Notes for Experiment #4 -- AC Circuits


Notes & Hazards

Random helpful notes for your experiment:

  1. Some theoretical considerations:

    If the sine wave is symmetric about the 0-point, then the peak value is simply the value from the 0-point to the top of a crest. If, however, the curve is not symmetric about the 0-point, then there is a DC Offset. In this case, the peak value is given by Peak-to-Peak/2 where the Peak-to-Peak value is measured from the top of one crest to the bottom of the successive trough. The difference between the actual location of the peak of the crest and the 0-point gives you the DC offset. E.g., if the peak value is 2 and the top of the crest is located at the 2-point mark, then the DC offset is 2-2 = 0. If, however, the peak value is 2 and the top of the crest is located at the 2.5 point mark, then the DC offset is 2.5 - 2 = 0.5.

    The period, T, is the time (or divisions * time/divisions) between 2 successive peaks (or troughs). The period has units of seconds/cycle. The frequency, n, is the inverse of the period (i.e., 1/T) and has units of cycles/second.

    Finally, remember that the plot of Current (I) vs. Time (t) is a straight line for a DC power source (since the current is constant) but varies with time for an AC power source (since current reverses polarity with time). It can be a square wave, a triangle wave, a sine wave, etc. If it happens to be a sine (or a cosine) curve, then we can take advantage of certain mathematical characteristics of sine waves to gain insight/info into our AC current and voltage. For sine (or cos) waves only, the RMS values for current or voltage are given by: Peak value/sqrt[2]. For all other waveforms (e.g., square, triangle, etc.), you're limited to reading the RMS values from your multimeter (e.g., the Goldstar) and cannot use the above formula for RMS. Also, please note that Ohm's Law and Kirchoff's Laws only apply to the RMS values when dealing with AC circuits.
  2. Misc. Experimental Notes:

  3. Some derivations (EQs 5-7 in your lab manual):

    EQ5    V = I1R1 + I1Req where Req is the resistance of the
           of the parallel resistors.  Since they're in parallel, this is equal to:
           1/Req = 1/R2 + 1/R3
    
           Plugging this in above yields,
                                 1
           ==>  V = I1R1 + I1(----------)
                             1/R2 + 1/R3
    
           The term in parantheses can be rearranged as:
                    R2R3
           Req =  ----------
                   R2 + R3
    
           Factoring out the I1 and dividing out yields:
                        V
           ==>  I1 = ----------
                    R1 +   R2R3
                         -------
                          R2 + R3
           
           Multiplying and dividing R1 by R2+R3, gives:
                        V
           ==>  I1 = ---------------------
                      R1(R2 + R3) +   R2R3
                      --------------------
                        R2 + R3
           
           Which finally yields:
                        V(R2 + R3)
           ==>  I1 = ---------------------              (EQ5)
                      R1R2 + R1R3 +   R2R3
           
    
    EQ6    I1Req = Veq = I2R2
    
           Using Req from above gives:
                I1Req            I1R2R3
           I2 = ------   ==>  ------------ 
                 R2             R2(R2 + R3)
           
           Cancelling out the R2's, gives:
                  I1R3
           ==>  ---------                               (EQ6)
                 R2 + R3
           
    
    EQ7    I1Req = Veq = I3R3
    
           Using Req from above gives:
                I1Req            I1R2R3
           I3 = ------   ==>  ------------ 
                 R3             R3(R2 + R3)
           
           Cancelling out the R3's, gives:
                  I1R2
           ==>  ---------                               (EQ7)
                 R2 + R3
           


Corrections

  1. Many minor errors.

Required Materials:

  1. Laboratory Manual (SGM 407)
  2. Laboratory Answer Book
  3. Calculator with statistical functions


Some Helpful Links & Miscellaneous Notes

  1. This lab has the potential to be really quick. Just be sure to read the lab and pay attention to the above tips/hints to speed you along.
  2. One of the best checks is to make sure that the table you fill out in section 4.2 has reasonable values (if it doesn't, then you screwed up and should fix it before you try to check-out because I'll just make you do it over).
  3. Feedback on if you're finding these pages helpful (or not) is definitely good. So if you have any strong opinions, or, dare I say it, ideas on how to make this better, drop me a line!


Ricky J. Sethi <rickys@sethi.org>
Last modified: Sun Apr 16 17:59:47 2000