Chapter 21-part1

1. Chapter 21-part1 Current and Resistance

2. 1 Electric Current • Whenever electric charges move, an electric current is said to exist • The current is the rate at which the charge flows through a certain cross-section • For the current definition, we look at the charges flowing perpendicularly to a surface of area A

3. Definition of the current: Charge in motion through an area A. The time rateof the charge flow through A defines the current (=charges per time): I=DQ/Dt Units: C/s=As/s=A SI unit of the current: Ampere - +

4. Electric Current, cont • The direction of current flow is the direction positive charge would flow • This is known as conventional (technical) current flow, i.e., from plus (+) to minus (-) • However, in a common conductor, such as copper, the current is due to the motion of the negatively charged electrons • It is common to refer to a moving charge as a mobile charge carrier • A charge carrier can be positive or negative

5. 2 Current and Drift Speed • Charged particles move through a conductor of cross-sectional area A • n is the number of charge carriers per unit volume V (=“concentration”) • nADx=nV is the total number of charge carriers in V

6. Current and Drift Speed, cont • The total charge is the number of carriers times the charge per carrier, q (elementary charge) • ΔQ = (nAΔx)q[unit: (1/m3)(m2 m)As=C] • The drift speed, vd, is the speed at which the carriers move • vd = Δx/Δt • Rewritten: ΔQ = (nAvdΔt)q • Finally, current, I = ΔQ/Δt = nqvdA Δx

7. Current and Drift Speed, final • If the conductor is isolated, the electrons undergo (thermal) random motion • When an electric field is set up in the conductor, it creates an electric force on the electrons and hence a current

8. Charge Carrier Motion in a Conductor The electric field force F imposes a drift on an electron’s random motion (106 m/s) in a conducting material. Without field the electron moves from P1 to P2. With an applied field the electron ends up at P2’; i.e., a distance vdDt from P2, where vd is the drift velocity (typically 10-4 m/s).

9. qvd Does the direction of the current depend on the sign of the charge? No! E vd (a) Positive charges moving in the same direction of the field produce the same positive current as (b) negative charges moving in the direction opposite to the field. E vd (-q)(-vd) = qvd

10. Current density: The current per unit cross-section is called the current density J: J=I/A= nqvdA/A=nqvd In general, a conductor may contain several different kinds of charged particles, concentrations, and drift velocities. Therefore, we can define a vector current density: J=n1q1vd1+n2q2vd2+… Since, the product qvd is for positive and negative charges in the direction of E, the vector current density J always points in the direction of the field E.

11. Example: An 18-gauge copper wire (diameter 1.02 mm) carries a constant current of 1.67 A to a 200 W lamp. The density of free electrons is 8.51028 per cubic meter. Find the magnitudes of (a) the current density and (b) the drift velocity.

12. Solution: (a) A=d2p/4=(0.00102 m)2p/4=8.210-7 m2 J=I/A=1.67 A/(8.210-7 m2)=2.0106 A/m2 (b) From J=I/A=nqvd, it follows: vd=1.510-4 m/s=0.15 mm/s

13. 3 Electrons in a Circuit • The drift speed is much smaller than the average speed between collisions • When a circuit is completed, the electric field travels with a speed close to the speed of light • Although the drift speed is on the order of 10-4 m/s the effect of the electric field is felt on the order of 108 m/s

14. Meters in a Circuit – Ammeter • An ammeter is used to measure current • In line with the bulb, all the charge passing through the bulb also must pass through the meter (in series!)

15. Meters in a Circuit - Voltmeter • A voltmeter is used to measure voltage (potential difference) • Connects to the two ends of the bulb (parallel)

16. Look at the four “circuits” shown below and select those that will light the bulb. QUICK QUIZ

17. 4 Resistance and Ohm’s law • In a homogeneous conductor, the current density is uniform over any cross section, and the electric field is constant along the length. b a V=Va-Vb=EL

18. Resistance The ratio of the potential drop to the current is called resistance of the segment: Unit: V/A=W (ohm)

19. Resistance, cont • Units of resistance are ohms (Ω) • 1 Ω = 1 V / A • Resistance in a circuit arises due to collisions between the electrons carrying the current with the fixed atoms inside the conductor

20. Ohm’s Law • VI V=const.I  V=RI • Ohm’s Law is an empirical relationship that is valid only for certain materials • Materials that obey Ohm’s Law are said to be ohmic • I=V/R • R, I0, open circuit; R0, I, short circuit

21. Ohm’s Law, final Ohmic Plots of V versus I for (a) ohmic and (b) nonohmic materials. The resistance R=V/I is independent of I for ohmic materials, as is indicated by the constant slope of the line in (a). Nonohmic

22. 5 Resistivity • Expected: RL/A  • The resistance of an ohmic conductor is proportional to its length, L, and inversely proportional to its cross-sectional area, A • ρ (“rho”) in m is the constant of proportionality and is called the resistivity of the material

23. Example • Determine the required length of nichrome (=10-6Wm) with a radius of 0.65 mm in order to obtain R=2.0 W. • R=L/AL=RA/

24. The resistivity depends on the material and the temperature

25. 6 Temperature Variation of Resistivity • For most metals, resistivity increases with increasing temperature • With a higher temperature, the metal’s constituent atoms vibrate with increasing amplitude • The electrons find it more difficult to pass the atoms (more scattering!)

26. Temperature Variation of Resistivity, cont • For most metals, resistivity increases approximately linearly with temperature over a limited temperature range • ρo is the resistivity at some reference temperature To • To is usually taken to be 20° C •  is the temperature coefficient of resistivity [unit: 1/(C)]

27. Temperature Variation of Resistance • Since the resistance of a conductor with uniform cross sectional area is proportional to the resistivity, the temperature variation of resistance can be written

28. Example • The material of the wire has a resistivity of 0=6.810-5m at T0=320C, a temperature coefficient of =2.010-3 (1/C) and L=1.1 m. Determine the resistance of the heater wire at an operating temperature of 420C.

29. Solution • =0[1+(T-T0)] • =[6.810-5m][1+(2.010-3 (C)-1)  • (420C-320C)]=8.210-5m • R=L/A • R=(8.210-5m)(1.1 m)/(3.110-6 m2) • R=29 

30. “normal” 7 Superconductors • A class of materials and compounds whose resistances fall to virtually zero below a certain temperature, TC • TC is called the critical temperature (in the graph 4.1 K)

31. Superconductors, cont • The value of TC is sensitive to • Chemical composition • Pressure • Crystalline structure • Once a current is set up in a superconductor, it persists without any applied voltage • Since R = 0

32. Superconductor Timeline • 1911 • Superconductivity discovered by H. Kamerlingh Onnes • 1986 • High-temperature superconductivity discovered by Bednorz and Müller • Superconductivity near 30 K • 1987 • Superconductivity at 92 K and 105 K • Current • More materials and more applications

33. Tc values for different materials; note the high Tc values for the oxides.

34. It’s magic!

35. 8 Electrical Energy and Power • In a circuit, as a charge moves through the battery, the electrical potential energy of the system is increased by ΔQΔV [AsV=Ws=J] • The chemical potential energy of the battery decreases by the same amount • As the charge moves through a resistor, it loses this potential energy during collisions with atoms in the resistor • The temperature of the resistor will increase

36. Electrical Energy and Power, cont The rate of the energy transfer is power (P): V Units: (C/s)(J/C) =J/s=W 1J=1Ws=1Nm W=AV

37. Electrical Energy and Power, cont • From Ohm’s Law, alternate forms of power are (use V=IR and I=V/R) Joule heat (I2R losses)

38. Electrical Energy and Power, final • The SI unit of power is Watt (W) • I must be in Amperes, R in Ohms and V in Volts • The unit of energy used by electric companies is the kilowatt-hour • This is defined in terms of the unit of power and the amount of time it is supplied • 1 kWh =(103 W)(3600 s)= 3.60 x 106 J

39. 9 Electrical Activity in the Heart Heart beat Initiation • Every action involving the body’s muscles is initiated by electrical activity • Voltage pulses cause the heart to beat • These voltage pulses (1 mV) are large enough to be detected by equipment attached to the skin

40. Electrocardiogram (EKG) • A normal EKG • P occurs just before the atria begin to contract • The QRS pulse occurs in the ventricles just before they contract • The T pulse occurs when the cells in the ventricles begin to recover

41. Abnormal EKG, 1 • The QRS portion is wider than normal • This indicates the possibility of an enlarged heart

42. Abnormal EKG, 2 • There is no constant relationship between P and QRS pulse • This suggests a blockage in the electrical conduction path between the SA and the AV nodes • This leads to inefficient heart pumping

43. Abnormal EKG, 3 • No P pulse and an irregular spacing between the QRS pulses • Symptomatic of irregular atrial contraction, called fibrillation • The atrial and ventricular contraction are irregular

44. Implanted Cardioverter Defibrillator (ICD) Dual chamber ICD • Devices that can monitor, record and logically process heart signals • Then supply different corrective signals to hearts that are not beating correctly Monitor lead