DIRECT CURRENT CIRCUITS ANALYSIS: THE ELECTRICAL ENGINEERING SERIES

Demetrios P. The Direct Current Circuits play an important role because, i) One can lay out the fundamental methods, techniques and theorems governing the operation of all types of circuits, but since in the DC case, the mathematics involved are rather simple, the DC circuits may serve as an introduction to the study of more complicated types of circuits. ii) The DC circuits are widely used in every day practical applications. The reader who will understand the operation of the DC circuits, will be able to follow rather easily more complicated cases, where the electrical signals v(t) and i(t) vary with time. In these cases, the study of the circuits is implemented by means of differential or even integro-differential equations, the solution of which is not an easy task. In this text we develop some systematic methods for the analysis of DC Circuits, by means of which one may write by inspection the governing circuit equations, and then proceed to the solution. Given that the circuits we consider are Linear Circuits, it turns out that the sought for equations for the voltages and / or the currents involved are linear equations, which can be expressed briefly and compactly, making use of Matrix Notation. Matrix Theory is therefore a valuable tool in analyzing Linear DC Circuits. In Chapter 1 we give a brief but systematic review of Matrix Theory, operation with Matrices, Determinants, Matrix Solution of Linear Systems, the Crammer’s Rule, etc. In Chapter 2 we develop the Mesh or Loop Analysis method, which is based on the notion of Loop Currents and is ideal for circuits containing voltage sources only, In Chapter 3 we develop the Nodal Analysis method, which is based on the notion of Nodal Potential and is ideal for circuits containing current sources only, In Chapter 4 we show how to convert a realistic voltage source into an equivalent current source, and vice versa, In Chapter 5 we state and prove the Millman’s Theorem, which reduces parallel connected realistic voltage sources to an equivalent single voltage source, In Chapter 6 we state and develop the extremely important Superposition Principle, which is widely used if the circuit contains both voltage and current sources, In Chapter 7 we state and prove the extremely powerful in circuit analysis Thevenin’s Theorem, In Chapter 9 we state and prove the extremely powerful in circuit analysis Norton’s Theorem, which is actually the dual of Thevenin’s Theorem, In Chapter 10 we state and prove the so called Kennelly’s Theorem, by means of which one may transform a Y (wye) circuit to a Δ (delta) circuit and vice versa, In Chapter 11 we state some more general problems, of increased complexity, the solution of which requires a suitable application of various circuit analysis methods, techniques and theorems, developed in the previous chapters. The 30 illustrative solved Examples and the 105 characteristic Problems to be solved are design to help students develop a solid theoretical background, broaden their knowledge and sharpen their analytical skills on the subject. Kanoussis Ph.D