resistance, r, and the reactance, x = 2irNLy - where A^ =Impedance, Reactance, And Admittance
Why This Family Matters
Section titled “Why This Family Matters”Routes the formulas that became the everyday language of AC circuit calculation.
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reviewable relation candidates.
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sources represented.
Candidate Formula Cards
Section titled “Candidate Formula Cards”the term conductance, g = 1 / r. If, then, a number of con-1.) If r = QO , or x = oo , since in this case no current2.) If r = 0, since in this case the current which passes1.) If x = oo , or r = oo .a maximum for r = x, where g - 1 / 2 r is equal to the1.) If r = oc , or ^ = 00 , since in this case no current2.) If r = 0, since in this case the current which passes1.) If ^ = Qo , or r = 00 .2.) If.r=0.hence, zY = (^’ + ^ (^’ + ^^ = 1 ;a maximum for r =x, where ^ = 1 / 2r is equal to the1. If r = oo^ or a: = co ^ since in this case there is no current,(d) If X = 0, that is, if the receiver circuit is non-inductive,E0> a resistance E.M.F., Er = fr, a reactance E.M.F.,the E.M.F. consumed by reactance is : <?2 = /v/;, :and the ratio, e I i = 2 ir A^Ly is the magnetic reactance :To overcome the reactance, x0 = 2 •*• n0 L0 , of the pri-y = Vr1 + P ;reactance x = 0, or in continuous-current circuits, is theAgain, only in circuits with zero resistance (r = 0) isb, decreases from b = 1 / x at r = 0, to # = 0 at r = cc ;while the conductance, g - 0 at r = 0, increases, reachesfrom g = 1 / r to 0, and the susceptance passing from 0 atx = 0 to the maximum, b = 1 / 2 r = g =1 / ‘2 x at x = r,Again, only in circuits with zero resistance (r = 0) iswhile the conductance, ^ = at r=0, increases, reachesjr = to the maximum, ^ = l/2r = ^=l/2;r at-r=r,is the sum of the individual resistances, K = ri + r2 + ra + …is the sum of the individual conductances, or G = gi -\- g2 -\-Again, only in circuits with zero resistance (r = 0) is theresistance, r, is varied from r = 0 to r = 00^ the susceptance,6, decreases from 6 = - at r = 0, to 6 = 0 at r = 00 ; while thez = \/r2 + x2 = -•^ = - to 0, and the susceptance passing from 0 at x = 0 to themaximum, 6 = i7- = y = .^ata; = r, and to 6 = 0 at x = oo .series reactance continues up to ;r^ = ± 1.6, or, ;r = - 2;r,At ;r^ = ± .8, ;r = ^ .8, the total impedance of the circuitEo = ^^7T^;LINDRESISTAJUGECONSTAJ^T n =.2V._^ n = .8(a) To = 0.2 ohm (Curve I)(6) ro = 0.8 ohm (Curve II)X = -1- 1.0 to a; = - 1.0 ohm.As shown, / and E are smallest for x = 0, r = 1.0, or forthe non-inductive receiver circuit, and largest for x = ± 1.0,r = 0, or for the wattless circuit, in which latter a series resist-For ro = 0.8 and x = 0, x = -^ 0.8, x = - 0.8, the vectorZ ^ r -^jx, z = Vr2”+x2-or, Xo = - 2x.E = ^0^ _ EoI r=1.0 x = 0 ■^ =HI r = -6 x=-.8z = 1.0, r = 1.0, a; = 0 (Curve I)z = 1.0, r = 0.6, X = 0.8 (Curve II)z = 1.0, r = 0.6, X = - 0.8 (Curve III).value £■ = 167 volts, or E = Eq- This rise of potential byseries reactance continues up to Xo = + 1.6, or, Xo = - 2x,At rro = ± 0.8, x = + 0.8, the total impedance of the circuitconstant susceptance b = - .142 \Z0 = r0 + jxo = primary self-inductive impedance;Zi = r2 + jx2 = self-inductive impedance at full frequency,Z0 = r0 + jx0 = primary self -inductive impedance, andl’”» = 8 - jk = primiiry exciting admittancethen X = 2, icNL = magnetic reactance.2. If r = 0, since in this case the current in the circuit is in1. If a; = 00, or r = oo .then decreases again, reaching gr = 0 at r = «» .ceiver circuit, for £“0 = const. = 100 volts, z = \ ohm; hencewhere E = 100 volts again; and for Xq > 1.6 the voltage drops2.) If * = 0.hence, 22^2 = (^.2 [ 3.2) (-^2 -|- 52) = ;[.