Week 12: First-Order Circuits | Source Free RC and RL Circuits

Now that we have considered the three passive elements (resistors, capacitors, and inductors) individually, we are prepared to consider circuits that contain various combinations of two or three of the passive elements.

In this lesson, we shall examine two types of simple circuits: a circuit comprising a resistor and capacitor and a circuit comprising a resistor and an inductor. These are called RC and RL circuits, respectively. As simple as these circuits are, they find continual applications in electronics, communications, and control systems, as we shall see. We carry out the analysis of RC and RL circuits by applying Kirchhoff’s laws, as we did for resistive circuits. The only difference is that applying Kirchhoff’s laws to purely resistive circuits results in algebraic equations while applying the laws to RC and RL circuits produce differential equations, which are more difficult to solve than algebraic equations. The differential equations resulting from analyzing RC and RL circuits are of the first order.

In addition to there being two types of first-order circuits (RC and RL), there are two ways to excite the circuits. In this lesson, We study and understand the first way, which is by initial conditions of the storage elements in the circuits. In these so-called source-free circuits, we assume that energy is initially stored in the capacitive or inductive element. The energy causes current to flow in
the circuit and is gradually dissipated in the resistors. Although source-free circuits are by definition free of independent sources, they may have dependent sources.

Video Links:

  1. https://www.youtube.com/watch?v=3YinmbkU0DE&list=PLwjK_iyK4LLBN9RIDQfl9YB4caBYyD_uo&index=29&t=0s
  2. https://www.youtube.com/watch?v=KylJ2v1_c-o&list=PLwjK_iyK4LLBN9RIDQfl9YB4caBYyD_uo&index=30&t=0s

Download Files

chapter-7-source-free-rc-and-rl-circuits.pdf (0.58 MB )