Lecture 10: RL & RC Circuits Nilsson & Riedel ENG17 (Sec. 2): Circuits I Spring May 1, 2014

Recap – Inductors / Capacitors 2

Overview Natural Response –RL Circuits –RC Circuits Step Response –RL Circuits –RC Circuits General Solution Sequential Switching Unbounded Response 3

Natural Response 4 Currents and voltages that arise from an inductor or capacitor immediately after being disconnected from a DC (direct current) source.

Current in RL Circuit 5 After Open Switch

Time Constant 6

RL Circuit Example 7

Voltage in RC Circuit 8 After Switching

RC Circuit Example 9

Overview Natural Response –RL Circuits –RC Circuits Step Response –RL Circuits –RC Circuits General Solution Sequential Switching Unbounded Response 10

Step Response 11 Currents and voltages that arise when energy is being acquired by an inductor or capacitor due to the sudden application of a dc voltage or current source.

Step Response in RL Circuit 12

Step Response in RC Circuit 13

Overview Natural Response –RL Circuits –RC Circuits Step Response –RL Circuits –RC Circuits General Solution Sequential Switching Unbounded Response 14

Generalized Solution 15

Overview Natural Response –RL Circuits –RC Circuits Step Response –RL Circuits –RC Circuits General Solution Sequential Switching Unbounded Response 16

Sequential Switching 17 Defined: whenever switching occurs more than once in a circuit

Overview Natural Response –RL Circuits –RC Circuits Step Response –RL Circuits –RC Circuits General Solution Sequential Switching Unbounded Response 18

Unbounded Response Defined: A circuit response that grows, rather than decays, exponentially with time. Possible with dependent sources 19

Recap Natural Response –RL Circuits –RC Circuits Step Response –RL Circuits –RC Circuits General Solution Sequential Switching Unbounded Response 20