Alexander-Sadiku
Fundamentals of Electric Circuits
Chapter 8
  Second-Order Circuits

Second-Order Circuits
Chapter 8
8.1 Examples of 2nd order RCL circuit
8.2 The source-free series RLC circuit
8.3 The source-free parallel RLC circuit
8.4 Step response of a series RLC circuit
8.5 Step response of a parallel RLC

8.1 Examples of Second
Order RLC circuits (1)
What is a 2nd order circuit?

8.2 Source-Free Series
RLC Circuits (1)

8.2 Source-Free Series
 RLC Circuits (2)
Method will be illustrated
during the lecture

8.2 Source-Free Series
RLC Circuits (3)

Slide 7

8.2 Source-Free Series
RLC Circuits (5)
Example 1
   If R = 10 Ω, L = 5 H, and   C = 2 mF in 8.8, find α, ω0, s1 and s2.
  What type of natural response will the circuit have?

8.2 Source-Free Series
RLC Circuits (6)
Example 2
  The circuit shown below has reached steady state at t = 0-.
  If the make-before-break switch moves to position b at t = 0, calculate i(t) for  t > 0.

8.3 Source-Free Parallel
RLC Circuits (1)

8.3 Source-Free Parallel
RLC Circuits (2)

8.3 Source-Free Parallel
RLC Circuits (3)
Example 3
 Refer to the circuit shown below.                   Find v(t) for t > 0.

8.4 Step-Response Series
RLC Circuits (1)

8.4 Step-Response Series
RLC Circuits (2)

8.4 Step-Response Series
RLC Circuits (3)
Example 4
  Having been in position for a long time, the switch in the circuit below is moved to position b at t = 0. Find v(t) and vR(t) for t > 0.

8.5 Step-Response Parallel
RLC Circuits (1)

8.5 Step-Response Parallel
RLC Circuits (2)

8.5 Step-Response Parallel
RLC Circuits (3)
Example 5
   Find i(t) and v(t) for t > 0 in the circuit shown in circuit shown below: