Summary
1.43
• In addition,
lumped parameter circuit theory assumes the following:
a. The electrostatic field created by charge distribution on an electrical device is confined to
space within the device and in the immediate vicinity of the device predominantly. Thus, the
terminal voltage across a device and the charge stored in that device can be related through a
unique ratio.
b. The induced electric field inside connecting wires and outside the devices is negligible. This
makes it possible to assign a unique voltage variable to a device.
c. The connecting wires are of infinite conductivity and near-zero thickness. Thus, there are no charges
distributed on their surface and no current component is needed to create charge distribution on
them. This makes it possible to assign a unique current variable to an electrical device.
d. The component of current needed to create the time-varying charge distribution on the surface
of the device is negligible except in those devices (capacitors) that are designed to make such
current flow the dominant electrical phenomenon in them.
e. The induced electric field inside devices is negligible except in those devices (inductors)
where induced electric field is the dominant electrical phenomenon by design. Such devices
are designed to confine the time-varying flux linkage to space within them.
f. The conductivity of metallic conductors employed in capacitors and inductors is infinity.
Hence, there is no resistive effect in them.
• A two-terminal element is a mathematical model of an electrical device with a terminal voltage variable
v(
t) and current variable
i(
t) assigned to it. These are functions of time only. The entire electrical
behaviour of the device can be characterized by these two variables and a relation between them.
• Passive sign convention assigns reference polarity for
v(
t) with
+
at one end and – at other end of
the element. Reference direction for
i(
t) is such that it flows into the
+
polarity of
v(
t)
from outside
the element. The power delivered to the element is given by
p(
t)
=
v(
t)
i(
t) with this sign convention.
•
The symbols and v –
i relations for the three passive two-terminal elements are shown in Fig. 1.9-1.
• Ideal independent voltage source is a
two-terminal
element with its voltage
variable specified as a function of time
and current variable as a free variable.
Ideal independent current source is a
two-terminal
element with its current
variable specified as a function of time
and voltage variable as a free variable.
• Circuit elements are classified into
linear
and
nonlinear
elements
depending on whether their
v –
i
relationship satisfy the
principle of
superposition or not.
Independent
sources are nonlinear elements.
• An element is a
passive element if the energy delivered to it from -
∞
to
t is non-negative for all
t
and for all permissible (
v(
t),
i(
t)) combinations.
R,
L and
C are passive elements.
•
A circuit element is a time-invariant element if the parameter of the element is a constant.
• Ideal dependent sources are four-terminal elements. The first terminal pair is connected at some
location in the circuit to sense a voltage variable or a current variable there. The second terminal
pair delivers either a voltage or a current at the location where it is connected. The value of voltage
or current delivered is a function of
controlling variable that is sensed by the first terminal pair.
Fig. 1.9-1
Passivetwo-terminalelements
v
(
t
)
+
+
+
–
–
–
v
(
t
)
v
(
t
)
i
(
t
)
i
(
t
) =
d
v
(
t
)
d
t
v
(
t
) =
v
(
t
) =
Ri
(
t
)
i
(
t
)
i
(
t
)
R
L
L
C
C
d
i
(
t
)
d
t
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1.44
CircuitVariablesandCircuitElements
• There are four kinds of dependent sources. They are Voltage-Controlled Voltage Source, Voltage-
Controlled Current Source, Current-Controlled Voltage Source and Current-Controlled Current
Source. A dependent source is a
linear element if the source quantity is a linear function of the
controlling-variable.
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