opposite end of the object positively charged.(induced charge) PHYS 1442-004, Dr. Andrew Brandt

11. Coulomb’s Law – The Formula Formula A vector quantity. Newtons • Direction of electric (Coulomb) force (Newtons) is always along the line joining the two objects. • Unit of charge is called Coulomb, C, in SI. • Elementary charge, the smallest charge, is that of an electron: -e where PHYS 1442-004, Dr. Andrew Brandt

12. Vector Problems • Calculate magnitude of vectors (Ex. force using Coulomb’s Law) • Split vectors into x and y components and add these separately, using diagram to help determine sign • Calculate magnitude of resultant |F|=(Fx2+Fy2) • Use = tan-1(Fy/Fx) to get angle PHYS 1442-004, Dr. Andrew Brandt

13. Angle: After calculating magnitudes, take x+y components and then get total force PHYS 1442-004, Dr. Andrew Brandt

14. The Electric Field • The electric field at any point in space is defined as the force exerted on a tiny positive test charge divided by magnitude of the test charge • The electric field inside a conductor is ZERO in a static situation PHYS 1442-004, Dr. Andrew Brandt

15. Example Calculate the total electric field (a) at point A and (b) at point B in the figure due to both charges, Q1 and Q2. Solution: The geometry is shown in the figure. For each point, the process is: calculate the magnitude of the electric field due to each charge; calculate the x and y components of each field; add the components; recombine to give the total field. a. E = 4.5 x 106 N/C, 76° above the x axis. b. E = 3.6 x 106 N/C, along the x axis. PHYS 1442-004, Dr. Andrew Brandt

16. Example • Electron accelerated by electric field. An electron (mass m = 9.1x10-31 kg) is accelerated from rest in a uniform field E (E = 2.0x104 N/C) between two parallel charged plates (d=1.5 cm), andpasses through a tiny hole in the positive plate. (a) With what speed does it leave the hole? PHYS 1442-004, Dr. Andrew Brandt

17. Electric Potential Energy • Concept of energy is very useful solving mechanical problems • Conservation of energy makes solving complex problems easier. • Defined for conservative forces (independent of path) PHYS 1442-004, Dr. Andrew Brandt

18. Electric Potential Energy • What is the definition of change in electric potential energy Ub –Ua? • The potential gained by the charge as it moves from point a to point b. • The negative work done on the charge by the electric force to move it from a to b. • Parallel plates w/ equal but opposite charges • The field between the plates is uniform since the gap is small and the plates are infinitely long… • What happens when we place a small charge, +q, on a point at the positive plate and let go? • The electric force will accelerate the charge toward negative plate and it gains kinetic energy PHYS 1442-004, Dr. Andrew Brandt

19. Electric Potential • The electric field (E) is defined as electric force per unit charge: F/q (vector quantity) • Electric potential (V) is defined as electrical potential energy per unit charge U/q (scalar) PHYS 1442-004, Dr. Andrew Brandt

20. m 2m • Let’s compare gravitational and electric potential energies Comparisons of Potential Energies • What are the potential energies of the rocks? • mgh and 2mgh • Which rock has a bigger potential energy? • The rock with a larger mass • Why? • It’s got a bigger mass. • What are the potential energies of the charges? • +QVba and +2QVba • Which object has a bigger potential energy? • The object with a larger charge. • Why? • It’s got a bigger charge. The “potential” is the same but the heavier rock or larger charge can do a greater work. PHYS 1442-004, Dr. Andrew Brandt

21. What are the differences between the electric potential and the electric field? • Electric potential (U/q) • Simply add the potential from each of the charges to obtain the total potential from multiple charges, since potential is a scalar quantity • Electric field (F/q) • Need vector sums to obtain the total field from multiple charges • Potential for a positive charge is large near a positive charge and decreases to 0 at large distances. • Potential for the negative charge is small (large magnitude but negative) near the charge and increases with distance to 0 Properties of the Electric Potential PHYS 1442-004, Dr. Andrew Brandt

22. Electrostatic Potential Energy; Three Charges • Work is needed to bring all three charges together • Work needed to bring Q1 to a certain place without the presence of any charge is 0. • Work needed to bring Q2 to a distance to Q1 is • Work need to bring Q3 to a distance to Q1 and Q2 is • So the total electrostatic potential of the three charge system is PHYS 1442-004, Dr. Andrew Brandt

23. Capacitors • A simple capacitor consists of a pair of parallel plates of area A separated by a distance d. • A cylindrical capacitors are essentially parallel plates wrapped around as a cylinder. Circuit Diagram PHYS 1442-004, Dr. Andrew Brandt

24. If a battery is connected to a capacitor, the capacitor gets charged quickly, one plate positive and the other negative with an equal amount.. • For a given capacitor, the amount of charge stored in the capacitor is proportional to the potential difference Vba between the plates. C is a proportionality constant, called capacitance of the device. • Should know how to add them, calculate based on geometry Capacitors C is a property of a capacitor so does not depend on Q or V. PHYS 1442-004, Dr. Andrew Brandt

25. Dielectrics • Capacitors generally have an insulating sheet of material, called a dielectric, between the plates to • Increase the breakdown voltage above that in air • Allows the plates get closer together without touching • Increases capacitance ( recall C=e0A/d) • Also increases the capacitance by the dielectric constant • Where C0 is the intrinsic capacitance when the gap is vacuum, and K or  is the dielectric constant PHYS 1442-004, Dr. Andrew Brandt

26. Electric Current • Electric Current: Any flow of charge • Current can flow whenever there is potential difference between the ends of a conductor • Electric current in a wire can be defined as the net amount of charge that passes through a wire’s full cross section at any point per unit time • Average current is defined as: • Current is a scalar • Current is flow of charge, charge is conserved, • so current in equals current out at a given point on circuit 1A=1C/s C/s PHYS 1442-004, Dr. Andrew Brandt

27. The exact amount of current flow in a wire depends on • The voltage • The resistance of the wire to the flow of electrons • The higher the resistance the less the current for the given potential difference V Ohm’s Law: Resistance PHYS 1442-004, Dr. Andrew Brandt

28. l Resistivity • It is experimentally found that the resistance R of a metal wire is directly proportional to its length l and inversely proportional to its cross-sectional area A • The proportionality constant r is called the resistivity and depends on the material used. The higher the resistivity the higher the resistance • The reciprocal of the resistivity is called the conductivity, s, A PHYS 1442-004, Dr. Andrew Brandt

29. Electric Power • Power -the rate at which work is done or the energy is transferred • P=IV can apply to any devices while the formulae involving resistance only apply to Ohmic resistors. I2R used for heat loss Temperature dependence PHYS 1442-004, Dr. Andrew Brandt

30. A quiz PHYS 1442-004, Dr. Andrew Brandt

31. Example Will a 30A fuse blow? Determine the total current drawn by all the devices in the circuit in the figure. The total current is the sum of current drawn by the individual devices. Solve for I Bulb Heater Stereo Dryer Total current What is the total power? PHYS 1442-004, Dr. Andrew Brandt

32. Magnetism • So are magnet poles analogous to electric charge? • No. Why not? • While the electric charges (positive and negative) can be isolated, magnet poles cannot. • So what happens when a magnet is cut? • You get two magnets! • The more they get cut, the more magnets are made • Single-pole magnets are called “monopoles,” but to date none have been observed… • Ferromagnetic materials: Materials that show strong magnetic effects • Iron, cobalt, nickel, gadolinium and certain alloys • Other materials show very weak magnetic effects PHYS 1442-004, Dr. Andrew Brandt

33. 1442 Test I Eq. Sheet |F|=(Fx2+Fy2) = tan-1(Fy/Fx) Electron charge: Electron mass: Proton mass: Colomb’s Law: : For a point charge: K.E.=mv2/2 Ugrav=mgh g=9.8 m/s2 Uelec=qV Q=CV C=capacitance parallel plate: dielectric: Cap. stored energy: Ohm’s Law: V=IR Power: P=IV Current: I=q/t AC: Resistivity: me = 9.1x10-31 kg mp =1.67x10-27 kg Ceq=C1+C2 (parallel) 1/Ceq=1/C1+1/C2 (series) Req=R1+R2 (series) 1/Req=1/R1+1/R2(parallel) V=Ed (uniform field) Eqs. of motion: