Routes the formulas that became the everyday language of AC circuit calculation.
These are OCR candidates. They remain plain text until a reviewer checks the scan and promotes the formula into a curated math page.
#1Theory and Calculation of Alternating Current PhenomenaChapter 4: Graphic Befrisxintation- line 2301Priority OCR formula candidateresistance, r, and the reactance, x = 2irNLy - where A^ =
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Priority OCR formula candidatethe term conductance, g = 1 / r. If, then, a number of con-
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Priority OCR formula candidate1.) If r = QO , or x = oo , since in this case no current
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Priority OCR formula candidate2.) If r = 0, since in this case the current which passes
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Priority OCR formula candidate1.) If x = oo , or r = oo .
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Priority OCR formula candidatea maximum for r = x, where g - 1 / 2 r is equal to the
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Priority OCR formula candidate1.) If r = oc , or ^ = 00 , since in this case no current
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Priority OCR formula candidate2.) If r = 0, since in this case the current which passes
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Priority OCR formula candidate1.) If ^ = Qo , or r = 00 .
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Priority OCR formula candidate2.) If.r=0.
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Priority OCR formula candidatehence, zY = (^’ + ^ (^’ + ^^ = 1 ;
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Priority OCR formula candidatea maximum for r =x, where ^ = 1 / 2r is equal to the
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Priority OCR formula candidate1. If r = oo^ or a: = co ^ since in this case there is no current,
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Priority OCR formula candidate(d) If X = 0, that is, if the receiver circuit is non-inductive,
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Priority OCR formula candidateE0> a resistance E.M.F., Er = fr, a reactance E.M.F.,
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Priority OCR formula candidatethe E.M.F. consumed by reactance is : <?2 = /v/;, :
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Priority OCR formula candidateand the ratio, e I i = 2 ir A^Ly is the magnetic reactance :
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Priority OCR formula candidateTo overcome the reactance, x0 = 2 •*• n0 L0 , of the pri-
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Priority OCR formula candidatey = Vr1 + P ;
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Priority OCR formula candidatereactance x = 0, or in continuous-current circuits, is the
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Priority OCR formula candidateAgain, only in circuits with zero resistance (r = 0) is
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Priority OCR formula candidateb, decreases from b = 1 / x at r = 0, to # = 0 at r = cc ;
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Priority OCR formula candidatewhile the conductance, g - 0 at r = 0, increases, reaches
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Priority OCR formula candidatefrom g = 1 / r to 0, and the susceptance passing from 0 at
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Priority OCR formula candidatex = 0 to the maximum, b = 1 / 2 r = g =1 / ‘2 x at x = r,
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Priority OCR formula candidateAgain, only in circuits with zero resistance (r = 0) is
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Priority OCR formula candidatewhile the conductance, ^ = at r=0, increases, reaches
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Priority OCR formula candidatejr = to the maximum, ^ = l/2r = ^=l/2;r at-r=r,
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Priority OCR formula candidateis the sum of the individual resistances, K = ri + r2 + ra + …
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Priority OCR formula candidateis the sum of the individual conductances, or G = gi -\- g2 -\-
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Priority OCR formula candidateAgain, only in circuits with zero resistance (r = 0) is the
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Priority OCR formula candidateresistance, r, is varied from r = 0 to r = 00^ the susceptance,
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Priority OCR formula candidate6, decreases from 6 = - at r = 0, to 6 = 0 at r = 00 ; while the
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Priority OCR formula candidatez = \/r2 + x2 = -•
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Priority OCR formula candidate^ = - to 0, and the susceptance passing from 0 at x = 0 to the
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Priority OCR formula candidatemaximum, 6 = i7- = y = .^ata; = r, and to 6 = 0 at x = oo .
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Priority OCR formula candidateseries reactance continues up to ;r^ = ± 1.6, or, ;r = - 2;r,
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Priority OCR formula candidateAt ;r^ = ± .8, ;r = ^ .8, the total impedance of the circuit
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Priority OCR formula candidateEo = ^^7T^;
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Priority OCR formula candidateLINDRESISTAJUGECONSTAJ^T n =.2
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Priority OCR formula candidateV._^ n = .8
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Priority OCR formula candidate(a) To = 0.2 ohm (Curve I)
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Priority OCR formula candidate(6) ro = 0.8 ohm (Curve II)
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Priority OCR formula candidateX = -1- 1.0 to a; = - 1.0 ohm.
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Priority OCR formula candidateAs shown, / and E are smallest for x = 0, r = 1.0, or for
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Priority OCR formula candidatethe non-inductive receiver circuit, and largest for x = ± 1.0,
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Priority OCR formula candidater = 0, or for the wattless circuit, in which latter a series resist-
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Priority OCR formula candidateFor ro = 0.8 and x = 0, x = -^ 0.8, x = - 0.8, the vector
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Priority OCR formula candidateZ ^ r -^jx, z = Vr2”+x2-
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Priority OCR formula candidateor, Xo = - 2x.
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Priority OCR formula candidateE = ^0^ _ Eo
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Priority OCR formula candidateI r=1.0 x = 0 ■^ =
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Priority OCR formula candidateHI r = -6 x=-.8
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Priority OCR formula candidatez = 1.0, r = 1.0, a; = 0 (Curve I)
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Priority OCR formula candidatez = 1.0, r = 0.6, X = 0.8 (Curve II)
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Priority OCR formula candidatez = 1.0, r = 0.6, X = - 0.8 (Curve III).
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Priority OCR formula candidatevalue £■ = 167 volts, or E = Eq- This rise of potential by
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Priority OCR formula candidateseries reactance continues up to Xo = + 1.6, or, Xo = - 2x,
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Priority OCR formula candidateAt rro = ± 0.8, x = + 0.8, the total impedance of the circuit
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Priority OCR formula candidateconstant susceptance b = - .142 \
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Priority OCR formula candidateZ0 = r0 + jxo = primary self-inductive impedance;
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Priority OCR formula candidateZi = r2 + jx2 = self-inductive impedance at full frequency,
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Priority OCR formula candidateZ0 = r0 + jx0 = primary self -inductive impedance, and
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Priority OCR formula candidatel’”» = 8 - jk = primiiry exciting admittance
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Priority OCR formula candidatethen X = 2, icNL = magnetic reactance.
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Priority OCR formula candidate2. If r = 0, since in this case the current in the circuit is in
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Priority OCR formula candidate1. If a; = 00, or r = oo .
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Priority OCR formula candidatethen decreases again, reaching gr = 0 at r = «» .
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Priority OCR formula candidateceiver circuit, for £“0 = const. = 100 volts, z = \ ohm; hence
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Priority OCR formula candidatewhere E = 100 volts again; and for Xq > 1.6 the voltage drops
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Priority OCR formula candidate2.) If * = 0.
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Priority OCR formula candidatehence, 22^2 = (^.2 _[_ 3.2) (-^2 -|- 52) = ;[.
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