A circuit element is an *idealised *mathematical model of a two-terminal electrical device that is completely characterised by its voltage-current relationship. Although ideal circuit elements are not “off-the-shelf” circuit components, their importance lies in the fact that they can be interconnected (on paper or on a computer) to approximate actual circuits that are composed of nonideal elements and assorted electrical components – thus allowing for the analysis of such circuits.

Circuit elements can be categorized as either *active *or *passive*.

**Active Circuit Elements**

Active circuit elements *can *deliver a non-zero average power indefinitely. There are four types of active circuit element, and all of them are termed an *ideal source*. They are:

- Independent voltage source
- Independent current source
- Dependent voltage source
- Dependent current source

**Passive Circuit Elements**

Passive circuit elements *cannot *deliver a non-zero average power indefinitely. Some passive elements are capable of storing energy, and therefore delivering power back into a circuit at some later time, but they cannot do so indefinitely.

There are three types of passive circuit element. They are:

- Resistor
- Inductor
- Capacitor

**Types of Circuits**

The interconnection of two or more circuit elements forms an electrical *network*. If the network contains at least one closed path, it is also an electrical *circuit*. A network that contains at least one active element, i.e. an independent or dependent source, is an *active *network. A network that does not contain any active elements is a *passive *network.

**Independent Sources**

Independent sources are *ideal *circuit elements that possess a voltage or current value that is independent of the behaviour of the circuits to which they belong.

**The Independent Voltage Source**

An independent voltage source is characterised by a terminal voltage which is completely independent of the current through it. The representation of an independent voltage source is shown below:

If the value of the voltage source is constant, that is, does not change with time, then we can also represent it as an *ideal battery*:

Although a “real” battery is not ideal, there are many circumstances under which an ideal battery is a very good approximation.

In general, however, the voltage produced by an ideal voltage source will be a function of time. In this case we represent the voltage symbolically as *v*(*t *) .

A few typical voltage waveforms are shown below. The waveforms in (a) and (b) are typical-looking amplitude modulation (AM) and frequency modulation (FM) signals, respectively. Both types of signals are used in consumer radio communications. The sinusoid shown in (c) has a wide variety of uses; for example, this is the shape of ordinary household voltage. A “pulse train”, such as that in (d), can be used to drive DC motors at a variable speed.

Since the voltage produced by a source is in general a function of time, then the most general representation of an ideal voltage source is as shown below:

**The Independent Current Source**

An independent current source establishes a current which is independent of the voltage across it. The representation of an independent current source is shown below:

In other words, an *ideal current source *is a device that, *when connected to **anything*, will always push current ( *is) out of terminal 1 and pull is into terminal 2*

Since the current produced by a source is in general a function of time, then the most general representation of an ideal current source is as shown below: