501:
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312:
305:
863:
783:
513:
922:
716:
199:
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37:
in an expression. The dual expression thus produced is of the same form, and the reason that the dual is always a valid statement can be traced to the
790:
720:
496:{\displaystyle v_{C}(t)=V_{0}+{1 \over C}\int _{0}^{t}i_{C}(\tau )\,d\tau \iff i_{L}(t)=I_{0}+{1 \over L}\int _{0}^{t}v_{L}(\tau )\,d\tau }
867:
953:
933:
667:
38:
157:
938:
1039:
51:
115:
111:
1044:
649:{\displaystyle v_{R_{1}}=v{\frac {R_{1}}{R_{1}+R_{2}}}\iff i_{G_{1}}=i{\frac {G_{1}}{G_{1}+G_{2}}}}
121:
93:
61:
22:
57:
75:
8:
125:
1007:
958:
16:
Association of electrical terms into pairs based on interchanging voltage and current
106:
986:
34:
70:
66:
990:
943:
137:
1033:
102:
300:{\displaystyle i_{C}=C{\frac {d}{dt}}v_{C}\iff v_{L}=L{\frac {d}{dt}}i_{L}}
1011:
97:
84:
948:
88:
79:
30:
140:
is due to
Alexander Russell who published his ideas in 1904.
1006:, volume 1, chapter XVII, Cambridge: University Press 1904
977:
Belevitch, V, "Summary of the history of circuit theory",
858:{\displaystyle Z_{C}={1 \over Cs}\iff Y_{L}={1 \over Ls}}
778:{\displaystyle Z_{G}={1 \over G}\iff Y_{R}={1 \over R}}
29:. A dual of a relationship is formed by interchanging
506:
203:
Capacitor and inductor – differential form
870:
793:
723:
670:
516:
315:
209:
160:
1026:, Gernsback Library, Inc, New York, 1954, Chapter 6.
25:, electrical terms are associated into pairs called
916:
857:
777:
710:
648:
495:
309:Capacitor and inductor – integral form
299:
193:
1031:
1004:A Treatise on the Theory of Alternating Currents
44:Here is a partial list of electrical dualities:
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826:
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507:Voltage division — current division
486:
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1032:
917:{\displaystyle Z_{L}=Ls\iff Y_{c}=Cs}
985:, Iss 5, pp. 848–855, May 1962
39:duality of electricity and magnetism
934:Duality (electricity and magnetism)
711:{\displaystyle Z_{R}=R\iff Y_{G}=G}
154:Resistor and conductor (Ohm's law)
13:
14:
1056:
939:Duality (mechanical engineering)
1024:Transistors Theory and Practice
954:Mechanical–electrical analogies
194:{\displaystyle v=iR\iff i=vG\,}
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991:10.1109/JRPROC.1962.288301
131:
659:Impedance and admittance
787:Capacitor and inductor
664:Resistor and conductor
116:Kirchhoff's voltage law
112:Kirchhoff's current law
52:parallel – series
48:voltage – current
1040:Electrical engineering
979:Proceedings of the IRE
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149:Constitutive relations
136:The use of duality in
23:electrical engineering
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1002:Alexander Russell,
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122:Thévenin's theorem
1022:Turner, Rufus P,
959:List of dualities
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126:Norton's theorem
71:current division
67:voltage division
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138:circuit theory
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120:
118:. KVL and KCL
117:
113:
110:
108:
104:
103:short circuit
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36:
32:
28:
24:
19:
1023:
1003:
998:
982:
978:
973:
510:
135:
107:open circuit
43:
26:
20:
18:
98:susceptance
85:capacitance
62:conductance
1034:Categories
965:References
949:Dual graph
89:inductance
80:admittance
58:resistance
54:(circuits)
1012:264936988
892:⟺
824:⟺
749:⟺
689:⟺
581:⟺
491:τ
481:τ
454:∫
404:⟺
400:τ
390:τ
363:∫
253:⟺
175:⟺
94:reactance
76:impedance
928:See also
144:Examples
124:–
114:–
105:–
96:–
87:–
78:–
69:–
60:–
132:History
35:current
31:voltage
1010:
983:vol 50
27:duals
1008:OCLC
33:and
987:doi
21:In
1036::
981:,
41:.
1014:.
993:.
989::
912:s
909:C
906:=
901:c
897:Y
888:s
885:L
882:=
877:L
873:Z
850:s
847:L
843:1
838:=
833:L
829:Y
817:s
814:C
810:1
805:=
800:C
796:Z
771:R
768:1
763:=
758:R
754:Y
743:G
740:1
735:=
730:G
726:Z
706:G
703:=
698:G
694:Y
685:R
682:=
677:R
673:Z
639:2
635:G
631:+
626:1
622:G
615:1
611:G
605:i
602:=
595:1
591:G
586:i
572:2
568:R
564:+
559:1
555:R
548:1
544:R
538:v
535:=
528:1
524:R
519:v
488:d
484:)
478:(
473:L
469:v
463:t
458:0
448:L
445:1
440:+
435:0
431:I
427:=
424:)
421:t
418:(
413:L
409:i
397:d
393:)
387:(
382:C
378:i
372:t
367:0
357:C
354:1
349:+
344:0
340:V
336:=
333:)
330:t
327:(
322:C
318:v
293:L
289:i
282:t
279:d
275:d
270:L
267:=
262:L
258:v
247:C
243:v
236:t
233:d
229:d
224:C
221:=
216:C
212:i
188:G
185:v
182:=
179:i
171:R
168:i
165:=
162:v
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