1. Basic Circuit Analysis

• Circuit analysis can be troubling because we are dealing with particles that have never been seen. We depend upon calculations and approximations to determine what is happening inside the circuit, and measuring instruments to verify our numbers.

1.1 Circuit Components and Quantities

• Although in reality circuits involve complex interactions of potential and magnetic fields, we tend to simplify components into discrete and independent parts.

• Typically each simple circuit component will act as a “black box” with an applied current creating a voltage, or an applied voltage creating a current.

• Current and voltage are very important terms that are not well understood by the beginner. Consider an electron/proton pair. If both are together they are stable and steady. If we separate them they exert a force of attraction, much like gravity. This potential of attraction is called voltage. If we create a channel for these electrons to flow back to the protons (electrons are much lighter and more mobile than protons), the flow of electrons is called a current. The electrons do not flow freely, the restriction of flow is called resistance.   • Resistance is the simplest of all circuit elements, and is found in all circuit elements, but there are a variety of other simple elements found in circuits,

capacitors

inductors

voltage sources

current sources • All of us have seen an electromagnet at least once in our lives. This is effectively a large inductor. The device is best described as resisting current flow changes (almost as if preserving the momentum of the current). The resulting relationship is,  • When you get a static shock you are touching a basic form of capacitor. An electrical capacitor typically allows current to flow freely when a voltage is applied, but the current will quickly reach a steady state. The relationship is,  • Voltage sources are also very common. Disposable batteries (e.g, 1.5V, 9V) are one good example. When we use these normally we assume that the batteries will supply any amount of current, at the rated voltage. The schematic symbol is shown below,  • A similar method is used when considering current sources • Some theoretical treatments of circuit elements make use of dependent (variable) voltage and current sources. The schematic symbols are often as shown below, 1.2 Circuit Diagrams

• Most of us will have seen a circuit diagram in the past, but there are some terms and conventions of importance when constructing and reading these diagrams.

• Generally,

we try to have positive voltages at the top, and sources on the left hand side.

each device has input/output terminals that are connected to nodes (black dots). They may not be drawn for simple connections, but are implied.

standard schematic symbols are available to reduce ambiguity.

All components are labeled with variable names or values.

• Consider the example, 