Transient Analysis of the RLC Circuit (with Examples)

In this video, you will learn about the transient analysis of the RLC circuit. So, in this video, the transient response for the series and parallel RLC Circuit have been discussed. And at the end, few problems related to this Series and Parallel RLC transients have been solved. Also, the response of the circuits in the given solved examples have been plotted for the better understanding of this transients in the RLC Circuit.

Now, in the case of RLC circuit, during the transient analysis, when we write KVL or KCL equation then we will get second order linear differential equation. And the response of the system depends upon the roots of this differential equation.
Now, in the RLC circuits, L and C have a tendency to induce the oscillation in the circuit, while Resistor R has a tendency to suppress or damp out this oscillation.
So, depending upon the value of R, L and C and ultimately on the roots of the equation, we can have 4 different types of response.

For, series RLC Circuit:

Case 1: (R/2L)^2 is greater than (1/LC)

If the roots are real, negative and different, then the response of the system will be an overdamped response.

Case 2: (R/2L)^2 = (1/LC)

If the roots are Real and equal, then the response of the system will be a critically damped response.

Case 3: (R/2L)^2 is less than (1/LC)

If the roots are complex conjugate then the transient response of the circuit will be underdamped and it will have some oscillation in the circuit, which will die out eventually.

Case 4: R=0
The roots will be purely imaginary, and response will be purely oscillatory without any damping.

For, parallel RLC Circuit:

Case 1: (1/2RC)^2 is greater than (1/LC)

If the roots are real, negative and different, then the response of the system will be an overdamped response.

Case 2: (1/2RC)^2 = (1/LC)

If the roots are Real and equal, then the response of the system will be a critically damped response.

Case 3: (1/2RC)^2 is less than (1/LC)

If the roots are complex conjugate then the transient response of the circuit will be underdamped and it will have some oscillation in the circuit, which will die out eventually.

Case 4: R=0
The roots will be purely imaginary, and response will be purely oscillatory without any damping.

The pdf file for the solution of differential equations for the different cases (critically damped and underdamped) is given here.

https://drive.google.com/file/d/0B3FO...


Timestamps for the different topics covered in this video is given below:

0:58 Transient Response of Series RLC Circuit

11:05 Graphical Representation of different transient Response

13:20 Transient Response of parallel RLC Circuit

18:48 Example 1: Series RLC Circuit

24:44 Example 2: Parallel RLC Circuit

Link for the other videos related to Transient Analysis:

1) Transient Analysis: Behaviour of basic circuit components
   • Transient Analysis: Behaviour of Basic Cir...  

2) Transient Analysis: First order RL and RC Circuits
   • Transient Analysis: First order R C and R ...  

3) Transient analysis: Solved Examples on First order RC and RL Circuits
   • Transient Analysis: Solved Examples on Fir...  

4) Transient Analysis using Laplace Transform:
   • Transient Analysis using Laplace Transform...  

This video will be helpful to all students of science and engineering in understanding the transient analysis for the series and parallel RLC circuit.

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