23
Fundamentals of Electric Capacitors
V ∑
n
⎛ n
1
=
V
⎜
⎟
i = Q ∑
⎞
o
Q
=
(1.38)
⎜
C i ⎟ C
⎠
Eq ,series
i=1
⎝ i=1
The equivalent capacitance of capacitors connected in series, which is the
sum of their reciprocal, is always smaller than any individual capacitor and
is more approximate to the smallest one.
1.6.3 Inductors
Inductors are analogous circuit elements used to generate a controlled magnetic field. An inductor is made from a continuously winded conducting
wire that results in a coil that is significantly shorter than the overall length
of the wire used. A current I passing through a coil can produce a magnetic
flux Φ B . The inductance, L is defined as
NΦ
L =
B
(1.39)
I
where N is the number of turns used in winding the coil. With the use of an
ideal inductor (i.e., negligible resistance through the conductor), an induced
potential difference V L can develop across the element following a change in
the current:
dI
V L = −L
(1.40)
dt
Equation (1.40) indicates that the generated inductance can oppose a change
in the flow of current. This principle is of more significance in AC applications.
1.6.4 Resistor–Inductor Circuits
Inductors are similar to capacitors in that they store an electric charge
through an induced magnetic field rather than an electric field. The storage
process can be described using an analysis of a single-loop series resistor–
inductor (RL) circuit as shown in Figure 1.9. When an RL circuit is closed at
time t = 0, a current is generated by the external power source with a potential V 0 and will flow through the resistor. However, a rapid increase of the
current to a stable value
V
o
R
Fundamentals of Electric Capacitors
V ∑
n
⎛ n
1
=
V
⎜
⎟
i = Q ∑
⎞
o
Q
=
(1.38)
⎜
C i ⎟ C
⎠
Eq ,series
i=1
⎝ i=1
The equivalent capacitance of capacitors connected in series, which is the
sum of their reciprocal, is always smaller than any individual capacitor and
is more approximate to the smallest one.
1.6.3 Inductors
Inductors are analogous circuit elements used to generate a controlled magnetic field. An inductor is made from a continuously winded conducting
wire that results in a coil that is significantly shorter than the overall length
of the wire used. A current I passing through a coil can produce a magnetic
flux Φ B . The inductance, L is defined as
NΦ
L =
B
(1.39)
I
where N is the number of turns used in winding the coil. With the use of an
ideal inductor (i.e., negligible resistance through the conductor), an induced
potential difference V L can develop across the element following a change in
the current:
dI
V L = −L
(1.40)
dt
Equation (1.40) indicates that the generated inductance can oppose a change
in the flow of current. This principle is of more significance in AC applications.
1.6.4 Resistor–Inductor Circuits
Inductors are similar to capacitors in that they store an electric charge
through an induced magnetic field rather than an electric field. The storage
process can be described using an analysis of a single-loop series resistor–
inductor (RL) circuit as shown in Figure 1.9. When an RL circuit is closed at
time t = 0, a current is generated by the external power source with a potential V 0 and will flow through the resistor. However, a rapid increase of the
current to a stable value
V
o
R