Measureinductance1 Understand experiment principle2 Design schemeformeasure(experimentalprocedure)3 Draw up Circuit diagram4Makea datatable5 Make data processing method clear版权：武汉理工大学物理实验中心：黄勇E-mail:hy2000@whut.edu.cn
Measure inductance 1 Understand experiment principle 2 Design scheme for measure （experimental procedure) 3 Draw up Circuit diagram 4 Make a data table 5 Make data processing method clear 版权：武汉理工大学物理实验中心：黄勇 E-mail:hy2000@whut.edu.cn
Measureinductance withthe resonance methodExperimentPurpose:1.UseresistanceboxR、inductanceL、capacitanceboxC、Signal generatorS、oscilloscopeXandsoontodesigna Circuitdiagramfor measure resonancefrequencyfo,and observeresonancephenomenon:2.Calculate inductance value and writetheexpressionofinductanceL=L±u
Measure inductance with the resonance method Experiment Purpose: 1. Use resistance box R、 inductance L、 capacitance box C、Signal generator S、 oscilloscope X and so on to design a Circuit diagram for measure resonance frequency f0 , and observe resonance phenomenon . 2. Calculate inductance value and write the expression of inductance L L = L u
Experiment Principle:RLC Series resonant circuitAAc circuit(Zr=r; Z=iwL;Zc=1/iwc)福We can see out from Vector diagram:z + (z-ze) = r2+oL-seZseries =eszmole = /Zz + (Zz-Z) = /(r+R)+(oL-OCRLC Series circuitbecause : R)>rDZLUso.,current: I =ZL-ZcZ串QolZrPhasedifference betweenZcOcCurrent and voltage :@=arctanVector diagramR
1 Experiment Principle: RLC Series resonant circuit ZL ZC Zr zL -zc Z串 D Ac circuit(Zr= r； ZL=iωL;ZC=1/i ωc) We can see out from Vector diagram： B A U R C r L Zse ries C ( ) 2 2 2 L C 2 s e r i e s r ω C 1 z Z Z Z r ω L = + − = + − 2 2 ) 1 ( C R L U I + − so.,current: = Phase difference between Current and voltage : R c l 1 arctan − = ( ) 2 2 2 L C 2 r R ω C 1 z Z Z Z ( r R ) ω L whole = + + − = + + − because : R r Vector diagram RLC Series circuit
1 Experiment Principle:RLC Series resonante circuitAGZseries = Z + (Z,-Ze)OI=wC福olPhase difference betweenSoc=arctanCurrent and voltage:oRwhenwL=1/wc,Zseriesisminimum obviously,BICSeriescircuitisresonante,(why?),atsametime,theAcvoltagebetweenAandCisDmaximum.(this is the method)ZLZ-ZcZseriesSo,whenweconfirmtheACvoltagebetweenAandCismaximum,Itmeans thatSeries circuitis resonante and we getwL=1/wc1ZrZcLSo inductanceL :二1(2元)℃Weget this formula:
1 Experiment Principle: RLC Series resonante circuit zL -zc ZL ZC Zr Zseries D when ωL=1/ωc， Zseries is minimum obviously， Series circuit is resonante，(why?) ,at same time, the Ac voltage between A and C is maximum. (this is the method) So, when we confirm the AC voltage between A and C is maximum, It means that Series circuit is resonante and we get ωL=1/ωc So inductance L ： We get this formula: (2πf ) C 1 L 2 0 = ( ) 2 2 2 L C 2 s e r i e s r ω C 1 z Z Z Z r ω L = + − = + − B A U R C r L Zsi ries C Phase difference between Current and voltage : R c l 1 arctan − =
2. Experiment Principle: RLC parallel resonant circuitRoscilloscopeZparallelLThe imaginary form of impedance in parallel resonant circuit is:1(oL-ir)1ioL+r7parallelparalleliocri+i(oLAfterderivation
2. Experiment Principle: RLC parallel resonant circuit oscilloscope + - + - C rL L R US The imaginary form of impedance in parallel resonant circuit is: parallel L i L r i C Z + = + 1 1 1 1 ) 1 ( ) 1 ( )( ~ C r i L C L ir Z L L parallel + − − = Zparallel After derivation
OLbecause : ->>1So,we get:YL(oL-ir,)(LICZZparaller1parallel=ri +i(oL -r +i(oL-00SO:LICOL.paralleoC@-arctanr'+(oL --rL0phaseanglePhase difference
: 1 L r L because ) 1 ( ~ / C r i L L C Z L parallel + − So , we get： so： L r C L 1 arctan − − ) 1 ( ) 1 ( )( ~ C r i L C L ir Z L L parallel + − − = 2 2 ) 1 ( / C r L L C Z L parallel + − phase angle Phase difference
when QLparallel circuit is resonant now.oCWhy?1)The resonant frequence fo:LICL/Cfo= 2元/LCZparallerr(oLOCL2)whenthe circuitisZwhole = R+parallel resonant,thercwhole impedance Z:
when 0 1 − = C L LC f 2 1 0 = r C L Z R L whole = + parallel circuit is resonant now. 1)The resonant frequence f0 : 2) when the circuit is parallel resonant , the whole impedance Z : L L parallel r L C C r L L C Z / ) 1 ( / 2 2 = + − Why?
Characteristicsof RLCSeriesresonantcircuit1:Therearesamephase9Ron currentandvoitageofLC2:lmpedancebetweenCand D is minimum3:Currentis maximumDZ= R+r+i(oL-=R+rOCZ..CD=r+i(oLseriesC
Characteristics of RLC Series resonant circuit : R L r C 1:There are same phase on current and voltage of LC 2:Impedance between C and D is minimum 3:Current is maximum R r C Z = R + r + i L − ) = + 1 ( ~ r C ZseriesCD = r + i L − ) = 1 ( ~ A C D
Characteristics of RLC parallel resonant circuit1:There are same phase on current and voltage onLOACR2:lmpedance Z(parallel)betweenCandDismaximumL3:votagebetweenCandDismaximumD1LICL/CZfo=parallel2元VLCrLOLO
R L C r 1:There are same phase on current and voltage on LC 2:Impedance Z(parallel) between C and D is maximum 3:votage between C and D is maximum L L r L C C r L L C Z / ) 1 ( / 2 2 parallel = + − Characteristics of RLC parallel resonant circuit : A C D LC f 2 1 0 =
Amplitudemethodforseriescircuit3Design scheme for measuring and drawing up Circuit diagramSeries resonant circuitRCAoscilloscope12345HZPFrequenceadjustMOD-500BCH1Sine Signal generatorsteps:1ChooseR?and setL=7mh,set C=?And write downthevalue ofthe capacitance2Connect circuit according to the circuit diagram that you design as above.3 Adjustfrequence and observethewaveform ontheoscilloscope,whenAmplitudeismaximum,write downthevalue ofthefrequence4Changethevalueof C to measure frequenceagainforsixtimes
3 Design scheme for measuring and drawing up Circuit diagram R C r L A B C D 12345HZ Frequence adjust Sine Signal generator CH1 oscilloscope steps： 1 Choose R? and set L=7mh,set C=? And write down the value of the capacitance 2 Connect circuit according to the circuit diagram that you design as above. 3 Adjust frequence and observe the wave form on the oscilloscope，when Amplitude is maximum, write down the value of the frequence 4 Change the value of C to measure frequence again for six times 50Ω Series resonant circuit Amplitude method for series circuit