Circuit elements are commonly categorized as either passive or
active. A circuit element is passive if the total amount of
energy it delivers to the rest of the circuit (over all time) is non-positive.
(Passive elements can temporarily deliver energy to a circuit, but only
if the energy was previously stored in the passive element by the circuit.) An
active circuit element has the ability to create and provide power to a circuit
from mechanisms external to the circuit. Examples of active circuit
elements are batteries (which create electrical energy from chemical processes)
and generators (which create electrical energy from mechanical processes. A good
example of this would be the spinning of a turbine).
There are a variety of types of active sources. They are broadly categorized as:
Ideal independent sources
Non-ideal independent sources
Dependent sources
In this exercise we will talk about ideal independent sources. We will consider
two basic types of sources: voltage sources and current sources. From a
practical standpoint, we will only implement voltage sources for now
—current sources can wait until later.
Ideal Independent Voltage Sources
An independent voltage source maintains a specified voltage across its terminals.
The symbol used to indicate a voltage source delivering a voltage
Vs(t) is shown in Fig. 1. As indicated in Fig. 1, the voltage
supplied by the source can be time varying or constant (a constant voltage is a
special case of a time varying voltage). An alternate symbol that is often used
to denote a constant voltage source is shown in Fig. 2; however, we will
generally use the symbol of Fig. 1 for both time-varying and constant voltages.
Figure 1. Independent Voltage Source.Figure 2. Constant Voltage Source.
Please keep in mind that, for ideal independent voltage sources, we know exactly
what the voltage difference is; it has to be the value shown next to the source
symbol. We also know the polarity of the voltage—the “+” and
“-” signs on the symbol tell us the polarity. However, we know
nothing about the current through the source! This tends to be confusing at
times, and can be the source of many silly mistakes. Even the current direction
is unknown1—anything we want to find out about current must be
determined (if necessary) from an analysis of the overall circuit.
Ideal voltage sources provide a specified voltage regardless of the
current flowing through the device. Ideal sources can, obviously, provide
infinite power; all real sources will provide only limited power to the circuit.
We will discuss approaches for modeling non-ideal sources in later projects.
Ideal Independent Current Sources
An ideal independent current source maintains a specified current. The circuit
symbol for an ideal independent source is shown in Fig. 3. Note that the current
value is listed next to the circuit symbol and that the direction of current flow
in the source is provided on the source symbol—there is no need to assume a
current direction2. The current supplied by the source can be
time-varying or constant.
The current provided on the circuit symbol is maintained regardless of
the voltage difference across the terminals. Even the voltage polarity is
unknown and must be determined (if necessary) from an analysis of the overall
circuit.
Figure 3. Independent current source.
Important Points
Ideal voltage sources provide a specified voltage regardless of the
current flowing through the device. Ideal sources can, obviously, provide
infinite power; all real sources will provide only limited power to the
circuit. We will discuss non-ideal sources in later projects.
Ideal current sources provide a specified current regardless of the
voltage difference across the device. Ideal current sources can, like ideal
voltage sources, provide infinite power; all real sources will provide only
limited power to the circuit; as with voltage sources, this is a topic for
later projects.
Test Your Knowledge!
A five volt ideal source is connected to a circuit element as shown. What do
you think the voltage across the element, V, and the current through the
element are? (This question is not entirely fair, since determining V
requires use of Kirchhoff's voltage law, which isn't presented in this
project. Take a guess, though, based on your gut feeling.)
A two amp ideal source is connected to a circuit element as shown. What do
you think the voltage across the element, V, and the current through the
element are? (This question is not entirely fair, since determining
I requires use of Kirchhoff's current law, which isn't presented in
this project. Take a guess, though, based on your gut feeling.)
What is the current, I, in the circuit below?
What is the voltage V in the circuit below?
A 3V ideal voltage source is connected across a perfect conductor. What
do you think will happen? What if we reduce the voltage to 0.01
milli-volts?
A 0.01 amp ideal current source is connected to an open circuit. What do
you think will happen? (Note: an open circuit allows no current to
flow.)
Selected Answers
The voltage is 5V (the source requires that it provide 5V across its
terminals. (The circuit element shares the same terminals as the voltage
source, so it also has 5V across its terminals.) We don't know anything
about the current, since we don't know anything about the electrical
component to which the source is connected.
The current is 2A (the source requires that it provide 2A. (There is
nowhere for the current to go except the circuit element, so 2A also goes
through the circuit element.) We don't know anything about the voltage,
since we don't know anything about the electrical component to which the
source is connected.
Not enough is known about the circuit element to determine current. The
ideal source can provide any current.
Not enough is known about the circuit element to determine voltage.
The voltage source requires that the voltage difference across the
perfect conductor be 3V. The perfect conductor doesn't allow any voltage
difference across it. The voltage source will deliver infinite current,
in an attempt to create a voltage difference across the conductor.
Reducing the voltage won't change this scenario.
The current source requires that 0.01A flow through the open circuit, but
the open circuit won't allow any current through it. The current source
will create an infinite voltage across the open circuit, in an attempt to
force current through the open circuit.