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Week5_1 Drexel PHYS 102
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  • Title: Week5_1
  • Type: Notes
  • School: Drexel
  • Course: PHYS 102
  • Term: Spring

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20.54. Problem (a) How much charge can be placed on a capacitor with air between the plates before it breaks down if the area of each of the plates is 5.00 cm2? (b) Find the maximum charge assuming polystyrene is used between the plates instead of air. 1 Chapter 21 Current and Direct Current Circuits Electric Current Electric current is the rate of flow of charge through a surface The SI unit of current is the Ampere (A) 1A=1C/s The symbol for electric current is I 3 Average Electric Current Assume charges are moving perpendicular to a surface of area A If Q is the amount of charge that passes through A in time t, the average current is Iavg Q = t 4 Instantaneous Electric Current If the rate at which the charge flows varies with time, the instantaneous current, I, can be found Q dQ I = lim = t 0 t dt 5 Problem 21.2. A small sphere that carries a charge q is whirled in a circle at the end of an insulating string. The angular frequency of revolution is . What average current does this revolving charge represent? 6 Direction of Current The charges passing through the area could be positive or negative or both It is conventional to assign to the current the same direction as the flow of positive charges The direction of current flow is opposite the direction of the flow of electrons It is common to refer to any moving charge as a charge carrier 7 Current and Drift Speed Charged particles move through a conductor of crosssectional area A n is the number of charge carriers per unit volume n A x is the total number of charge carriers 8 Current and Drift Speed, cont The total charge is the number of carriers times the charge per carrier, q Q = (n A x) q The drift speed, vd, is the speed at which the carriers move Rewritten: Q = (n A vd t) q Finally, current, I = Q/t = nqvdA 9 vd = x/ t Consider positive and negative charges moving horizontally through the four regions shown in Figure 21.3. Rank the currents in these four regions, from lowest to highest. 1. 2. 3. (d), (b) = (c), (a) (b), (c), (a), (d) (c) = (b), (a), (d) 33% 33% 33% (c ), ), (c ), (a ) = ), (b ) (d (b (c )= (b ) ,( a) ,( d) (a ) ,( d) 10 10 Charge Carrier Motion in a Conductor The zig-zag black line represents the motion of charge carrier in a conductor The net drift speed is small The sharp changes in direction are due to collisions The net motion of electrons is opposite the direction of the electric field 11 Motion of Charge Carriers , cont When the potential difference is applied, an electric field is established in the conductor The electric field exerts a force on the electrons The force accelerates the electrons and produces a current 12 Motion of Charge Carriers, final The changes in the electric field that drives the free electrons travel through the conductor with a speed near that of light This is why the effect of flipping a switch is effectively instantaneous Electrons do not have to travel from the light switch to the light bulb in order for the light to operate The electrons are already in the light filament They respond to the electric field set up by the battery 13 Drift Velocity, Example Assume a copper wire, with one free electron per atom contributed to the current The drift velocity for a 12 gauge copper wire carrying a current of 10 A is 2.22 x 10-4 m/s This is a typical order of magnitude for drift velocities 14 Current Density J is the current density of a conductor It is defined as the current per unit area J = I / A = n q vd This expression is valid only if the current density is uniform and A is perpendicular to the direction of the current J has SI units of A / m2 The current density is in the direction of the positive charge carriers 15 Resistance In a conductor, the voltage applied across the ends of the conductor is proportional to the current through the conductor The constant of proportionality is the resistance of the conductor V R I 16 Resistance, cont SI units of resistance are ohms () 1=1V/A Resistance in a circuit arises due to collisions between the electrons carrying the current with the fixed atoms inside the conductor 17 Ohm's Law Ohm's Law states that for many materials, the resistance is constant over a wide range of applied voltages Most metals obey Ohm's Law Materials that obey Ohm's Law are said to be ohmic 18 Ohm's Law, cont Not all materials follow Ohm's Law Materials that do not obey Ohm's Law are said to be nonohmic Ohm's Law is not a fundamental law of nature Ohm's Law is an empirical relationship valid only for certain materials 19 Ohmic Material, Graph An ohmic device The resistance is constant over a wide range of voltages The relationship between current and voltage is linear The slope is related to the resistance 20 Nonohmic Material, Graph Non-ohmic materials are those whose resistance changes with voltage or current The current-voltage relationship is nonlinear A diode is a common example of a non-ohmic device 21 In Figure 21.6b, as the applied voltage increases, does the resistance of the diode 1. 2. 3. Increase decrease remain the same? 33% 33% 33% cr ea In de cr ea re m ai n th e sa m 10 22 se se e? Resistivity Resistance is related to the geometry of the device: l R= A is called the resistivity of the material The inverse of the resistivity is the conductivity: = 1 / and R = l / A Resistivity has SI units of ohm-meters ( . m) 23 Some Resistivity Values 24 Resistance and Resistivity, Summary Resistivity is a property of a substance Resistance is a property of an object The resistance of a material depends on its geometry and its resistivity An ideal (perfect) conductor would have zero resistivity An ideal insulator would have infinite resistivity 25 Resistors Most circuits use elements called resistors Resistors are used to control the current level in parts of the circuit Resistors be can composite or wirewound 26 Resistor Values Values of resistors are commonly marked by colored bands 27 Resistance and Temperature Over a limited temperature range, the resistivity of a conductor varies approximately linearly with the temperature = o [1 + (T - To )] o is the resistivity at some reference temperature To To is usually taken to be 20 C is the temperature coefficient of resistivity SI units of are oC-1 28 Temperature Variation of Resistance Since the resistance of a conductor with uniform cross sectional area is proportional to the resistivity, you can find the effect of temperature on resistance R = Ro [1 + (T - To )] 29 Resistivity and Temperature, Graphical View For metals, the resistivity is nearly proportional to the temperature A nonlinear region always exists at very low temperatures The resistivity usually reaches some finite value as the temperature approaches absolute zero 30 Residual Resistivity The residual resistivity near absolute zero is caused primarily by the collisions of electrons with impurities and imperfections in the metal High temperature resistivity is predominantly characterized by collisions between the electrons and the metal atoms This is the linear range on the graph 31 Superconductors A class of metals and compounds whose resistances go to zero below a certain temperature, TC TC is called the critical temperature The graph is the same as a normal metal above TC, but suddenly drops to zero at TC 32 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 several years Since R = 0 33 Superconductors, cont. HTC 1986 Copper-oxide based 34 Superconductor Application An important application of superconductors is a superconducting magnet The magnitude of the magnetic field is about 10 times greater than a normal electromagnet 35 Electrical Conduction A Model The free electrons in a conductor move with average speeds on the order of 106 m/s Not totally free since they are confined to the interior of the conductor The motion is random The electrons undergo many collisions The average velocity of the electrons is zero There is zero current in the conductor 36 Conduction Model, 2 An electric field is applied The field modifies the motion of the charge carriers The electrons drift in the direction opposite of the field The average drift speed is on the order of 10-4 m/s, much less than the average speed between collisions 37 Conduction Model, 3 Assumptions: The excess energy acquired by the electrons in the field is lost to the atoms of the conductor during the collision The energy given up to the atoms increases their vibration and therefore the temperature of the conductor increases The motion of an electron after a collision is independent of its motion before the collision 38 Conduction Model, 4 The forcerexperienced by an electron is r F = -eE a= me From Newton's Second Law, the acceleration r r r is r F Fe -eE = me = me Applying a motion equation r r r r r eE v = v o + at = v o - t me Since the initial velocities are random, their average value is zero 39 Conduction Model, 5 Let be the average time interval between successive collisions The average value of the final velocity is the drift velocity r r -eE vd = me This is also related to the current: I = n e vd A = (n e2 E / me) A 40 Conduction Model, final Using Ohm's Law, an expression for the resistivity of a conductor can be found: me = 2 ne Note, the resistivity does not depend on the strength of the field The average time is also related to the free mean path: = L avg/vavg 41 Conduction Model, Modifications A quantum mechanical model is needed to explain the incorrect predictions of the classical model developed so far The wave-like character of the electrons must be included The predictions of resistivity values then are in agreement with measured values 42 Electrical Power Assume a circuit as shown As a charge moves from a to b, the electric potential energy of the system increases by QV The chemical energy in the battery must decrease by this same amount 43 Electrical Power, 2 As the charge moves through the resistor (c to d), the system loses this electric potential energy during collisions of the electrons with the atoms of the resistor This energy is transformed into internal energy in the resistor Corresponding to increased vibrational motion of the atoms in the resistor 44 Electric Power, 3 The resistor is normally in contact with the air, so its increased temperature will result in a transfer of energy by heat into the air The resistor also emits thermal radiation After some time interval, the resistor reaches a constant temperature The input of energy from the battery is balanced by the output of energy by heat and radiation 45 Electric Power, 4 The rate at which the system loses potential energy as the charge passes through the resistor is equal to the rate at which the system gains internal energy in the resistor The power is the rate at which the energy is delivered to the resistor 46 Electric Power, final The power is given by the equation: =I V = dU/dt = d(QV)/dt Applying Ohm's Law, alternative expressions can be found: V2 = I V = I 2R = R Units: I is in A, R is in , V is in V, and P is in W 47 Electric Power Transmission Real power lines have resistance Power companies transmit electricity at high voltages and low currents to minimize power losses 48 Problem 21.20. We estimate that 270 million plug-in electric clocks are in the United States, approximately one clock for each person. The clocks convert energy at the average rate 2.50 W. To supply this energy, how many metric tons of coal are burned per hour in coal-fired electric generating plants that are, on average, 25.0% efficient? The heat of combustion for coal is 33.0 MJ/kg. 49

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Path: American University of Sharjah >> MECHANICAL >> 223,224,22 Spring, 2008
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Description: Poetry in the Umayyad Period: Al-Farazdaq, Jarir and al-Akhtal Poetry in the Umayyad Period Tammm b. Ghalib (Ab Firs) al- Farazdaq \"the lump of dough\", famous Arab satirist and panegyrist, died at Basra about 110/728 or 112/730. Born in Yamma on a ...
al-Farazdaq EI [1]
Path: American University of Sharjah >> ARA >> 101,102 Spring, 2008
Description: al- Farazda \"the lump of dough\", properly Tammm b. lib (Ab Firs), famous Arab satirist and panegyrist, died at Ba ra about 110/728 or 112/730. Born in Yamma (Eastern Arabia) on a date which is uncertain (probably after 20/640), this poet i, of the Dr...
ḤassÄn b. Thabit EI [1]
Path: American University of Sharjah >> ARA >> 101,102 Spring, 2008
Description: bit - ir b. arm Of the tribe of rib (later Medna), traditionally known as the \"poet laureate\" of the Prophet, is more correctly the most prominent of several poets who were associated with the rise of Islam , and one who already had an establis...
Ḳaṣīda EI [1]
Path: American University of Sharjah >> ARA >> 101,102 Spring, 2008
Description: a da 1. In Arabic. a da collective a d is the name given in Arabic to some poems of a certain length. It is derived from the root a ada, \"to aim at\", for the primitive a da was intended to eulogize the tribe of the poet and denigrate the opposi...
Ḳabīla EI [1]
Path: American University of Sharjah >> ARA >> 101,102 Spring, 2008
Description: abla Denotes a large agnatic group, the members of which claim to be descended from one common ancestor; this word is generally understood in the sense of tribe. It derives from the Arabic root -b-l, of which the form bala signifies to meet, to be...
Jarir EI [1]
Path: American University of Sharjah >> ARA >> 101,102 Spring, 2008
Description: arr b. A iyya b. al- a ayfa) b. Badr Was among the most important -writers of the Umayyad period (the other two were his rivals al and al-Farazda [qq.v.], and may be considered one of the greatest Islamic-Arabic poets of all time. He belonged...
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Path: American University of Sharjah >> ARA >> 101,102 Spring, 2008
Description: ...
al-Farazdaq [1]
Path: American University of Sharjah >> ARA >> 101,102 Spring, 2008
Description: From the wafayat al-a`yan of Ibn Khallikan Abu-l ,Abbas Ahmad b. Khallikan (1211-1282 CE) was born at Arbela, Iraq. By his talents and his writings he received the title of the most learned man and the ablest historian of that city. He studied jurisp...
Statics HW _6 Spring 2008
Path: American University of Sharjah >> MCE >> 240 Spring, 2008
Description: American University of Sharjah College of Engineering Mechanical Engineering Department Spring 2008 Due Date: Sunday, February 24th, 2008. Statics MCE 220 Assignment # 6 Solve the following problems from the textbook (Engineering Mechanics: Static...
Statics HW _5 Spring 2008
Path: American University of Sharjah >> MCE >> 240 Spring, 2008
Description: American University of Sharjah College of Engineering Mechanical Engineering Department Spring 2008 Due Date: Tuesday, February 19th, 2008. Statics MCE 220 Assignment # 5 Solve the following problems from the textbook (Engineering Mechanics: Stati...

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