Student Ramuel Mendoza Raagas  for Teaching Fellow Ron Newburgh, Ph.D. 

Physics E1b Electromagnetism  PreLab for Experiment #3: Alternating Current Circuits  Spring Term 2003 

Looking at the most basic ResistorLnductorCapacitor circuit (and getting there with simple samples of first the RC and then the LC circuit as precursors), we find that the RLC circuit cannot hold back current with greater counteraction (impedance) than either of the two less compounded RC and RL circuits, although all three noticeably outdo the mere batteryrestistor ground circuit, except upon extreme situations of frequency ;(as when the latter is zero, i.e., with the function generator being turned off, a trivial situation quite inimical to the spirit and purpose of alternating current; or alternatively, if the frequency is so intense as to make the RC duet circuit but not the comprehensive RLC circuit, nor what would be mywhataninductanceandreactancethereofboosted LR circuit practically reactancedeCAPacITated).
Whereas capacitance, as much as inductance, is a key player in the defense against current (reactance is what either provides the root of conjunction of two squares: the first being that of the twicerelevant resistance and the second being the mutuallydisruptive reactance contributions angularvelocitymultiplied inductance and the inverselyresembling capacitance.
All in all, we have two power boxes (one being the function generator, the other the oscilloscope).
We will use all throughout only a low output (colorcoded red) on our function generator. The wave we will drive through each of this lab's three circuits will be two volts abovethenbelow zero (four volts all in all = V_{pk=pk}). We will do a splitscreen simultaneous viewing of both the kinds of voltage which will interest us: the source voltage which is the function generator's on the lower hand (the wind beneath the wings); and the resistor's V = IR drop (which we will find ending up in three valuebearings, all in all) on the upper hand
Just like a Bausch and Lomb Spectrometer model 20, our functiongenerator is ever in the need of the user's manual calibration: which shall be occasioned with each change of frequency we step into (and several frequencies each lab pair will get into) whereas a spectrometer would need the manual calibration after each invagination of a liquid sample tube into such contraption.
Our oscilloscope must be gently dialsteered to maintain the fine quality of a Four Volt peaktopeak amplitude output.
As I examine my own graph, I shall set out to verify if the voltage which our lab room's function generator feeds into the inductor indeed leads current by a fourthcycle. Considering the law about voltage leading current in a inductor, I guess it would be the voltage displayed on the oscilloscope's upper hand that would matter more.
Frequency (in Hertz)  X_{C}= capacitive reactance 

Frequency (in Hertz)  X_{C}= 
 

0 Hertz  undefined  
1 Hertz  159,155  W Ohms  10 Hz  15,915  1x10^{n} Hz n = nonnegative integer/whole number between zero and six  1.59155x10^{5n} W  
2 Hertz  79,577 W (around eighty kiloW Ohms  20 Hz  7,957.7 around eight kiloW Ohms  2x10^{n} Hz  7.9577x10^{4n} W  
3 Hertz  53052 W  thirty (30) Hz  5,305.2 around fivepointthree kiloW Ohms  3x10^{n} Hz  5.3052x10^{4n} W  
4 Hz  39789 W  40 Hz  3978.9 W about four kiloW  4x10^{n} Hz  3.9789x10^{4n} W  
5 Hz  31831  W  
6 Hz  26526  W Ohms  
7 Hz  22736  W Ohms  
8 Hz  19894  W Ohms  
9 Hz  17684 W  9x10^{n} Hz  5.3052x10^{4n} W 
X_{C} units  = 

= 

= 

= 
X_{C} units  = 

= 

= 

= 
Frequency f (Hz) (in Hertz)  X_{L}=  2pfL  inductive reactance  

0 Hertz  0 Whms  
1 Hertz  6.3 microWhms  10 Hz  15,915  1x10^{n} Hz n = nonnegative integer/whole number between zero and six  1.59155x10^{5n} W  
2 Hertz  13 microW  79,577 W (around eighty kiloW Ohms  20 Hz  7,957.7 around eight kiloW Ohms  2x10^{n} Hz  7.9577x10^{4n} W 
3 Hertz  19 microW  thirty (30) Hz  5,305.2 around fivepointthree kiloW Ohms  3x10^{n} Hz  5.3052x10^{4n} W  
4 Hz  25 mW  40 Hz  3978.9 W about four kiloW  4x10^{n} Hz  3.9789x10^{4n} W  
5 Hz  31 mW  W  
6 Hz  38 mW  
7 Hz  44 mW  
8 Hz  50 mW  
9 Hz  57 mW  9x10^{n} Hz  5.7x10^{n5} W 
with Ben and Con


When we refer to either a capacitor or an inductor as being a "short" for a certain orientation of frequency (as the kind of thing we get Urone's Figure 22.44(b), where the capacitor shorts out high frequencies from a lefthand "blackbox" circuit to ground, so as to deprive them from getting to the righthand circuit), we would like to think of the component as, in effect, causing a short circuit (as contrasted to an open circuit) dishing off to ground a certain quality of wavefrequqency being fed into a circuit in which it has been installed.
What a fuse is to current, a nonresistor reactancecomponent is to frequency, and yet inductors and capacitors are ministers of a taller order against frequency extremities when compared to the footsoliders that are fuses, which are like bees that sting to kill audacious uprisings of current, only to themselves ending out used up.
Consulting Tipler (Chapter 31 Section 3 page 962 Volume 2, Physics, Freeman), we find that the capacitor is indeed a short for high frequencies. The inductor shorts out both direct current and lowfrequency alternating currents. This summary goes well with calculations of reactance. A capacitor becomes an open (rather than short) circuit with low frequencies that bend the reactance calculation's denominator so low that the numerator's mere value of one can end up translating into great achievements of reactance making the capacitor a dead end to the alternating current.
10 Hertz  15,915 like sixteen kiloohms  W Ohms 
200 Hz  795.77 W  
300 Hz  530.52 W  
400 Hz  397.89 W 
1000 Hertz  W Ohms  
10000 Hertz  W Ohms  
100000 Hertz  W Ohms  
10000000 Hertz  W Ohms 
100 Hertz  W Ohms  
500 Hertz  W Ohms  
1000 Hertz  W Ohms  
10000 Hertz  W Ohms  
100000 Hertz  W Ohms  
10000000 Hertz  W Ohms 