How to Solve Switched RL Circuits - The Transient (Natural) Response (Electrical FE Exam)

[Zach Stone P.E.]

Switched RL circuits can be pretty difficult. In this video, we cover how to quickly solve for iL(t), the transient (natural) response of switched RL circuits by analyzing the circuit before and after the switch is opened.



Video Table of Contents:

0:16 - Problem Statement

1:10 - Transient Response Definition

2:15 - The circuit at time less than 0 (switch closed)

3:17 - Solving for the inductor current iL(t), and the two-loop currents (i1, and i2) using KCL - Kirchoff's Current Law

6:29 - The circuit at time = 0 (when the switch opens)

6:42 - Inductor and Capactiro behavior when time is infinity (∞) and the system is stable

7:45 - Simplified circuit when time is equal to infinity (∞)

8:59 - IiL(0-) and iL(0+)

10:04 - Solving for k1, the constant of the Transient Response

10:57 - Solving for 𝞃, the time constant of the Transient Response (Tau)

12:47 - Solving for the equivalent resistance using the Thevenin equivalent circuit

14:55 - Solving for the transient response iLN(t)

Answers:

Current in loop 1: i1 = 1/2 mA

Current in loop 2: i2 = 1 mA

Current through the inductor: iL = 1/2 mA

Current through the inductor at time equals infinity: iL(t = ∞) = -1/2 mA

Current through the inductor right before the switch is opened: iL(0-) = 1/2 mA

Current through the inductor right after the switch is opened: iL(0+) = 1/2 mA

Current through the inductor right when the switch is opened: iL(0) = 1/2 mA

Thevenin equivalent resistance seen by the inductor: RTH = 2/3 Ω

Transient Response Constant: k1 = 1

Transient Response Time Constant 𝞃 = 15/2,000 seconds = 7.5 mS

The Transient (or Natural) Response of the RL Circuit: iLN(t) = e^(-2000t/15) mA

Can you solve it?

 

[Zach Stone P.E.]

Looking for specific help on Linear Systems for the FE exam? Direct message me.