Direct Current and Transient Analysis
109
The voltage across a resistor presents the following polarities: it is always positive
at the terminal at which the current enters the resistor and negative at the point
where it leaves.
The inverse of a resistance is called a conductance (denoted by G), where G = 1/R
with the units given in siemens (sie), where 1 sie = 1/Ω.
R.2.43 The resistance of electrical material (including a wire) is a function of its dimensions as well as its physical properties, and is given by the following equation:
R = * l/a
where α is called the resistivity factor of the material in Ω * meters, l is its length in
meters, and a is its cross-sectional area in meters squared.
The resistivity factor α of a good conductor is bounded by the following (resistivity) limits 1.6 * 10
−6 Ω cm < α < 2.5 * 10
−6 Ω cm, whereas the resistivity factor of an
insulator is given by
> 200 * 10
−6
cm
For example, the resistivity factor of copper is α = 1.7 * 10
−6 Ω cm (conductor),
whereas the resistivity factor of carbon is α = 3500 * 10
−6 Ω cm (insulator). The
equation R = α * l/a is especially useful when evaluating the resistance of a segment of a wire.
R.2.44 The current through and voltage across an inductor* L are related by
v t
L
di t
dt
L
L
( ) ϭ
( )
and
i t
L
v t dt
L
L
( ) ϭ
1
( )
∫
R.2.45 The current through and the voltage across a capacitor C are related by the following equations:
i t
C
dv t
dt
C
C
( )
( )
ϭ
and
v t
C
i t dt
C
C
( )
( )
ϭ
1
∫
* An inductor L is a coil of wire, which when connected across a voltage source, produces a magnetic fi eld in
the coil that opposes current changes. According to Faraday’s law, the induced voltage is proportional to the
change in fl ux linkage which in turn is proportional to its current.
CRC_47760_CH002.indd 109
CRC_47760_CH002.indd 109
7/23/2008 1:38:36 PM
7/23/2008 1:38:36 PM
109
The voltage across a resistor presents the following polarities: it is always positive
at the terminal at which the current enters the resistor and negative at the point
where it leaves.
The inverse of a resistance is called a conductance (denoted by G), where G = 1/R
with the units given in siemens (sie), where 1 sie = 1/Ω.
R.2.43 The resistance of electrical material (including a wire) is a function of its dimensions as well as its physical properties, and is given by the following equation:
R = * l/a
where α is called the resistivity factor of the material in Ω * meters, l is its length in
meters, and a is its cross-sectional area in meters squared.
The resistivity factor α of a good conductor is bounded by the following (resistivity) limits 1.6 * 10
−6 Ω cm < α < 2.5 * 10
−6 Ω cm, whereas the resistivity factor of an
insulator is given by
> 200 * 10
−6
cm
For example, the resistivity factor of copper is α = 1.7 * 10
−6 Ω cm (conductor),
whereas the resistivity factor of carbon is α = 3500 * 10
−6 Ω cm (insulator). The
equation R = α * l/a is especially useful when evaluating the resistance of a segment of a wire.
R.2.44 The current through and voltage across an inductor* L are related by
v t
L
di t
dt
L
L
( ) ϭ
( )
and
i t
L
v t dt
L
L
( ) ϭ
1
( )
∫
R.2.45 The current through and the voltage across a capacitor C are related by the following equations:
i t
C
dv t
dt
C
C
( )
( )
ϭ
and
v t
C
i t dt
C
C
( )
( )
ϭ
1
∫
* An inductor L is a coil of wire, which when connected across a voltage source, produces a magnetic fi eld in
the coil that opposes current changes. According to Faraday’s law, the induced voltage is proportional to the
change in fl ux linkage which in turn is proportional to its current.
CRC_47760_CH002.indd 109
CRC_47760_CH002.indd 109
7/23/2008 1:38:36 PM
7/23/2008 1:38:36 PM