1、GRE Physics Review1GRE Review: Lab MethodsOfficially, this section contains: “data and error analysis, electronics, instrumentation, radiationdetection, counting statistics, interaction of charged particles with matter, lasers and opticalinterferometers, dimensional analysis, fundamental application
2、s of probability and statistics”After looking through the practice tests, the key things to review are how to calculate errors, howlasers work, how to read data charts or instrumentation output, and how to calculate I, R, and Vgiven a circuit diagram (i.e. Kirchoffs Law, series vs. parallel, capacit
3、ance, etc.).A good textbook to skim over for the basics is Giancoli “Physics for Scientists and Engineers:Volume II”.(And I noticed a few practice problems involving the Michelson Interferometer check outhttp:/ .B. CAPACITORSThe Capacitance of two oppositely charged conductors in a uniform dielectri
4、c medium isUnits: Farads = 0QCVcoulwhere Q = the total charge in either conductorV0 = the potential difference between the two conductors.EXAMPLE:Capacitance of the parallel-plate capacitor:Esza is the permittivity of the homogeneous dielectricsD.On lower plate: nzDn is the normal value of D.On uppe
5、r plate:Dn = DzV0 = The potential difference lowerupE.dL0sz0QCV+ + + + + + +z=0+pss- - - - - - - z=dpconductorsurfaceGRE Physics Review2Q = sS and V0 = sdconsidering conductor planes of area S are of linear dimensions much greater than d.Total energy stored in the capacitor:22011sdEvolWzsCVCMultiple
6、 dielectric capacitorsA parallel-plate capacitor containing two dielectrics with the dielectric interface parallel to the conducting plates;C = 1/(d1/1S) + (d2/2S).Cwhere 1Sd2CV0 = A potential difference between the plates= E1d1 + E2d2E1 = s1 = The surface charge density = D1 = 1E1= 021d01212.sSQCVd
7、sCC. CURRENT AND RESISTANCEDEFINITIONSCurrent: amperesdqitArea S12d2d1dc22c11conductingplatesGRE Physics Review3where i = Electric Currentq = Net Charget = TimeCurrent Density and Current:Amperes/m2ijAwhere j = Current Densityi = CurrentA = Cross-sectional AreaMean Drift Speed:Djvnewhere v0 = Mean D
8、rift Speedj = Current Densityn = Number of atoms per unit volume.Resistance:Ohms ()VRiwhere R = ResistanceV = Potential Differencei = CurrentResistivity:Ohm meters ( m)Ejwhere = ResistivityE = Electric Fieldj = Current DensityPower:Watts (w)2VPIRwhere P = PowerI = CurrentV = Potential DifferenceR =
9、Resistance D. CIRCUITSElectromotive Force, EMF() dwqGRE Physics Review4where = Electromotive Forcew = Work done on Chargeq = Electric ChargeCurrent in a Simple CircuitiRwhere i = Current = Electromotive ForceR = ResistanceResistances:RTotal = (R1+R2+R3) (in series)(in parallel)123TotalRRThe Loop The
10、oremV1 + V2 + V3 . = 0For a complete circuit loopEXAMPLESimple circuit with resistorVab = iR = + ir iR ir = 0Then +Raiibri l+R1R2R3GRE Physics Review5NOTE: If a resistor is traversed in the direction of the current, the voltage change is represented as a voltage drop, iR. A change in voltage while t
11、raversing the EMF (or battery) in the direction of the EMF is a voltage rise +.Circuit With Several Loops 0niEXAMPLEi1 + i2 + i3 = 0Multiloop circuitRC CIRCUITS (RESISTORS AND CAPACITORS)RC charging and dischargingDifferential Equations dqRtCOAn RC circuitCharge in the Capacitor 1tRCtqeR2AF1 2R1 R3C
12、BE Di1 i2i3(Charging)(Discharging)a iCRsb+(Charging)(Discharging)GRE Physics Review6Charge in the Resistor tRCtieiwhere e = 2.71828 (Exponential Constant)KIRCHOFFS CURRENT LAWThe algebraic sum of all currents entering a node equals the algebraic sum of all current leaving it. 10NniKIRCHOFFS VOLTAGE
13、LAW (SAME AS LOOP THEOREM)The algebraic sum of all voltages around a closed loop is zero.THEVENINS THEOREMIn any linear network, it is possible to replace everything except the load resistor by an equivalent circuit containing only a single voltage source in series with a resistor (Rth Thevenin resi
14、stance), where the response measured at the load resistor will not be affected.Procedures to Find Thevenin Equivalent:1) Solve for the open circuit voltage Voc across the output terminals.Voc = Vth2) Place this voltage Voc in series with the Thevenin resistance which is the resistance across the ter
15、minals found by setting all independent voltage and current sources to zero. (i.e., short circuits and open circuits, respectively.)RLC CIRCUITS AND OSCILLATIONSThese oscillations are analogous to, and mathematically identical to, the case of mechanical harmonic motion in its various forms. (AC curr
16、ent is sinusoidal.)SIMPLE RL AND RC CIRCUITSSource Free RL Circuit(Charging)(Discharging)LinearActiveNetworkxyxy+RL VL+i(t)GRE Physics Review7Properties: Assume initially i(0) = I0.A) RLdiitB) , = time constant = 0()titIeI LRC) Power dissipated in the resistor = .22RtLRPiD) Total energy in terms of
17、heat in the resistor = WR = LI02.1Source Free RC CircuitProperties: Assume initially (0) = V0A) .dvCtRB) ./()0etCtRCC) 1()tii()tRCieTHE RLC CIRCUITSParallel RLC Circuit (source free)Circuit Diagram:KCL equation for parallel RLC circuit: 01();tdiCRLtand the corresponding linear, second-order homogene
18、ous differential equation is2dvCTtLGeneral Solution: 12;SttVAe+i(t)RC v(t)R CL iVGRE Physics Review8where 21,21SRCLCor 2,0;where = exponential damping coefficient never frequency = 1RCand 0 = resonant frequency = 1LCCOMPLETE RESPONSE OF RLC CIRCUITThe general equation of a complete response of a sec
19、ond order system in terms of voltage for an RLC circuit is given by. 12Sttf(t) =V+ AeB(i.e., constant for DC excitation)NOTE: A and B can be obtained by1) Substituting at t = 0+2) Taking the derivative of the response, i.e.,12SttdvAeBwhere at t = 0+ is known.D. THE LASERLight Amplification by Stimul
20、ated Emission of Radiation Properties1. The light is coherent. (Waves are in phase)2. Light is nearly Monochromatic. (One wavelength)3. Minimal divergence4. Highest intensity of any light source.Many atoms have excited energy levels which have relatively long life-times. (10-3s instead of 10-8 s). T
21、hese levels are known as metastable.overdampedcritically dampedunderdampedt(a)v(t)forcedresponse Natural responseGRE Physics Review9Through a process known as population inversion, the majority of an assembly of atoms is brought to an excited state.Population inversion can be accomplished through a
22、process known as optical pumping, where atoms of a specific substance, such as ruby, are exposed to a given wavelength of light. This wavelength is enough to excite the ruby atoms just above metastable level. The atoms rapidly lose energy and fall to the metastable level.RubyTransition (energy lossw
23、ithout radiation)Laser TransmissionOptical PumpingOnce population inversion has been obtained, induced emission can occur from photons dropping from an excited metastable state to ground state. The photons have a wavelength equal to the wavelength of photons produced by each individual atom. The radiated light waves will be exactly in phase with the incident waves, resulting in an enhanced beam of coherent light. Hence the familiar Laser effect.Ground State2.25 eV1.79 eV
