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

Physics E-1b
Electromagnetism
Pre-Lab for Experiment #3:
Alternating Current Circuits
Spring Term 2003
Submitted April 4, 2003
  1. Hypothesis:

    Looking at the most basic Resistor-Lnductor-Capacitor 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 battery-restistor 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 my-what-an-inductance-and-reactance-thereof-boosted LR circuit--- practically reactance-deCAPacITated).

    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 twice-relevant resistance and the second being the mutually-disruptive reactance contributions angular-velocity-multiplied inductance and the inversely-resembling capacitance.

  2. A series of three procedure-components
    with parallel methodologies
      Apparati:
        boxes of invaluable utility
      1. function generator (the sinusoidal agent designated on the left hand of all this lab's schematic circuit diagrams)
      2. oscilloscope with 10x probe
    • breadboard
        three breadboard components
      1. one (1) 100 ohm resistor
      2. one (1) single-microFarad capacitor
      3. a forty-four (44 mH) milliHenry inductor
    • gator clips to clamp on bus bar (which serves as ground) as well as right before and after the voltage drops IR, Q/C and Ld2Q/dt2 cause by the above trio of breadboard components

    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 (color-coded red) on our function generator. The wave we will drive through each of this lab's three circuits will be two volts above-then-below zero (four volts all in all = Vpk=pk). We will do a split-screen 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 value-bearings, all in all) on the upper hand

    Just like a Bausch and Lomb Spectrometer model 20, our function-generator 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 dial-steered to maintain the fine quality of a Four Volt peak-to-peak amplitude output.

    1. The Resistor-Capacitor circuit (through which we will filter out high frequencies) Set up and accomplish a lab graph made-out to have current on the standing (i.e., y) axis and frequencies in Hertz read across the x-axis. You might want to superimpose a trace of voltage which will share the underlying abscissae. Such a voltage trace
    2. The Resistor-Inductor circuit (through which we will filter out low frequencies)

      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 fourth-cycle. 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.

    3. The Resistor-Lnductor-Capacitor circuit (our bi-pass filter)
    1. Capacitive reactance calculations follow...
      Frequency
      (in Hertz)
      XC=
      capacitive
      reactance
      1

      2pfC
      Frequency
      (in Hertz)
      XC=
      1

      2pfC
      0 Hertzundefined
      1 Hertz159,155W Ohms 10 Hz15,9151x10n Hz
      n = non-negative
      integer/whole
      number between
      zero and six
      1.59155x105-n W
      2 Hertz79,577 W
      (around eighty
      kilo-W Ohms
      20 Hz7,957.7
      around eight
      kilo-W Ohms
      2x10n Hz7.9577x104-n W
      3 Hertz53052 Wthirty
      (30) Hz
      5,305.2
      around five-point-three
      kilo-W Ohms
      3x10n Hz5.3052x104-n W
      4 Hz39789 W40 Hz3978.9 W
      about four
      kiloW
      4x10n Hz3.9789x104-n W
      5 Hz31831W
      6 Hz26526W Ohms
      7 Hz22736W Ohms
      8 Hz19894W Ohms
      9 Hz17684 W9x10n Hz5.3052x104-n W
    2. Without a doubt, the units of XC are W hms, as may be shown as follows...
      XC units =
      1

      2pfC
      =
      1

      6.2832·(a/second)·C
      frequency = a # of cycles per second
      =
      1

      6.2832·(a/second)·(b (milli/micro/pico-)Farads)
      Capacitance = b # of (milli/micro/pico-)Farads
      =
      XC units =
      1·seconds

      6.2831853...·(ab) Farads
      =
      seconds·Volts

      6.2832·(ab)Coulombs
      as 1 Volt = 1 Joule per Coulomb
      =
      seconds·Joules

      6.28..·(ab) Coulomb2
      C = b # of (milli/micro/pico-)Farads
      =
    3. Inductive reactance calculations follow...
      Frequency
      f (Hz)
      (in Hertz)
      XL= 2pfL inductive
      reactance
      0 Hertz0 Whms
      1 Hertz6.3 micro-Whms10 Hz15,9151x10n Hz
      n = non-negative
      integer/whole
      number between
      zero and six
      1.59155x105-n W
      2 Hertz13 micro-W79,577 W
      (around eighty
      kilo-W Ohms
      20 Hz7,957.7
      around eight
      kilo-W Ohms
      2x10n Hz7.9577x104-n W
      3 Hertz19 micro-Wthirty
      (30) Hz
      5,305.2
      around five-point-three
      kilo-W Ohms
      3x10n Hz5.3052x104-n W
      4 Hz25 mW40 Hz3978.9 W
      about four
      kiloW
      4x10n Hz3.9789x104-n W
      5 Hz31 mWW
      6 Hz38 mW
      7 Hz44 mW
      8 Hz50 mW
      9 Hz57 mW9x10n Hz5.7x10n-5 W
    4. Around 1550 Hertz would work well for the RC cirucit. Around 361.7 Hertz woumight be good for the LR circuite.m Allin all, a range spanning from 500 to 200 hertz freequency would give an ample allowance for resalsts we;dwatch out for./
    5. 758.74 Hertz
    6. One Hundred (100) W hms
    7. Forty (40 mA) milliamperes
      please click to get to source of formula pic

Lab Proper

with Ben and Con

RLC CIrcuitfinal
circuit
tested
RLC CIrcuitZI
5 HertzVolts
10 Hertz.19 Volts15913 Ohms
30 HertzVolts5297.8 ohms
48.6 Hertz0.15 Volts
60 Hertz.175 Volts2.638 kiloohms66.338 microAmps
90 Hertz.28 V1.7464 kiloOhms.16 milliAmps
100 Hertz.3 V1567.1 Ohms.1914364 milliAmperes
200 Hz.6 V747.2 Ohms.8 milliAmperes
300 Hz.96 Volts458.61 Ohms2.1 milliAmperes
360 Hz1.1 V356.87 Ohms3.08 milliAmperes
400Hertz304.21Amperes
500 HzV 205.98 ohm
550 Hz1.8 V169.87 ohms10.588 milliAmperes
600 Hz1.95 V140.99 Ohms
141 Ohms
13.83 milliAmps
710 HzV103.81 Ohms
760 Hz2.1 Volts100 Ohms21 milliAmps
800 HzV102.44 Oh
900 Hz2 V123.21 Ohms16.23245 milliAmp
RLC CIrcuitfinal
circuit
tested
RLC CIrcuitZI
1000 HzV154.14 Ohms
1200 Hz1.6 V222.82 Ohms7.18 milliA
1600 Hz.65 V357.15Ohms1.82 milliA
2100 Hz.86 V514.59 Ohms1.6712 milliA
2400 Hz.74 V605.5 Ohms1.22213 milliA
2700 Hz.66 V694.73 Ohms.9505977 milliA
3000 Hz.6 V782.74 Ohms.766538 milliA
4500 Hz.39 V1212.8 Ohms.32157 milliA
4800 Hz.36 V1297.7 Ohms.2774 milliA
5400 Hz.32 V1466.8 Ohms.218162 milliA
7000 Hz.25 V1915.1 Ohms.13 milliA
7500 Hz.23 V2054.7 Ohms.112 milliAmperes
8000 Hz.26 V2194.1 Ohms.1185 milliA
10000 Hz.19 V2750.5 Ohms69 microA

Analysis

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 left-hand "black-box" circuit to ground, so as to deprive them from getting to the right-hand 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 wave-frequqency being fed into a circuit in which it has been installed.

What a fuse is to current, a non-resistor reactance-component is to frequency, and yet inductors and capacitors are ministers of a taller order against frequency extremities when compared to the foot-soliders 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 low-frequency 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.

  • Conclusion


    10 Hertz15,915
    like sixteen kiloohms
    W Ohms
    200 Hz795.77 W
    300 Hz530.52 W
    400 Hz397.89 W
    1000 HertzW Ohms
    10000 HertzW Ohms
    100000 HertzW Ohms
    10000000 HertzW Ohms
    100 HertzW Ohms
    500 HertzW Ohms
    1000 HertzW Ohms
    10000 HertzW Ohms
    100000 HertzW Ohms
    10000000 HertzW Ohms