Lab12:RLCCircuits
Objective: To study resonance in an RLC circuit by examining the current through the circuit as a
functionofthefrequencyoftheappliedvoltage.
Procedure
1. Acquire a voltage sensor and an RLC circuit. Plug the voltage sensor into Analog Channel A. Run
PASCO Capstone and configure the software so it knows a voltage sensor is in Channel A. Click on
Output1andchooseOutputVoltage-CurrentSensor.
2. UsetwobananaplugleadstocreatethefollowingcircuitusingtheRLCcircuitboard.Forthevoltage
source, connect the RLC circuit to the hot and ground Output 1 jacks on the interface box. The hot
(red)plugshouldconnectwithproperpolarityasillustratedbelow.
3. Attachthevoltagesensoracrosstheresistor.Makesuretheredplugcorrespondstothe“hot”sideof
thecircuit.CreateaScopedisplaythatshowstheapplied(output)voltageVA(OutputVoltage,Ch01)
andtheresistancevoltageVR(Voltage,ChA)vs.time.Toaddasecondvoltagedisplayyouwillneedto
click on the
button (Add new y-axis to slope display). The right and left vertical axes can be
adjustedindependentlyofeachother.Knowingtheresistancevoltageallowsustofindthecurrentin
theresistor,since I =
VR
R
.ThisalsoallowsustoseethephaserelationshipbetweenVAandIsincethe
phaserelationshipbetweenVAandVRarethesameasthephaserelationshipbetweenVAandI.
4. Click on the Signal Generator tool in the vertical toolbar on the left. Set the signal generator for
Output 1 to a frequency of 10 Hz and an Amplitude of 3.0 V and turn the output On. Click on
ContinuousModeandselectFastMonitorMode.ClickMonitortobeginmonitoringdataandadjust
thescopesettingssotwoclearsinusoidaltracesarevisible.
5. Usethe button(Showdatacoordinates)tochangethecursortoacrosshair.Makesurethecolorof
theSmartToolisthesameasVR.MeasureVRatitspeakandrecordinatableliketheonebelow:
f(Hz) VR(V) I(A)
10
20
…
320
6. Increasethefrequencyby10Hzandrepeattheprocessuntil320Hzisreached.
7. LookattheDataTableanddetermineapproximatelytheresonantfrequency(wherevoltageacross
theresistorreachesamaximumandtheoutputvoltageandresistorvoltageareinphase).
8. MakefineadjustmentstothefrequencyuntilthetraceofvoltagefromChannelAisinphasewiththe
traceofOutputVoltage.TocheckwhetherthetraceofvoltagefromChannelAisinphasewiththe
trace of Output Voltage, switch the Scope display to X-Y mode: To do this, make the scope display
Voltage,ChA(VR)vs.OutputVoltage,Ch01(VA).
9. Whenthetwoinputsareinphase,theScopedisplaybetweenVAandVRwillshowadiagonalline.Any
phasedifferencewillcauseahalf-ovaltrace.Enterafrequencyof300Hzsoyoucanseewhatanoval
lookslikebeforedialingintheresonantfrequencytothenearest1Hz.Recordtheresonantfrequency
belowyourDataTable.
10. CalculatethecurrentthroughtheresistortocompletethethirdcolumnoftheDataTableusingOhm’s
V
Law, I = R .
R
11. Use Vernier Graphical Analysis to graph the current versus the frequency. Print a graph for each
memberinthegroup.Onyourgraphmarkandlabeltheresonantfrequency.
12. Calculate the theoretical resonant frequency using the values of L and C labeled on the RLC Circuit
1
boardusing ftheo =
.Calculateapercenterrorforyourmeasuredresonantfrequency,usingthe
2
π
LC
theoreticalresonantfrequencyasastandard.
13. Determinewhethertheresonantfrequencydependsontheresistance.Inyourlabnotebookbriefly
describewhatyoudidtodeterminethis,alongwithyourfindings.
14. Reconfigureyourscopetodisplaybothvoltageswithahorizontaltimesweep.
15. Set the frequency to 250 Hz. Rewire your circuit to remove the capacitor. You can either change
whereyourconnectionsaremadeoryoucanuseawiretoshortoutthecapacitortodothis.Nowyou
arelookingatanLRcircuit.Printandattachthescopetraceinyournotebookandlabelittoshow
thatELItheICEmanisonthejob.
16. Set the frequency to 300 Hz. Reconnect the original LCR circuit. Measure the peak value of the
V
resistancevoltageVRandrecord.Weusedthefactbeforethat I = R .Thiscurrentisrelatedtothe
R
appliedvoltageandthetotalimpedanceofthecircuitbyVA=IZ.Substitutingandsolving,wegetthe
VR
measuredimpedanceofthecircuit, Z meas = A (notethatwearerelatingpeakcurrentsandvoltages
VR
here,notRMSvalues).UsingthepeakappliedvoltageofVA=3.0Vand10Ωfortheresistanceofthe
circuit,calculateZmeas.
(
)
2
17. Nowcalculatethetheoreticalimpedanceforthecircuit, Ztheo = R2 + X L − X C ,where X L = 2π fL and
1
XC =
. Compare with your measured impedance and comment on the difference between the
2
π
fC
two.