GRE,SUB,physics 考试总结 必备 资料.doc

GRE Physics ReviewGRE 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 applications 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, capacitance, 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 out/physics/MichelsonInterferometer.html .B. CAPACITORS The Capacitance of two oppositely charged conductors in a uniform dielectric medium isUnits: Farads = where Q = the total charge in either conductor V0 = the potential difference between the two conductors.EXAMPLE: + + + + + + +z=0+pss- - - - - - - z=dpconductorsurfaceCapacitance of the parallel-plate capacitor: e is the permittivity of the homogeneous dielectricOn lower plate:Dn is the normal value of D.On upper plate:Dn = DzV0 = The potential difference Q = rsS and V0 = considering conductor planes of area S are of linear dimensions much greater than d.Total energy stored in the capacitor:Multiple dielectric capacitorsArea Se1e2d2d1dc2e2c1e1conductingplatesA parallel-plate capacitor containing two dielectrics with the dielectric interface parallel to the conducting plates; C = 1/(d1/e1S) + (d2/e2S).where V0 = A potential difference between the plates = E1d1 + E2d2E1 = rs1 = The surface charge density = D1 = e1E1 = C. CURRENT AND RESISTANCEDEFINITIONSCurrent:ampereswhere i = Electric Current q = Net Charge t = TimeCurrent Density and Current: Amperes/m2where j = Current Density i = Current A = Cross-sectional AreaMean Drift Speed:where v0 = Mean Drift Speed j = Current Densityn = Number of atoms per unit volume.Resistance: Ohms (W)where R = Resistance V = Potential Difference i = CurrentResistivity:Ohm meters (W m)wherer = ResistivityE = Electric Fieldj = Current DensityPower:Watts (w)whereP = PowerI = CurrentV = Potential DifferenceR = Resistance D. CIRCUITSElectromotive Force, EMF(e)wheree = Electromotive Forcew = Work done on Chargeq = Electric ChargeCurrent in a Simple Circuit where i = Currente = Electromotive ForceR = ResistanceResistances:+R1R2R3RTotal = (R1+R2+R3) W (in series) (in parallel)The Loop TheoremDV1 + DV2 + DV3 . = 0For a complete circuit loopRaiibrileEXAMPLESimple circuit with resistorVab = e iR = + ir e iR ir = 0Then NOTE: 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 traversing the EMF (or battery) in the direction of the EMF is a voltage rise +e.Circuit With Several LoopsEXAMPLEi1 + i2 + i3 = 0R2AFe1e2R1R3CBEDi1i2i3Multiloop circuitRC CIRCUITS (RESISTORS AND CAPACITORS)RC charging and dischargingDifferential Equations(Discharging)(Charging)aiCRsbe+An RC circuitCharge in the Capacitor(Charging)(Discharging)9Charge in the Resistor(Charging)(Discharging)where 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.KIRCHOFFS VOLTAGE 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 resistance), where the response measured at the load resistor will not be affected.xy+LinearActiveNetworkxyProcedures 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 terminals 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 current is sinusoidal.)SIMPLE RL AND RC CIRCUITSRLVL+i(t)Source Free RL CircuitProperties: Assume initially i(0) = I0.A)B), t = time constant = C)Power dissipated in the resistor = .D)Total energy in terms of heat in the resistor = +i(t)RC v(t)WR = LI02.Source Free RC CircuitProperties: Assume initially n(0) = V0A).B).C)THE RLC CIRCUITSRCLiVParallel RLC Circuit (source free)Circuit Diagram:KCL equation for parallel RLC circuit:and the corresponding linear, second-order homogeneous differential equation isGeneral Solution:whereor where a = exponential damping coefficient never frequency = overdampedcritically dampedunderdampedt(a)v(t)and w0 = resonant frequency = COMPLETE RESPONSE OF RLC CIRCUITThe general equation of a complete response of a second order system in terms of voltage for an RLC circuit is given by.forcedresponseNatural response(i.e., constant for DC excitation)NOTE: A and B can be obtained by1) Substituting n at t = 0+2) Taking the derivative of the response, i.e., where at t = 0+ is known.D. THE LASERLight Amplification by Stimulated 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). These levels are known as metastable.Through 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 process known as optical pumping, where atoms of a specific substance, such as ruby, are exposed to a gi