Page 261 - Mechatronics with Experiments

Printer: Yet to Come
October 28, 2014 11:15 254mm×178mm
JWST499-Cetinkunt
JWST499-c05
ELECTRONIC COMPONENTS FOR MECHATRONIC SYSTEMS 247
applications where the resistance value is color coded on the component using a four color
code. The maximum power rating of a resistor defines the maximum power it can dissipate
without damage,
2
V 12
2
P = V 12 ⋅ i = V 12 ⋅ (V ∕R) = R ⋅ i = < P max (5.6)
12
R
which defines the maximum voltage drop or maximum current that can be present across
the resistor.
A capacitor stores electric charges, and hence creates an electric field (electric volt-
age) across its terminals. It is made of two conducting materials separated by an insulating
material such as air, vacuum, glass, rubber, or paper. The two conductor surfaces store
equal but opposite charges. As a result, there is a voltage potential across the capacitor.
The voltage potential is proportional to the amount of charge stored and the characteristics
of the capacitor. There are four major capacitor types: mica, ceramic, paper/plastic film,
and electrolytic. Electrolytic type capacitors are polarized. Therefore, the positive terminal
must be connected to the positive side of the circuit.
An ideal capacitor generates a voltage potential difference between its two nodes
proportional to the stored electrical charge (integral of current conducted)
Q 1 t
V (t) = = i( ) ⋅ d (5.7)
12
C C ∫ 0
◦
where C is called the capacitance. An ideal capacitor induces a 90 phase angle between
its voltage and current across its terminals due to the integral function. When a capacitor is
fully charged, it stores a finite amount of charge,
t
Q = i( ) ⋅ d = C ⋅ V 12 (5.8)
∫
0
The size of a capacitor is indicated by the amount of charge it can store (capacitance, C).
A given capacitor can hold voltage up to a certain amount, V max (called the rated voltage).
Capacitance (C) is a measure of how much charge (Q) the capacitor can hold for a given
voltage potential, (V). A capacitor cannot hold a voltage potential above a maximum value,
V max . If the rated voltage is exceeded, the capacitor breaks down and cannot hold the
charges. The construction principle of a capacitor includes two conductors separated by
insulating material. The capacitance is proportional to the surface area of the capacitor
(conductors inside the capacitor) which holds the charge and inversely proportional to the
distance between them. The proportionality constant is the permittivity of the medium that
separates the conductors, ,

⋅ A ⋅ A
0
C = = (5.9)
l l
where is the dielectric constant, is the permittivity of free space. The dielectric constants
0
for some materials are as follows: = 1.00 for vacuum, = 3.4 for nylon, = 5.6 for glass,
= 3.7 for paper. Clearly, as the dielectric constant of the insulating material increases,
the capacitance of the capacitor increases. The capacitance is proportional to the surface
area of the capacitor plates and inversely proportional to the distance between them. The
maximum voltage that the capacitor can handle before break-down, called break-down
voltage or rated voltage, increases with the increase in dielectric constant of the insulator.
The break-down voltage of the capacitor also increases with the distance parameter l.