Transients, Oscillation, And Damping

#1Theory and Calculation of Transient Electric Phenomena and OscillationsChapter 4: Inductance And Resistance In Alternating Current Circuits- line 3525

At the moment 0 = 0, let the e.m.f. e = E cos (0 - 00) be

#2Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 6: Double-Energy Transients- line 3660

i = io cos (0 - 7) = io cos 7 cos <j> + i0 sin 7 sin

#3Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 7: Line Oscillations- line 4573

e = 2;oCe-”’ sin (0 =F co - 7) j

#4Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 7: Line Oscillations- line 5086

i = e~ ”’ J ai cos </) cos co + 6i sin cf) cos co + Ci cos 0 sin co

#5Theory and Calculation of Transient Electric Phenomena and OscillationsChapter 4: Inductance And Resistance In Alternating Current Circuits- line 3545

Since e = E cos (0 - 00) = impressed e.m.f.,

#6Theory and Calculation of Transient Electric Phenomena and OscillationsChapter 4: Inductance And Resistance In Alternating Current Circuits- line 3661

i = -z | cos (I? - 00- 0J- i~x° cos (00 + OJ j (9)

#7Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 6: Double-Energy Transients- line 3943

if = 140 cos 0.2 1 - 80 sin 0.2 1,

#8Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 2: The Electric Field- line 1035

w=j*pdt, (10)

#9Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 2: The Electric Field- line 1232

f = j (13)

#10Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 2: The Electric Field- line 1339

K = j^; (21)

#11Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 2: The Electric Field- line 1440

(B = -j =/z JClinespercm2.

#12Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 2: The Electric Field- line 1446

7 = -j = yG am-

#13Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 6: Double-Energy Transients- line 3456

io = eo y j = e02/o. (11)

#14Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 5: Single-Energy Tra.Nsient Of Ironclad Circuit- line 3462

(S!,J = 20,000 lines per cm^. *

#15Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 6: Double-Energy Transients- line 3543

ii = IQ cos 7 = initial transient current. (14)

#16Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 6: Double-Energy Transients- line 3555

e = e0 sin (0 - 7), (15)

#17Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 6: Double-Energy Transients- line 3559

ei = - e0 sin 7 = initial value of transient voltage. (16)

#18Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 6: Double-Energy Transients- line 3671

i = i\ cos 1/001 sin - , (21)

#19Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 6: Double-Energy Transients- line 3677

e = e\ cos - + z0ii sin - , (22)

#20Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 5: Single-Energy Tra.Nsient Of Ironclad Circuit- line 3688

T = 2.92 - { 9.21 log’^ , ,\ . + .921 log’^ i ’ ^ ^

#21Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 5: Single-Energy Tra.Nsient Of Ironclad Circuit- line 3694

division with log^^e = .4343.

#22Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 5: Single-Energy Tra.Nsient Of Ironclad Circuit- line 3700

t = im^log’H- .507.

#23Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 6: Double-Energy Transients- line 3934

e = e-3<S2000 cos 0.2 1 + 3500 sin 0.2 «},

#24Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 6: Double-Energy Transients- line 3944

er = 2000 cos 0.2 1 + 3500 sin 0.2 1.

#25Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 6: Double-Energy Transients- line 3974

^l = ^o cos 7 = initial transient current. (14)

#26Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 6: Double-Energy Transients- line 3986

e = eo sin (0 - 7), (15)

#27Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 6: Double-Energy Transients- line 3990

ei = - 60 sin 7 = initial value of transient voltage. (16)

#28Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 7: Line Oscillations- line 3992

ii = IQ cos (</> - 7)

#29Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 7: Line Oscillations- line 3995

ei = e0 sin (0 - 7) l

#30Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 7: Line Oscillations- line 4017

e = - €Q sin 7

#31Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 7: Line Oscillations- line 4021

i = loe-^cos (0 - 7)

#32Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 7: Line Oscillations- line 4057

i = c<rui cos (0 - 7) ) n 1 x

#33Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 6: Double-Energy Transients- line 4089

i = ^o cos (0 - t) = io cos y cos 4> + io sin y sin 0

#34Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 6: Double-Energy Transients- line 4100

i = ii cos 2/0^1 sin-, (21)

#35Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 7: Line Oscillations- line 4112

i = ce~ut cos (0 T co - 7) ) ,17,

#36Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 6: Double-Energy Transients- line 4251

I = e~^^ < Zi cos 2/0^1 sm -

#37Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 6: Double-Energy Transients- line 4344

{ = e-3^U40cos0.2^ -80 sin 0.2^ J

#38Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 6: Double-Energy Transients- line 4345

e = e- ^‘S 2000 cos 0.2 ^ + 3500 sin 0

#39Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 6: Double-Energy Transients- line 4357

i’ = 140 cos 0.2 t - 80 sin 0.2 1,

#40Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 6: Double-Energy Transients- line 4358

e’ = 2000 cos 0.2 i + 3500 sin 0.2 1.

#41Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 7: Line Oscillations- line 4409

ii = Iq cos (0 - 7)

#42Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 7: Line Oscillations- line 4446

e = eoe~ ^^ sin (0 - 7)

#43Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 7: Line Oscillations- line 4463

e’ = -eo sin 7

#44Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 7: Line Oscillations- line 4571

i = ce-”’ COS ((/) =F CO - 7) ) .

#45Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 7: Line Oscillations- line 4846

lo = vto = -.J (32)

#46Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 7: Line Oscillations- line 5089

e = e- w« 5 di cos <f) cos co + W sin </> cos co + c/ cos </> sin co

#47Theory and Calculation of Transient Electric Phenomena and OscillationsChapter 2: Introduction- line 2467

i = I cos (d - 45°),

#48Theory and Calculation of Transient Electric Phenomena and OscillationsChapter 3: Inductance And Resistance In Continuous Current Circuits- line 2949

e = ir (l - -J; (10)

#49Theory and Calculation of Transient Electric Phenomena and OscillationsChapter 3: Inductance And Resistance In Continuous Current Circuits- line 2970

t = 0, i = iv log cii = 0, c = - ,

#50Theory and Calculation of Transient Electric Phenomena and OscillationsChapter 3: Inductance And Resistance In Continuous Current Circuits- line 3325

t = 26.8 log $- 17.9 log (31.25 - 2.5$ ) + 79.6 (37)

#51Theory and Calculation of Transient Electric Phenomena and OscillationsChapter 3: Inductance And Resistance In Continuous Current Circuits- line 3329

t = 26.8 log e - 17.9 log (31.25 - 0.125 e) - 0.8. (38)

#52Theory and Calculation of Transient Electric Phenomena and OscillationsChapter 3: Inductance And Resistance In Continuous Current Circuits- line 3459

t = 0.04 log e - 0.01333 log (600 - e) - 0.08. (44)

#53Theory and Calculation of Transient Electric Phenomena and OscillationsChapter 3: Inductance And Resistance In Continuous Current Circuits- line 3481

t = 0.0274 log e - 0.00073 log (876 - e) - 0.1075, (45)

#54Theory and Calculation of Transient Electric Phenomena and OscillationsChapter 4: Inductance And Resistance In Alternating Current Circuits- line 3553

i = 7 cos (6 - d) + A£~a°, (2)

#55Theory and Calculation of Transient Electric Phenomena and OscillationsChapter 4: Inductance And Resistance In Alternating Current Circuits- line 3580

E cos 00 - Ir cos d - Ix sin d = 0,

#56Theory and Calculation of Transient Electric Phenomena and OscillationsChapter 4: Inductance And Resistance In Alternating Current Circuits- line 3582

E sin 00 - Ir sin d + Ix cos d = 0,

#57Theory and Calculation of Transient Electric Phenomena and OscillationsChapter 4: Inductance And Resistance In Alternating Current Circuits- line 3638

i = - cos (0 - 00 - 0X) + As x , (7)

#58Theory and Calculation of Transient Electric Phenomena and OscillationsChapter 4: Inductance And Resistance In Alternating Current Circuits- line 3672

i =— cos (d - 60 - ^)-cos (00 + 0,)- e* . (10)

#59Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 4: Single-Energy Transients In Alternating Current Circuits- line 2600

transient, starts with the value ij = mi0, and if eQ is the e.m.f.

#60Theory and Calculation of Transient Electric Phenomena and OscillationsChapter 3: Inductance And Resistance In Continuous Current Circuits- line 2768

Let e0 = 125 volts = impressed e.m.f. of the circuit, and

#61Theory and Calculation of Transient Electric Phenomena and OscillationsChapter 3: Inductance And Resistance In Continuous Current Circuits- line 2861

e.m.f., and the constants of the circuit then are: e0 = 250

#62Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 1: Nature And Origin Of Transients- line 707

where c = - - -r;1 = constant, and the minus sign is chosen, as

#63Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 3: Single-Energy Transients In Continuous Current Circuits- line 1898

zero of time, Zo = 0, and equations (5) then assume the simpler

#64Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 3: Single-Energy Transients In Continuous Current Circuits- line 2127

zero of time, ^o = 0, and equations (5) then assume the simpler

#65Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 4: Single-Energy Transients In Alternating Current Circuits- line 2617

where L0 = inductance, r0 = total resistance of field-exciting cir-

#66Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 6: Double-Energy Transients- line 3469

io = eo2/o, where e0 = voltage between cable conductor and ground.

#67Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 5: Single-Energy Tra.Nsient Of Ironclad Circuit- line 3512

where Q = a plus the reluctance of the air gap. Equation (1),

#68Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 6: Double-Energy Transients- line 3789

This is correct only if g = 0, that is, the conductance, which rep-

#69Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 6: Double-Energy Transients- line 4228

This is correct only if g = 0, that is, the conductance, which rep-

#70Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 7: Line Oscillations- line 4400

length Z0 = 4 Zi, and therefore the period tQ = cr0/o = 4 o-0/i, that

#71Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 7: Line Oscillations- line 4408

the frequencies (2 k - 1)/0, where k = 1, 2, 3 …

#72Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 7: Line Oscillations- line 4539

tuting {t =F ^i) instead of t into the equations (11), where ^i is the

Transients, Oscillation, And Damping

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