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              "text": "plex quantities. "
            },
            {
              "line": 64,
              "text": ""
            },
            {
              "line": 65,
              "text": "In graphical representation impedances have not to be added, "
            },
            {
              "line": 66,
              "text": "but are combined in their proper phase by the law of parallelo- "
            },
            {
              "line": 67,
              "text": "gram in the same manner as the e.m.fs. corresponding to them. "
            },
            {
              "line": 68,
              "text": ""
            },
            {
              "line": 69,
              "text": "The term impedance becomes inconvenient, however, when "
            },
            {
              "line": 70,
              "text": "dealing with parallel-connected circuits; or, in other words, when "
            },
            {
              "line": 71,
              "text": "several currents are produced by the same e.m.f., such as in "
            },
            {
              "line": 72,
              "text": "cases where Ohm's law is expressed in the form, "
            },
            {
              "line": 73,
              "text": ""
            },
            {
              "line": 74,
              "text": "/ = I "
            },
            {
              "line": 75,
              "text": ". Z "
            },
            {
              "line": 76,
              "text": ""
            },
            {
              "line": 77,
              "text": "It is preferable, then, to introduce the reciprocal of impe- "
            },
            {
              "line": 78,
              "text": "dance, which may be called the admittance of the circuit, or "
            },
            {
              "line": 79,
              "text": ""
            },
            {
              "line": 80,
              "text": "Z "
            },
            {
              "line": 81,
              "text": ""
            },
            {
              "line": 82,
              "text": "As the reciprocal of the complex quantity, Z = r -{- jx, the "
            },
            {
              "line": 83,
              "text": "admittance is a complex quantity also, or Y = g — jh; it con- "
            },
            {
              "line": 84,
              "text": "sists of the component, g, which respresents the coefficient of "
            },
            {
              "line": 85,
              "text": "current in phase with the e.m.f., or the power or active com- "
            },
            {
              "line": 86,
              "text": "ponent, gE, of the current, in the equation of Ohm's law, "
            },
            {
              "line": 87,
              "text": ""
            },
            {
              "line": 88,
              "text": "I =YE ={g- jh)E, "
            },
            {
              "line": 89,
              "text": ""
            },
            {
              "line": 90,
              "text": "and the component, h, which represents the coefficient of current "
            },
            {
              "line": 91,
              "text": "in quadrature with the e.m.f., or wattless or reactive component, "
            },
            {
              "line": 92,
              "text": "hE, of the current. "
            },
            {
              "line": 93,
              "text": ""
            },
            {
              "line": 94,
              "text": "g is called the conductance, and h the susceptance, of the cir- "
            },
            {
              "line": 95,
              "text": "cuit. Hence the conductance, g, is the power component, and "
            },
            {
              "line": 96,
              "text": ""
            },
            {
              "line": 97,
              "text": ""
            },
            {
              "line": 98,
              "text": "56 ALTERNATING-CURRENT PHENOMENA "
            },
            {
              "line": 99,
              "text": ""
            },
            {
              "line": 100,
              "text": "the susceptance, h, the wattless component, of the admittance, "
            },
            {
              "line": 101,
              "text": "Y = g ~ jb, while the numerical value of admittance is "
            },
            {
              "line": 102,
              "text": ""
            },
            {
              "line": 103,
              "text": "y = Vg' + h^; "
            },
            {
              "line": 104,
              "text": ""
            },
            {
              "line": 105,
              "text": "the resistance, r, is the power component, and the reactance, "
            },
            {
              "line": 106,
              "text": "X, the wattless component, of the impedance, Z = r -^ jx, the "
            },
            {
              "line": 107,
              "text": "numerical value of impedance being "
            },
            {
              "line": 108,
              "text": ""
            },
            {
              "line": 109,
              "text": "z = Vr^ + x^. "
            },
            {
              "line": 110,
              "text": ""
            },
            {
              "line": 111,
              "text": "50. As shown, the term admittance implies resolving the cur- "
            },
            {
              "line": 112,
              "text": "rent into two components, in phase and in quadrature with the "
            },
            {
              "line": 113,
              "text": "e.m.f., or the power or active component and the wattless or "
            },
            {
              "line": 114,
              "text": "reactive component; while the term impedance implies resolving "
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              "line": 115,
              "text": "the e.m.f. into two components, in phase and in quadrature "
            },
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              "line": 116,
              "text": "with the current, or the power component and the wattless or "
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              "line": 117,
              "text": "reactive component. "
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              "line": 118,
              "text": ""
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              "line": 119,
              "text": "It must be understood, however, that the conductance is not "
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              "text": "the reciprocal of the resistance, but depends upon the reactance "
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              "text": "as well as upon the resistance. Only when the reactance x = 0, "
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              "line": 122,
              "text": "or in continuous-current circuits, is the conductance the recip- "
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              "line": 123,
              "text": "rocal of resistance. "
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            {
              "line": 124,
              "text": ""
            },
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              "line": 125,
              "text": "Again, only in circuits with zero resistance (r = 0) is the "
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              "line": 126,
              "text": "susceptance the reciprocal of reactance; otherwise, the suscep- "
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              "line": 127,
              "text": "tance depends upon reactance and upon resistance. "
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              "line": 128,
              "text": ""
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              "line": 129,
              "text": "The conductance is zero for two values of the resistance: "
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              "line": 130,
              "text": ""
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              "line": 131,
              "text": "1. If r = oo^ or a: = co ^ since in this case there is no current, "
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              "text": "and either component of the current = 0. "
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              "line": 133,
              "text": ""
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              "text": "2. If r = 0, since in this case the current in the circuit is in "
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              "line": 135,
              "text": "quadrature with the e.m.f., and thus has no power component. "
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              "line": 136,
              "text": ""
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              "line": 137,
              "text": "Similarly, the susceptance, b, is zero for two values of the "
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              "line": 138,
              "text": "reactance: "
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              "line": 139,
              "text": ""
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              "line": 140,
              "text": "1. If a; = 00, or r = oo . "
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              "line": 141,
              "text": ""
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              "line": 142,
              "text": "2. Ux = 0. "
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              "line": 143,
              "text": ""
            },
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              "line": 144,
              "text": "From the definition of admittance, Y = g — jb, as the recip- "
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              "line": 145,
              "text": "rocal of the impedance, Z = r -\\- jx, "
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              "line": 146,
              "text": "we have "
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              "line": 147,
              "text": ""
            },
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              "line": 148,
              "text": "\\^ "
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            {
              "line": 149,
              "text": "f "
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              "line": 150,
              "text": ""
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              "line": 151,
              "text": "or, multiplying numerator and denominator on the right side by "
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              "line": 152,
              "text": "(r - jx), "
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              "line": 153,
              "text": ""
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              "text": "h — r — jx "
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              "line": 155,
              "text": ""
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              "line": 156,
              "text": "■ ^ ~ 3 - (r+jx) (r - jx)' "
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              "line": 157,
              "text": ""
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              "text": ""
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              "line": 159,
              "text": "ADMITTANCE, CONDUCTANCE, SUSCEPTANCE 57 "
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              "line": 160,
              "text": "hence, since "
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              "text": ""
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              "line": 162,
              "text": ""
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              "line": 163,
              "text": "(r + "
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              "text": ""
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              "line": 165,
              "text": "jx) (r - "
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              "line": 166,
              "text": ""
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              "line": 167,
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              "text": ""
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              "text": "_ J.2 _j_ 2^2 "
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              "line": 170,
              "text": ""
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              "line": 171,
              "text": "= "
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              "text": ""
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              "text": ""
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              "text": "jb = "
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              "text": ""
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              "text": "r "
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              "text": ""
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              "line": 179,
              "text": "-^r "
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            {
              "line": 180,
              "text": ""
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              "line": 181,
              "text": "X "
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            {
              "line": 182,
              "text": ""
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              "line": 183,
              "text": "r "
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              "line": 184,
              "text": ""
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              "text": "22 "
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              "line": 186,
              "text": ""
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              "line": 187,
              "text": ". aj "
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              "line": 188,
              "text": ""
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              "text": "J.2 _|_ -J.2 "
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              "text": ""
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              "text": "■2 + a;2 "
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              "line": 192,
              "text": ""
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              "line": 193,
              "text": "•^2^ "
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              "line": 194,
              "text": ""
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              "line": 195,
              "text": "or "
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            {
              "line": 196,
              "text": ""
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            {
              "line": 197,
              "text": ""
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              "line": 198,
              "text": "9 ^2 _^ 2-2 "
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              "line": 199,
              "text": ""
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              "text": "0 = o 1 o 2' "
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              "line": 201,
              "text": ""
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              "text": ""
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              "text": "and conversely "
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              "text": ""
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              "text": ""
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              "text": "r = "
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              "text": ""
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              "text": ""
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              "text": "J.2 "
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              "text": ""
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              "text": "g' "
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              "text": "6 "
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              "text": "•\" ~ ^2 _|_ 52 - ^2 "
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