• Source: Duality (electrical circuits)

In electrical engineering, electrical terms are associated into pairs called duals. A dual of a relationship is formed by interchanging voltage and current 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 duality of electricity and magnetism.
Here is a partial list of electrical dualities:

voltage – current
parallel – series (circuits)
resistance – conductance
voltage division – current division
impedance – admittance
capacitance – inductance
reactance – susceptance
short circuit – open circuit
Kirchhoff's current law – Kirchhoff's voltage law. KVL and KCL
Thévenin's theorem – Norton's theorem




History


The use of duality in circuit theory is due to Alexander Russell who published his ideas in 1904.




Examples






= Constitutive relations

=
Resistor and conductor (Ohm's law)



v
=
i
R

⟺

i
=
v
G



{\displaystyle v=iR\iff i=vG\,}


Capacitor and inductor – differential form




i

C


=
C


d

d
t




v

C



⟺


v

L


=
L


d

d
t




i

L




{\displaystyle i_{C}=C{\frac {d}{dt}}v_{C}\iff v_{L}=L{\frac {d}{dt}}i_{L}}


Capacitor and inductor – integral form




v

C


(
t
)
=

V

0


+


1
C



∫

0


t



i

C


(
τ
)

d
τ

⟺


i

L


(
t
)
=

I

0


+


1
L



∫

0


t



v

L


(
τ
)

d
τ


{\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 }





= Voltage division — current division

=





v


R

1




=
v



R

1




R

1


+

R

2






⟺


i


G

1




=
i



G

1




G

1


+

G

2







{\displaystyle v_{R_{1}}=v{\frac {R_{1}}{R_{1}+R_{2}}}\iff i_{G_{1}}=i{\frac {G_{1}}{G_{1}+G_{2}}}}





= Impedance and admittance

=
Resistor and conductor




Z

R


=
R

⟺


Y

G


=
G


{\displaystyle Z_{R}=R\iff Y_{G}=G}






Z

G


=


1
G



⟺


Y

R


=


1
R




{\displaystyle Z_{G}={1 \over G}\iff Y_{R}={1 \over R}}


Capacitor and inductor




Z

C


=


1

C
s




⟺


Y

L


=


1

L
s





{\displaystyle Z_{C}={1 \over Cs}\iff Y_{L}={1 \over Ls}}






Z

L


=
L
s

⟺


Y

c


=
C
s


{\displaystyle Z_{L}=Ls\iff Y_{c}=Cs}





See also


Duality (electricity and magnetism)
Duality (mechanical engineering)
Dual impedance
Dual graph
Mechanical–electrical analogies
List of dualities




References



Turner, Rufus P, Transistors Theory and Practice, Gernsback Library, Inc, New York, 1954, Chapter 6.

Kata Kunci Pencarian:

• Buku ilmu antik
• Duality (electrical circuits)
• Duality
• Dualism
• Duality (electricity and magnetism)
• Kirchhoff's circuit laws
• List of dualities
• Distribution board
• Series and parallel circuits
• Duality (mechanical engineering)
• Dual