110 Practical MATLAB® Applications for Engineers
R.2.46 A capacitor (C) basically consists of two conductor plates called electrodes, sepa-
rated by insulating material referred to as dielectric. When a voltage V is applied
across the plates, an electric fi eld is established and the capacitor C charges. The
capacitance C is defi ned in terms of its electrical variables by
C
Q
V
The capacitance C, in terms of its physical dimensions is defi ned by
C
A
d ∈ 0 (farads)where ∈ = ∈r (^) ∈ 0 , ∈ 0 = 8.85 10 −^12 F/m (permittivity of vacuum), and ∈r is the rela-
tive permittivity or dielectric constant of a particular material.
For example, ∈r (vacuum) = 1, ∈r (mica) = 5, and ∈r (glass) = 7. 5.
A = area of the plates = width * height (in meters^2 )
and
d = distance between the plates (in meters)
R.2.47 The behavior of the voltages and currents in an electrical network is governed by
KCL and KVL stated in R.2.48 and R.2.49.
R.2.48 KCL states that the sum of the currents entering a junction (also referred to as a
node) must equal the sum of the currents leaving that junction (node), or the sum
of the currents at any node is always equal to zero, illustrated in Figure 2.1.
R.2.49 KVL states that the sum of the voltage raises (gains) are equal to the sum of the volt-
age drops (losses) in any close electrical loop (which is a consequence of the law of
conservation of energy) illustrated in Figure 2.2.
KVL must be applied around a closed electric loop in which the referred loop
may or may not have current (open circuit), but the sum of all the voltage drops
around it (loop) is always zero.
R.2.50 When two (or more) electrical elements, denoted by A and B, have the same current
fl ow and are connected in cascade, as shown in Figure 2.3, they are referred to as a
series connection.
FIGURE 2.1
An electric node (KCL).
i 1 + i 2 + i 3 = i 4 + i 5 + i 6
i 1
i (^3) i 6
i 4
i 5
i 2