Lab 12 - The RLC Series Circuit

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					Name____________________________________ Date____________ Partner(s)_________________________

                                                                           __________________________

                                            Physics Laboratory
                                           The RLC Series Circuit

In this experiment, we will record and graph how the current amplitude in an RLC series circuit responds
as the frequency of the inputted signal changes, and will use the graph to determine the experimental
resonant frequency of the circuit.. Through our analysis, we know that the current amplitude is a
maximum at the resonant frequency of the system. This experimental value will then be compared to the
theoretical value.


I.   Relationship between the Current Amplitude Im and frequency f in the RLC Series Circuit

A.   A circuit consisting of a resistor R, inductor L,
     and capacitor C are connected in series and
                                                                R                         C
     then connected to a function generator                                  L
     producing a sinusoidal signal with a constant
     voltage amplitude Vm . We know that the
     relationship between the current amplitude
     and the voltage amplitude is Vm = ImZ ,
     where Z is the impedance of the RLC series                           v = Vm sin t
     circuit. The current amplitude can then be
     written as

                           Vm
          Im                          .
                       
                 R 2  L  1 C   
                                   2




     Rewrite this in terms of the frequency f.




     Find the frequency at which the current amplitude is a maximum. The frequency is called the
     resonant frequency of the circuit. Show and explain how you found this value.
B.    Draw the graph of how the current amplitude Im varies with frequency f. Be sure to show the
      resonant frequency.
               Im




                                                                                          f




II.   The Experimental Set-up

A.    Equipment:    oscilloscope w/ two BNC leads                inductor
                    function generator w/ one BNC lead           capacitance box
                    two wire connectors                          decade resistance box


B.    Connect a function generator, inductor, capacitance
      box and decade resistance box as an RLC series circuit.
      Be sure that the resistance box is connected to the
      ground terminal of the AC generator. Connect Channel
                                                                                               Inductor        Channel 2
      1 of the oscilloscope across the resistance box and
      Channel 2 across the entire RLC circuit. Remember the
      ground of the AC generator and the ground of the
      oscilloscope must be connected to the same location.
      (Do you know why? If not ask your instructor.) Set            Function
      the decade resistance box at 100 ohms (500 ohms) and          Generator                  Capacitance
                                                                                                   Box
      the value of capacitance to between 0.006 and 0.060 F.
      Have your instructor check your circuit.
                                                                                                   Channel 1
C.    Instead of measuring the current amplitude directly,
      we will measure the voltage amplitude across the                  Decade
                                                                      Resistance
      decade resistance box. In this case remember that the
                                                                          Box
      voltage amplitude across the resistor is proportional to
      the current amplitude (VmR = ImR). We will also
      divide this value by the voltage amplitude coming
      from the function generator (Vm) in order to eliminate any effects caused by variations in the voltage
      supplied by the function generator. This is referred to as “normalizing.”

D.    Data: Report your values of resistance, capacitance, and inductance. Adjust the frequency of your
      function generator to 1000 Hz and record the subsequent voltages on channel 1 (V1 = VmR) and
      channel 2 (V2 = Vm). Repeat these measurements at 2000, 4000, 7000, 10000, 20000, 40000, 70000, and
      100000 Hz. Make more measurements close to and around the resonant frequency so that you can
      draw a smooth curve through the points.
               L = _______________ mH, RL = _______________ ohms; C = _______________ F



                            Trial 1 – R = 100 ohms                        Trial 2 – R = 500 ohms
     Frequency
        (Hz)      Ch-1 voltage   Ch-2 voltage                  Ch-1 voltage    Ch-2 voltage
                                                     V1/V2                                         V1/V2
                   V1 (volts)     V2 (volts)                    V1 (volts)      V2 (volts)
        1000

        2000

        4000

        7000

       10000

       20000

       40000

       70000

      100000




E.   Graph these two sets of data on the same sheet of two cycle semilog graph paper, and draw a
     smooth curve through your points.

F.   Calculations and Results: Locate the resonant frequency for each set of data on your graph and
     report these values as your experimental values of the resonant frequency. Calculate your
     theoretical value from the values of your circuit elements and report this value. Find the percentage
     error between the experimental values and the theoretical value.
                    Experimental Value of          Theoretical Value of
                     Resonant Frequency            Resonant Frequency              Percentage Error
                            (Hz)                          (Hz)


     Trisl 1



     Trial 2




III. Questions

A.   Does changing the value of resistance in the circuit affect the value of the resonant frequency?
     Explain.




B.   Which of the two circuits above when connected to an antenna would make a better receiver for a
     radio? Why?

				
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