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23 Pages

### chapter28

Course: PHYS 1304, Spring 2008
School: SMU
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Word Count: 1178

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28 Direct Chapter Current Circuits 1. 2. 3. 4. 5. R connections in series and in parallel Define DC (direct current), AC (alternating current) Model of a battery Circuits with 2+ batteries Kirchhoff's Rules RC circuit :&quot;&quot; Confucius says, reviewing helps one learn new knowledge. Concepts: Charge: positive, negative, conserve, induction. potential Electric: field flux Electrostatic equilibrium:...

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28 Direct Chapter Current Circuits 1. 2. 3. 4. 5. R connections in series and in parallel Define DC (direct current), AC (alternating current) Model of a battery Circuits with 2+ batteries Kirchhoff's Rules RC circuit :"" Confucius says, reviewing helps one learn new knowledge. Concepts: Charge: positive, negative, conserve, induction. potential Electric: field flux Electrostatic equilibrium: no moving charge. Current: moving charge Capacitance: potential over charge Resistance: potential over current Resistance and Resistivity (conductivity) and temperature: Laws: Coulomb's: force and charge. Gauss's: Ohm's: electric flux and charge. electric potential and current. Circuits and components: Symbols: Power: Capacitor: Resistor: wire, battery, C, Switch... current time potential difference: in parallel in series discuss today Resistor connections In series. Condition: Req V I V1 I V1 V2 I V2 I1 I2 V V1 I1 V1 V2 I2 V2 R1 R2 In parallel. Condition: 1 Req I V I1 I2 V I I1 I2 V I1 V1 V1 V1 I2 V2 V2 1 R1 1 R2 V2 Resistor connections In series, I I1 I2 : voltage sharing power sharing V1 V2 P1 P2 R1 R2 R1 R2 V1 V2 In parallel, V V1 current sharing I1R1 P1R1 V2 : R2 R1 R2 R1 power sharing I1 I2R2 , or I2 P1 P2R2 , or P2 Resistors connections, summary In series Req R1 R2 R3 ... V1 V2 P1 P2 R1 R2 R1 R2 In parallel 1 Req 1 R1 1 R2 1 R3 ... I1R1 I2R2 PR1 P2R2 1 Resistors in Series Example Use the active figure to vary the battery voltage and the resistor values Observe the effect on the currents and voltages of the individual resistors PLAY ACTIVE FIGURE Resistors in Parallel Example Use the active figure to vary the battery voltage and the resistor values Observe the effect on the currents and voltages of the individual resistors PLAY ACTIVE FIGURE Combinations of Resistors The 8.0- and 4.0resistors are in series and can be replaced with their equivalent, 12.0 The 6.0- and 3.0resistors are in parallel and can be replaced with their equivalent, 2.0 These equivalent resistances are in series and can be replaced with their equivalent resistance, 14.0 More examples Direct Current and Alternating Current When the current direction (not magnitude) in a circuit does not change with time, the current is called direct current Most of the circuits analyzed will be assumed to be in steady state: with constant magnitude and direction, like the one powered through a battery. When the current direction (often also the magnitude) in a circuit changes with time, the current is call alternating current. The current from your car's alternator is AC. Model of a battery Two parameters, electromotive force (emf), , and the internal resistance r, are used to model a battery. When a battery is connected in a circuit, the electric potential measured at its + and terminals are called The terminal voltage V, with V = Ir If the internal resistance is zero, the terminal voltage equals the emf The internal resistance, r, does not change with external load resistance R, and this provides the way to measure the internal resistance. V battery V load PLAY ACTIVE FIGURE Battery power figure The power the battery generates (through chemical reactions): p I (R r ) I 2 The power the battery delivers to the load, hence efficiency: pload V I R I2 efficiency = pload p R R r battery V load The maximum power the battery can deliver to a load R pload 2 2 We have From pload R I and (R r ) I (R r )2 Where the emf is a constant once the battery is given. From dpload dR 1 (R r ) 2 2R 2 (R r )3 0 We get R r to be the condition for maximum pload , or power delivered to the load. Battery power figure One can also obtain this result from the plot of pload Where when R battery V 2 (R r )2 r R pload reaches the maximum value The efficiency of the battery at this point is 50% because load pload efficiency = p R R r More complicated circuits, circuits with 2+ batteries: Kirchhoff's Rules A typical circuit that goes beyond simplifications with the parallel and series formulas: the current in the diagram. Kirchhoff's rules can be used to solve problems like this. Rule 1: Kirchhoff's Junction Rule Junction Rule, from charge conservation: The sum of the currents at any junction must equal zero Mathematically: I junction 0 The example on the left figure: I 1 - I2 - I3 = 0 Rule 2: Kirchhoff's Loop Rule Choose your loop Loop Rule, from energy conservation: The sum of the potential differences across all elements around any closed circuit loop must be zero Mathematically: V1 V2 Loop direction V closed loop 0 Remember two things: 1. A battery supplies power. One needs to pay attention the Potential rises from the "" sign (+ or -) of these potential terminal to "+" terminal. changes, following the chosen loop 2. Current follows the direction of direction. electric field, hence the decrease of potential. Kirchhoff's rules Strict steps in solving a problem Step 1: choose and mark the loop. Step 2: choose and mark current directions. Mark the potential change on resistors. Step 3: apply junction rule: I1 I2 L1 + I3 + L2 + I1 I2 I3 0 Step 4: apply loop rule: L1: +2.00I3 12.0 4.00I2 L2: 0 8.00 2.00I3 6.00I1 0 Step 5: solve the three equations for the three variables. RC Circuits, solve with Kirchhoff's rules When a circuit contains a resistor and a capacitor connected in series, the circuit is called a RC circuit. Current in RC circuit is DC, but the current magnitude changes with time. There are two cases: charging (b) and discharging (c). Not a circuit charging Discharging Charging a Capacitor When the switch turns to position a, current starts to flow and the capacitor starts to charge. + Loop + Kirchhoff's rule says: Vc VR 0 Re-write the equation in terms of the charge q in C and the current I, and then only the variable q: q q dq RI 0 and then R 0 C C dt Solve for q: The current I is q t C 1 e t RC I t dq dt t RC e R Here RC has the unit of time t, and is called the time constant. Charging a Capacitor, graphic presentation The charge on the capacitor varies with time q(t) = C (1 e-t/RC) = Q(1 e-t/RC) The current decrease with time I( t ) e R t RC is the time constant = RC Discharging a Capacitor When the switch turns to position b, after the capacitor is fully charged to Q, current starts to flow and the capacitor starts to discharge. + Loop + Kirchhoff's rule says: Vc VR 0 Re-write the equation in terms of the charge q in C and the current I, and then only the variable q: q q dq RI 0 and then R 0 C C dt Solve for q: The current I is t t dq Q RC I t e q t Qe RC dt RC Ii Q RC RC Circuit, Example Adjust the values of R and C Observe the effect on the charging and discharging of the capacitor PLAY ACTIVE FIGURE
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SMU - PHYS - 1304
A different reviewA review of the following topics by working on problems1. Electric charge, potential, force, field and flux. Coulomb's Law Gauss's Law. 2. Capacitance and resistance. Ohm's Law. 3. Circuits. Kirchhoff's Rules.Electric field of a
SMU - PHYS - 1304
Reviews on electrastatics Electric charges: Two types, positive and negative. Like charges repel, unlike charges attract. Charges conserve. The force between two point charges is governed by Coulomb's Law. Electric charges generate electric fields.
SMU - PHYS - 1304
Refraction, the Snell law Light in geometric optics is discussed in rays and represented by a straight line with an arrow indicating the propagation direction. Light propagates in straight lines in homogenous medium. Light reflects on interface of
SMU - PHYS - 1304
Quiz 1Name:ID:Key1.Positive charges with magnitudes 3.50 mC (=3.5010-3C) and 6.75 mC are located at the origin and at the point (10.00, 0) meters on the x axis, respectively. What are the strength and direction of the field they generate at
SMU - PHYS - 1304
Geometric optics Light in geometric optics is discussed in rays and represented by a straight line with an arrow indicating the propagation direction. Light propagates in straight lines in homogenous medium. The speed of light in vacuum is a consta
SMU - PHYS - 1304
Chapter 36Image Formation 2 1. Thin Lens 2. Multi lens/mirror systemThin lenses Lenses are commonly used to form images by refraction. We discuss about spherical lenses only. They are part of two spheres. There are two types of lensesPrinci
SMU - PHYS - 1304
Quiz 0Name: ID:Mathematics is the language in sciences. Certain amount of knowledge in mathematics is required to understand the material in this course. To help you check how well you are prepared in math for this course, please complete this qu
SMU - PHYS - 1304
Electric Current Electric field exerts forces on charges inside it; Charges move under the influence of an electric field. EVV V VIdq dt The amount of charge moves through a cross section in unit time is defined as the electric current. Fo
SMU - PHYS - 1304
Electric field and its work on chargesWe introduced the concept of electric field and this formula: F = q E What can you associate force with? Motion or acceleration from F = ma. Work, from W = FX (a review on vector dot product here). Exampl
SMU - PHYS - 1304
Direct Current Circuits Direct Current (DC) and circuits: Direct Current: the DIRECTION of the current in a circuit does not change with time. The amplitude of the current may or may not change with time. The opposite, the Alternating Current (A
SMU - PHYS - 1304
Name Quiz 4 ID1.A long, straight wire carries current I = 10 A. A right-angle bend is made in the middle of the wire. The bend forms an arc of a circle of radius r = 50 cm. Determine the magnetic filed at the center of the arc (both magnitude and
SMU - PHYS - 1304
Electrostatics1. Charge force:Like sign charges repel, unlike sign charges attract. Coulomb's Law: direction and magnitude of force between two point charges. Introduced to explain interaction over a distance. Field lines: start from positive c
SMU - PHYS - 1304
Mid-termName:ID:(8 points each question) 1. Calculate the electric field strength 2 meters away from charge Q of quantity k is 8.99109 Nm2/C2, the constant in Coulomb's Law. 2. State Coulomb's Law and Gauss's Law in your own language and write o
SMU - PHYS - 1304
Magnets Magnet; an object that Attract certain types of material, like iron. Attract or repel another magnet. All magnets have two poles, named the &quot;north pole&quot; and the &quot;south pole&quot;. The reason for the poles are called north or south is because
SMU - PHYS - 1304
Homework 11. In a process known as beta decay, a neutron (charge 0) in an unstable atomic nucleus becomes a proton (charge +e), ejecting an electron (charge e) and an antineutrino. (a) Use conservation of charge to determine the charge of an antineu
SMU - PHYS - 1304
Chargespositive (+) negative (-) conservationForce (field) qq 1 q1 q 2 F12 k e 1 2 2 r12 r12 4 0 r 2 rForce between point charges Force on charge in the field Fe qE E E dA q0Connect field with its source: chargePotential (e
SMU - PHYS - 1304
Capacitance, Capacitors and Circuits. Start with a reviewThe capacitance C is defined asQ C VTo calculate the capacitance, one starts by introduce Q to the object, and use the Laws we have so far to calculate for the V.Example: Capacitance of
SMU - PHYS - 1304
Electromagnetic Induction Moving charges inside a magnetic field experience magnetic force. This force will redistribute charges in a moving conductor so that an electric field will be established because of these displaced charges. This is called
SMU - PHYS - 1304
Homework 151. The focal length of a thin lens is 0.110 m. You want to use it to produce a real image at 0.600 meters from the lens. How far from the lens should the object be placed? The focal length of a thin lens is -9.00 cm. You place an object 1
SMU - PHYS - 1304
Quiz 4Name:ID:1.You place an object 34.0 cm in front of a convex mirror and the image produced is half the height of the object. What is the focal length of the mirror? State your answer with the correct sign.2.A convex mirror has a radius
SMU - PHYS - 1304
Homework 131. Two 3.0 meter-tall planar mirrors are placed facing and parallel to each other 0.75 m apart. If a ray of light just passes the bottom edge of one mirror and strikes the other at an incident angle of 10, how many reflections will the li
SMU - PHYS - 1304
Discussion about the mid-term 4. A high voltage generator is made of a metal sphere with a radius of 6 cm sits on an insulating post. A wire connects to the sphere's inner surface through a small hole. The wire carriers a current of 1 A and flows int
SMU - PHYS - 1304
Homework 111. A laser beam with vacuum wavelength 632.8 nm (1nm = 10-9m) is incident from air onto a block of Lucite. The line of sight of the photograph is perpendicular to the plane in which the light moves. Use a protractor to measure the angles
SMU - PHYS - 1304
Mid-termName:ID:(8 points each question) 1 1. Charge Q1 of is placed 1 meter away from charge Q2 of k1 . The quantity k is k8.99109 Nm2/C2, the constant in Coulomb's Law. What is the force on Q2? 2. State Gauss's Law and Ampere's Law in your
SMU - PHYS - 1304
Chapter 27Current Resistance And ResistorElectric Current, the definitionAssume charges are + + moving perpendicular to a A + + surface of area A + + If Q is the amount of charge that passes through A in time t, then I the average current is
SMU - PHYS - 1304
The Gauss' Law Electric field of A point charge Q1The Gauss' Law Electric field of An infinitely long straight wire with charge density .2The Gauss' Law3The Gauss' Law Electric field of An infinitely large plane with charge densi
SMU - PHYS - 1304
Mid-termName:ID:Key1. FkQ1 Q 2 r2k1 k1 k 2r1 121NF on Q2 follows the line defined by Q1 and Q2, and points to Q1. 2. Gauss' Law: the electric flux through an enclosed surface equals to the charge inside divided by the consta
SMU - PHYS - 1304
Chapter 33Alternating Current (AC) R, L, C in AC circuitsAC, the descriptionA DC power source, like the one from a battery, provides a potential difference (a voltage) that does not change its polarity with respect to a reference point (often t
SMU - PHYS - 1304
Geometric optics Light reflects on interface of two media, following the law of reflection:Reflected light r iNormal of the interfaceIncident lightwith respect to the normal of the interface. with respect to the normal of the interface.
SMU - PHYS - 1304
Homework 91. A current pulse is fed to the partial circuit shown in the figure. The current pulse is 10.0 A and its duration is from t =0 to t = 200 s. Determine the current in the inductor and the resistor as a function of time.2.A 1.00 F capac
SMU - PHYS - 1304
Chapter 27Current Resistance And ResistorElectric Current, the definitionAssume charges are + + moving perpendicular to a A + + surface of area A + + If Q is the amount of charge that passes through A in time t, then I the average current is
SMU - PHYS - 1304
Homework 71. A conductor consists of a circular loop of radius R and two straight, long sections as shown in the figure. The wire lies in the plane of the paper and carries a current I. Find an expression for the vector magnet field at the center of
SMU - PHYS - 1304
Coulomb's Law Charges: A property of matter. Positive and Negative charges, the unit of charge is Coulomb. Like sign charges repel, unlike sign charges attract. Charges conserve in a system. Conductor, insulator and ground. Force between two
SMU - PHYS - 1304
Introductory Physics IIWelcome and Congratulations This is the largest class I have ever had at SMU. Let's work together to make it the best one. I congratulate you on making this wise decision to learn physics, especially Electricity and Magneti
SMU - PHYS - 1304
Quiz 2Name:ID:1.A straight, infinitely long insulating rod has a radius a. Positive charges are evenly distributed on the rod with a charge density . Calculate the electric field in space including that inside the rod.2.A flat, infinitely
SMU - PHYS - 1304
Homework 5Step 1, formulas or related concepts.In serial:In parallel: Step 2, known quantities.,,Step 3, direct application of the formulas/concept or the condition to form an equation. 1 1 a) 5.96( F ) 1 1 1 20 6 15 3
SMU - PHYS - 1304
Electric Charge and Coulomb's Law Electric charge The positive charge and negative charge: Matter is made of atoms. Inside an atom, there is the nucleus that is surrounded by electrons. Inside the nucleus, there are two particles called proton and
SMU - PHYS - 1304
Chargespositive (+) negative (-) conservationForce (field) qq 1 q1 q 2 F12 k e 1 2 2 r12 r12 4 0 r 2 rForce between point charges Force on charge in the field Fe qE E E dA q0Connect field with its source: chargePotential (e
SMU - PHYS - 1304
Quiz 0Name: ID:Mathematics is the language in sciences. Certain amount of knowledge in mathematics is required to understand the material in this course. To help you check how well you are prepared in math for this course, please complete this qu
SMU - PHYS - 1304
Capacitance, Capacitors and Circuits. Start with a reviewThe capacitance C is defined asQ C VTo calculate the capacitance, one starts by introduce Q to the object, and use the Laws we have so far to calculate for the V.Example: Capacitance of
SMU - PHYS - 1304
Homework 31. Four closed surfaces, S1 through S4, together with the charges -2Q, Q and Q are sketched in the following figure (The colored lines are the intersections of the surfaces with the page.) find the electric flux through each surface.2.
SMU - PHYS - 1304
Homework 2 1. Two charges of +2q and -5q are placed on a line. The distance between the two charges is d. (a) There is a point on the line where the strength of the electric field due to the two charges is zero. Describe where the point is, relative
SMU - PHYS - 1304
Class projectName:ID:Please select two and only two questions out of the three questions. Write clearly your answers to the questions you choose. Each correctly answered question is 2 bonus points counted towards the final grade. Very limited p
SMU - PHYS - 1304
Homework 11. In a process known as beta decay, a neutron (charge 0) in an unstable atomic nucleus becomes a proton (charge +e), ejecting an electron (charge e) and an antineutrino. (a) Use conservation of charge to determine the charge of an antineu
SMU - PHYS - 1304
Outline and review Review on Coulomb's Law and electric field. Discussion about electric potential (energy). Coulomb's Law in electrostatics governs the forces between two point charges:1Review: Coulomb's Law While magnitude of the force i
SMU - PHYS - 1304
Chapter 28Direct Current Circuits1. 2. 3. 4. 5. R connections in series and in parallel Define DC (direct current), AC (alternating current) Model of a battery Circuits with 2+ batteries Kirchhoff's Rules RC circuit:&quot;Confucius says, reviewing h
SMU - PHYS - 1304
Quiz 1Name:ID:1.Positive charges with magnitudes 3.50 mC (=3.5010-3C) and 6.75 mC are located at the origin and at the point (10.00, 0) meters on the x axis, respectively. What are the strength and direction of the field they generate at the p
SMU - PHYS - 1304
Electromagnetic Induction We introduced motional emf and Faraday's Law through these two examples: Today we will the discussion about Faraday's Law of Induction and introduce the following new law and concepts: Lenz's Law, mutual induction and sel
SMU - PHYS - 1304
Chapter 35The Laws of Geometric OpticsThe Ray Approximation of Light in Geometric Optics Geometric optics studies the propagation of light. Light travels in a straight-line path in a uniform medium. Light changes its direction when it meet
SMU - PHYS - 1304
Capacitors in Direct Current Circuits One capacitor in a DC circuit: Two capacitors in a DC circuit: In series:1Capacitors in Direct Current Circuits Two capacitors in a DC circuit: In parallel: Multiple capacitors: In series: In par
SMU - PHYS - 1304
Chapter 36Image Formation 1: 1. Flat mirror 2. Spherical mirrorsFind the image, method 2, the mirror/lens equationWhen a spherical mirror is given, we know its radius R. Under paraxial condition, the angle NCF is small, and from the law of reflec
SMU - PHYS - 1304
Chapter 27Current Resistance And ResistorReviewThe current is defined and its unit is ampere (A), a base unit in the SI system.++ ++A+ +IdQ dtIThe charges passing through the area could be positive or negative or both. They are ca
SMU - PHYS - 1304
Mid-term review Charges and current. Coulomb's Law. Electric field, flux, potential and Gauss's Law. Passive circuit components. Resistance and resistor, Ohm's Law. Resistance as a function of temperature. Power dissipated through a resistor. C
SMU - PHYS - 1304
Chapter 30Sources of the Magnetic FieldA whole picture helpsCharge q as source Gauss's Law Faraday's Law Electric field ECurrent I as source Ampere's LawMagnetic field B FE qEAmpere-Maxwell Law FB qv BForce on q in the fieldForc
SMU - PHYS - 1304
Final ExamName:ID:1.(10 points) In an X-Y coordinate system with unit in meter, charge Q1 of 7.865 C is placed at (-1,0). Charge Q2 of -7.865 C is placed at (1,0). A third charge Q3 of charge 1 C is placed at (0,1), (a) What is the total force
SMU - PHYS - 1304
abc1
SMU - PHYS - 1304
Find image with a thin lenshodoFFdiObjectfhihodohiFFObjectdif1Analytical calculations Thin lens equation.hohi1 di1 do1 fmagnification : mhi hodi do2Analytical calculations Lens maker's equa
SMU - PHYS - 1304
Electric Flux and Gauss LawElectric flux, definition Ei Ai cos i Ei EE AilimAiEEi Ai 0 E dAsurfaceGauss lawE E dAqin0qin is the net charge inside the surfaceApplying Gauss Law To use Gauss law, you need to choose
SMU - PHYS - 1304
Quiz on the math needed todayBWhat is the result of this integral:B1 dx 2 A x1 xBA1 A1 B1 dx 2 A xIf y( x) is known and y( x)z ( x) dy( x) dxz ( x)dx, what is z ( x)? If y(r ) is known and y(r ) z (r ) y (r ), z(r )
SMU - PHYS - 1304
A different reviewA review of the following topics by working on problems1. Electric charge, potential, force, field and flux. Coulomb's Law Gauss's Law. 2. Capacitance and resistance. Ohm's Law. 3. Circuits. Kirchhoff's Rules.Electric field of a
SMU - PHYS - 1304
Chapter 36Image Formation 2 1. Thin Lens 2. Multi lens/mirror systemSpherical mirror formulasFocal length and sphere radius:fR 2Converging mirrorfR 2Diverging mirrorObject distance, image distance and focal length:1 pM1 qhI hO