Chapter 7. First Order Circuits

This part of the book introduces capacitors  and examines circuits comprised of these circuit elements. Capacitors, like resistors, are passive, linear circuit elements. Therefore,  previously discussed linear analysis techniques, such as node voltage analysis,  apply to circuits built from resistors and capacitors. Recall that the resistor has a linear algebraic relationship between voltage and current, and circuit analysis involving resistors and sources led to linear system of linear algebraic equations to solve for circuit variables. As we shall see, the voltage and current relationship for capacitors are first-order derivative and integral relationships. Consequently, analysis of circuits involving capacitors leads to linear differential equations and, for multi-node circuits, systems of linear  differential equations. We will examine the solution to first order systems and consider the relaxation oscillator as one particular application.