This chapter presents the culmination of the analysis of DC circuits that employ resistors along with any number of voltage and/or current sources. Here we shall focus on nodal analysis and mesh analysis. Both nodal analysis and mesh analysis generate a system of simultaneous linear equations that are used to solve the circuit for various voltages or currents. There are several methods that can be used to solve the simultaneous equations including substitution, Gauss-Jordan elimination and expansion by minors. These methods are reviewed in Appendix B and are not covered in this chapter. Instead, to keep clutter to a minimum and focus on the circuit analysis aspects, the explanations and examples will simply detail the process of examining the circuit and applying basic circuit laws to create the system of equations. From there, the specific technique used to solve these simultaneous equations is up to you based on your personal preferences.
It is particularly efficient to obtain a more advanced scientific calculator that can solve these equations directly rather than plowing through the solution manually. By doing so, you can spend your precious time mastering the process of circuit analysis and creating the equations. Manual solution techniques, though not necessarily difficult, can be tedious, time consuming and error prone. If you plan on continuing your study into AC electrical circuits, you should consider obtaining a calculator that can solve simultaneous equations with complex coefficients. Such calculators can be expensive when purchased new, such as the Texas Instruments TI-89 and Nspire models. On the used market, perfectly satisfactory older models such as the TI-85 and TI-86 can be found at considerable discount. Another model to consider is the Casio FX-9750GII, although it is not quite as powerful as some of the other units mentioned.
Along with nodal and mesh, we shall also introduce the concept of dependent sources. These are current and voltage sources whose value is not fixed to some particular value, but rather is dependent on some other current or voltage in the circuit. What makes this interesting is that this controlling current or voltage may itself be affected by the value produced by the dependent source. Dependent sources are often used to model the behavior of active electronic devices such as bipolar and field effect transistors.