Routes equations involving field storage, charge, discharge, and frequency-dependent opposition.
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#1Theory and Calculation of Alternating Current PhenomenaChapter 8: Circuits Containing Resistance, Inductance, And Capacity- line 4580Priority OCR formula candidateThen, if E0 = impressed E.M.F.,-
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Priority OCR formula candidatee-o.296 1 = 0.5, - 0.296 Mog e = log 0.5, t =
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Priority OCR formula candidatefor the constant impressed E.M.F., E0 = 100 ; for the con-
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Priority OCR formula candidate(a) M strength: i = ~, hence (1 - €-°-29«0 = 0.5.
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Priority OCR formula candidate(d) If i = 0 at * = 0.0005, then
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Priority OCR formula candidate(e) If t = - I = - 90 at t = 0.001, then
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Priority OCR formula candidatecircuits. Hence the inductance is L = $/ i = ;/2/(R.
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Priority OCR formula candidatecircuits. Hence the inductance is L = ^ / 1 = n^ / iR.
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Priority OCR formula candidatebut E = E0,I= E0/z. If x0 < - 2 x, it raises, if x0 > - Zv,
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Priority OCR formula candidated.} If x = 0, that is, if the receiver circuit is non-
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Priority OCR formula candidatemaximum for x0= +1.0, x = - 1.0, and r = 0, where
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Priority OCR formula candidated.) If ;r = 0, that is, if the receiver circuit is non-
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Priority OCR formula candidatesince x = ~Vz2 - r2, if rr0 -f- x0 ~\/z2 - r2 is a maximum.
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Priority OCR formula candidatef = rr0 + *0 Vs2 - r2 = maximum or minimum, if
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Priority OCR formula candidatemaximum for x^ = +10, x = - 1.0, and r = 0, where
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Priority OCR formula candidateei = E € L = i0re £ the generated e.m.f.
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Priority OCR formula candidateIn this case, at t = 0, e\ = E, that is, the e.m.f. does not rise.
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Priority OCR formula candidateafter impressing the required e.m.f. E = 230 volts will it take
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Priority OCR formula candidateimpressing the e.m.f. E = 500 volts will it take for the field to
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Priority OCR formula candidatethe impressed e.m.f. is E = 230, the final value of current
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Priority OCR formula candidateIMPRESSED E.M.F. CONSTANT, E0=IOO
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Priority OCR formula candidateIMPRESSED E.M.F. CONSTANT, E0 = IOOO VOLTS.
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Priority OCR formula candidateL2 = inductance of the second circuit, and M = mutual induc-
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Priority OCR formula candidateor Li = Si + - M L2 = Sz + - M,
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Priority OCR formula candidateor M2 = (Li - Si)(Lz - Sz).
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Priority OCR formula candidateH = 0.4 TT/ = - - , and the flux in the zone dlx is
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Priority OCR formula candidate-’ «i = 0.
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Priority OCR formula candidateei = - = - 0.368 E.
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Priority OCR formula candidateiei = io2 (r + n) c L ;
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Priority OCR formula candidateio = - = 6.95 amp. Thus the current at time t is
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Priority OCR formula candidatet = * - 6
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Priority OCR formula candidate(2) To get io = 6.95 amp., with E = 500 volts, a resist-
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Priority OCR formula candidateance r = ^-f-= = 72 ohms, and thus a rheostat having a resist-
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Priority OCR formula candidatei = io (l € 2)
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Priority OCR formula candidate(a) i = ^, after t = 1.08 seconds.
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Priority OCR formula candidate(b) i = 0.9 i0, after i = 3.6 seconds.
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Priority OCR formula candidate(3) Impressing E = 500 volts upon a circuit of r = 33.2,
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Priority OCR formula candidate33. (5) A coil of resistance r = 0.002 ohm and inductance
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Priority OCR formula candidateL = 0.005 mh., carrying current / = 90 amp., is short circuited.
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Priority OCR formula candidate(6) i = 0.1 7, c-400< = 0.1, after t = 0.00576 second.
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Priority OCR formula candidateE = 1 volt is inserted in the circuit of this coil, in opposite direc-
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Priority OCR formula candidateThus, - E + 61 = - E - L jt, the total e.m.f.;
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Priority OCR formula candidateAt t = 0, i = /, thus c = / + -;
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Priority OCR formula candidate(6) i = o, e-400 « = 0.85, after t = 0.000405 second.
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Priority OCR formula candidate(c) i = - I = - 90, e-400 « = 0.694, after t = 0.00091 second.
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Priority OCR formula candidateE = joTITi = °-81 volt-
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Priority OCR formula candidateE = - = 0.91 volt.
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Priority OCR formula candidateor i = /osin (6 - 8’),
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Priority OCR formula candidatemachine is E = 4«4>7V10~8 volts, independent of the num-
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Priority OCR formula candidateand *%E = 0 in a closed circuit,
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Priority OCR formula candidateZ = r -jx, z = Vr2 + x’2,
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Priority OCR formula candidateZ + r0 = r + r0-jx\
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Priority OCR formula candidateE = EnJ >* + *2 . Eo
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Priority OCR formula candidatea.) r0 = .2 ohm (Curve I.)
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Priority OCR formula candidateb.) r0 = .8 ohm (Curve II.)
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Priority OCR formula candidatewith values of reactance, x = V^2 - r2, for abscissae, from
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Priority OCR formula candidatex = + 1.0 to x = - 1.0 ohm.
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Priority OCR formula candidateAs shown, / and E are smallest for x = 0, r = 1.0,
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Priority OCR formula candidateFor r0 = .8, and x = 0, x = + .8, x = - .8, the polar
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Priority OCR formula candidateZ = r - jx, z = -\/r2 -|- x’2.
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Priority OCR formula candidatec.) E = E0 , or the insertion of a series inductance, x0 ,
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Priority OCR formula candidate^z*-\-2xx0 + x02 = 2;
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Priority OCR formula candidateor, x0 = - 2 x.
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Priority OCR formula candidateII. r=.6 X=H-,8
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Priority OCR formula candidate111. r=.e i=-.8
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Priority OCR formula candidateE^ = const. = 100 volts, -cr = 1 ohm, and -
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Priority OCR formula candidateX = + 1.0 to ;r = + 1.0 ohm.
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Priority OCR formula candidateAs shown, / and E are smallest for ;r = 0, r = 1.0,
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Priority OCR formula candidateFor r^ = .8 and x = 0,x = + .8, and x = - .8, the polar
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Priority OCR formula candidate2=1.0, r= .6,^= .8(CurveII.)
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Priority OCR formula candidate2= 1.0, r= .6, AT= - .8 (Curve III.)
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Priority OCR formula candidateThis rise is a maximum for x0 = i .8, or, x0 = - x (the
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