PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

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 dimen-

sions 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 (resistiv-
ity) 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 seg-
ment of a wire.
R.2.44 The current through and voltage across an inductor* L are related by
vt L
di t
L dt

()
L()

and

it

L

LL()
 vtdt

1

∫ ()

R.2.45 The current through and the voltage across a capacitor C are related by the follow-

ing equations:

it C

dv t

C dt

()
C()

and

vt

C

CC()
 itdt()

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.