We will consider that our electrical circuits consist of two or more circuit elements interconnected by perfect conductors. The circuit elements can be resistors, transistors, capacitors, inductors, integrated circuits, or any other device which has an effect on voltage or current. Our “perfect” conductors can be wires that allow current to flow from one element to another. This representation of electrical circuits contains an underlying assumption: only the circuit elements have an effect on the energy storage or transfer in the circuit1. Since the energy is lumped at discrete points in the circuit (in the components), a circuit which is represented this way is called a lumped-parameter circuit2.
Figure 1 shows an example of a lumped parameters circuit. The circuit elements A, B, C, and D affect the energy in the circuit; the connecting lines between them are perfect conductors —they can transfer any amount of current without storing or dissipating energy.
Circuit elements in lumped parameters circuits are connected at nodes. Identification of circuit nodes will be extremely important to us when we are creating and analyzing circuits. Every node has a single unique voltage, so there can be no voltage drops (and thus no circuit elements) within a node. Perfect conductors do not cause voltage drops, so a node can contain perfect conductors. An example circuit is shown in Fig. 2(a). A common error would be to identify seven nodes in the circuit, as indicated by points a, b, c, d, e, f, and g. However, nodes b and c are connected only by a perfect conductor, so there is no voltage difference between those two points; they are part of the same node. Likewise, a perfect conductor connects points f and g. Therefore, there are only five nodes in the circuit, as shown in Fig. 2(b).
Physically, circuit elements can be interconnected in a number of ways. We will be creating our circuits on solderless breadboards, however, so we only have a couple of options:
Obviously, identifying any physical connector (such as a wire) as a “perfect” conductor will be incorrect; any wire will have some non-zero resistance, and will cause an amount of voltage difference between its ends. The trick is that the resistance of the conductor should be negligible compared to the resistance of the other components in the circuit in order for it to be considered “close enough” to zero to make no difference. For example, a wire with a resistance of 0.1Ω can probably be neglected if it connects two 10kΩ resistors.