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.
drive.google.c...
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: Be...
2) Transient Analysis: First order RL and RC Circuits
• Transient Analysis: Fi...
3) Transient analysis: Solved Examples on First order RC and RL Circuits
• Transient Analysis: So...
4) Transient Analysis using Laplace Transform:
• Transient Analysis usi...
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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[@ALLABOUTELECTRONICS]

Transient Analysis using Laplace Transform: kzbin.info/www/bejne/fqrcamtuh76kiNEsi=puEO7yIz45hMCKqC The downloadable PDF file link has been updated in the description for the solution of the differential equation for different cases.(Under-damped and Critically damped)

[@surajkumartiwari759]

ALL ABOUT ELECTRONICS

[@adithyareddy5361]

Sir please do a video for state space response and 2 port network

[@frankreiserm.s.8039]

I like how you dive into the calculus. I dropped out of electrical engineering school because I got lost in the calculus. I think that you should have given the resonant frequency equation, f = 1/ 2 pi times the square roof of L times C.. I have memorized all electronics equation, and know them well. I like to put circuitry on a breadboard and then screw around with the external components to create new engineered circuits. I am intending to try to change an am radio ic, where the frequency depends on the exterior descrete components, and try to turn it into an low frequency receiver. We will see, but that is the fun of it! NOW TEACH ME PROFESSOR!

[@justmanojkc]

Best video about transient response yet. Thanks for such a crystal clear video.

[@ketansharma8094]

At @8:11 it should be D1,D2 instead of -D1,-D2 which will make the solution C1*exp(D1*t)+C2*exp(D2*t)

[@mysteryigen]

Characteristic equation was also wrong

[@secondjar]

I ended up getting a bad grade on my midterm because I had this in my notes. It would be nice if he could fix his mistakes with annotations. It's 100% D1, D2 because I have verified with circuit solvers and you won't get the right answer with negative D1, D2

[@rachitmittal448]

@@mysteryigen Yeah he forgot the t in second term

[@CorporateCat]

This is the best explanation of RLC ever!

[@adityasaurabh4487]

Sorry to say but Your concepts are very Confusing....Plz don't skip little concepts

[@lioneldynasty]

Please check your arithmatic. on the solution equations "e" was raised to the -D and in the first example, D1=-4 and D2=-5 and when you plug those into the equation, i=c1e^4t + c2e^5t not i = c1e^-4t + c2e^-5t, unless if we supposed to substitute D and not -D. Please rectify those and besides that, your explanations were on point. keep up the good work!

[@ALLABOUTELECTRONICS]

Yes, you need to substitute D and not -D. As D's are the roots of the equations. So, if D1=-4, and D2=-5, the solution will be, i= c1e^(-4t) + c2e^(-5t).

[@mnada72]

Please add subtitle, I use it to keep notes for important point in the discussion Great Explanation 👍👏

[@Naga_9271]

Excellent explanation sir. Due to your explanation with examples I have learnt transient response in RLC case. I am requesting you sir please send depth of contents or basics or tricks to find easy way to solve problems etc. Thank you sir

[@martinzupet3359]

When you solve the differential equation that is equal to 0 (solving homegenus differential equation), you get system's natural response, not tranzient. Tranzient response is a particular solution of a differential equation with a given voltage imput function (non-homogenus).

[@bagadivenkatramesh9046]

A good detailed explanation. Thank you very much. Keep it up. 🙏

[@ugotmail5651]

WOW one of THE BEST EXPLANATION!!!! Thank you sir.

[@neeltej4123]

simply perfect master !!!

[@johnpatrickobra5405]

Thank you sir you save me from getting zero ❤️

[@user-lp1rb9kg1b]

So, this is nothing, but a perfect video!

[@noweare1]

This is definitly one of your more math intensive videos. Excellent presentation compard to other videos I have watched. There is a free math program, I think it is also open source, called wxMaxima which is the graphical front end for Maxima. It is a computer algerbra system software. Very powerfull that allows you do engineering mathmatics and much more. Much better than doing the math by hand if you have to do it more than once.

[@BentHestad]

Superb stuff! Thanks also for excellent PDF!

[@psychei669]

Under dc inductor behaves as short circuit and voltage across it would be 0. But u took 20 as voltage ? Why ,sir?

[@thugstatZ]

can you explain for series RLC why L is getting Open at t=0+?? and for parallel RLC why C is getting short at t=0+? edit: I think its because of initial conditions: for series: il=vc=0 which means inductor is open and cap is short while for parallel: il=vc=0 so that means cap is shorted and inductor is open

[@RabbitStewification]

In the first example at 20:00 aren't the roots -3.5 and -5.5??

[@RabbitStewification]

And the following exercise I obtained -1 +/- j*2 instead of -1 +/- j

[@houssemsaber4303]

Please tell me at 3:50 Why you assumed that there is no excitation

[@harish4515]

Super sir very useful

[@billionaire7147]

Amazing bro ..... concepts r understood very well...

[@shaziatabassum980]

Best explanation of rlc circuit...thank u sir😊

[@raghuvardhanchowdam974]

In quadratic solution c = vc/LC . But you have written just LC

[@meetpatel6049]

sir thanks for making me pass i was not knowing transient RL, RC and RLC but by learning from your videos i can easily learn what's going on.

[@sivasaikrishna6169]

Mastero of subject Thank u sir

[@saifsatti7029]

Are you using same formulas for finding current and voltage both or am i got stuck?

[@bandarab7a757]

Thank you, Very supportive, very understandable

[@yogeshkumar8450]

Formule me 4ac h to only 1/lc kyu

[@faisaliqbal1086]

sir Good job....and these lectures are too much helpful .

[@poojashah6183]

you explains sooo good 👌👍

[@shivam-ui1cj]

in the last example the value of c2 should be 4.....please tell me if I am wrong

[@nethmisathsarani1679]

4:45 sir, could you please explain why Vc is taken as 1 when taking solutions from the equation D^2+R/L D+Vc/(LC) =0

[@joelsathiyendra8837]

I am also confused

[@lahirusilva3129]

That is a differential equation rule

[@TheLostEngineer19]

D^0= 1, I guess I'm a bit late.

[@serdartoren]

Thanks fot clear tutorial !

[@bituphukon6954]

Thank u sir. Upp jesa teacher hone sa. Porna ma moja ata ha

[@tanjiro3285]

Great value 👌

[@sheetalmadi336]

Sir please provide pdfs of the slides you make in the videos..that will be very helpful.Thank you so much for these explanations 🙏.

[@AbhishekSingh-up4rv]

I made the notes, but i only use whatsapp if u could provide me ur contact, i can provide u notes

[@rengincabadag3538]

From 20:35 you write the equation of i(t). I am a bit confused because you tell all the way in the beginning i(t)=C*(dVC/dt). You write the equation of voltage, not current. Please correct me if I am mistaken. Thanks in advance!

[@ALLABOUTELECTRONICS]

In that question, it has been asked to find the expression of the current. That's why the equation of the current is written. (Using the KVL, the equation of current has been found). I hope it will clear your doubt.

[@vbidawat93]

Could you please shed some light as in why a current source was choosen for Parallel combination of RLC instead of a voltage source. I hear it many places that it kills the resonance but couldn't wrap my head around it. It will be helpful if you can explain this by using a voltage source for it and showing the problem in the parallel RLC circuit and explain the need for current source

[@tharrshanmanoharan7507]

Thanks alot ❤ for the explanation

[@santanupanja3350]

16:41 in the equation -D1 and -d2 will be only D1 and D2 according to formula. please ensure it.

[@thirumal1086]

Yeah I think you are correct

[@sibisibi7359]

Yes.

[@neeltej4123]

yes,u r correct !!

[@dimitargeorgiev5732]

Super informative, very understandable video!

[@shashankcholleti8855]

20:25 sir both D1 N D2 are negative n u told to write as c1e^-D1t+c2 factor then the power becomes positive but why di u write it as negative

[@vishalsingh3765]

Isnt it that inductor acts as short circuit and capacitor as open?

[@neeltej4123]

@16:41 u wrote -D1 & -D2 in the powers,rather they wuld be only D1 & D2.pls correct it !

[@rohanrao8370]

How did u take i(t) as that equation in a problem while u where equating that to v(t) in explanation ?

[@cosmosXverse]

I think after 1yeae u know this..? ... Plz help

[@spdas5942]

The characteristic eq. is wrongly written . In place of Vc/LC it would be 1/LC , sir . Kindly correct the mistake . Thanks for your full derivation .

[@adithyanthrithallor6559]

How can you apply klichoffs rule. Closed integral of E. dl is not zero in the circuit

[@ridashah1210]

best Work...kindly tell me sir these example are solved in time domain or not?

[@arvindthakur1791]

I have notice few error that need to be corrected , at 20:45, values are putted -5 and -4, you have given formula for solution for over damp response exp(-Dt); -(-5)t must come there !!!! Either solution or example has mistake

[@pvkeshavakrishna6281]

when r=0 in parallel rlc circuit in case 4 the whole eqn becomes infinity, as r is getting divided by 1.what will be the roots of the eqn ????

[@ALLABOUTELECTRONICS]

Good to point it out that. For parallel RLC circuit, the fourth case should be R is equal to infinity or Conductance G=0. If R=0, then it will be short circuit and C as well as L will also get shorted. So, the fourth case should be when R is not connected in the circuit (i.e LC tank circuit) and it possible when R is equal to infinity. Thank you for pointing it out that 👍

[@keshavakrishna4162]

ALL ABOUT ELECTRONICS If r is infinity then the voltage across the circuit will be zero.. how can we find the conditions if voltage is zero??

[@ALLABOUTELECTRONICS]

No, for the parallel RLC circuit, if R is infinite, then the circuit will act as if there is no resistor connected in the circuit and only capacitor and inductor in parallel with a current source. And you will get voltage across capacitor or inductor. I hope you undersood what i mean to say.

[@thugstatZ]

makes perfect sense, thanks!

[@krishnatejus2388]

very clear and very helpful ... thank you !!!!

[@vishwajeetkumar9599]

how can we take fourth case of parallel RLC circuit, where R=0 , it makes the D undefined. Plz explain

[@bryanfoot]

Beautiful video

[@srey_as]

13:21 I don't understand why voltage source is connected for series RLC but a current source in parallel RLC circuit. Please explain

[@ALLABOUTELECTRONICS]

You can also do the analysis by applying voltage source in parallel circuit.

[@thugstatZ]

excellent sir, thanks. Liked and subscribed to channel. can you also explain laplace solution to series and parallel rlc circuits? which way is simpler to solve? Thanks!

[@ALLABOUTELECTRONICS]

Yes, I am planning to make the videos on it.

[@anuragguptamr.i.i.t.2329]

Is RLC series circuit an active circuit, as it amplfies the voltage obtained at capacitor and inductor, at resonance?

[@avinashjha7428]

such an awesome and perfect explanation one could provide ... thanq so much sir !🙏

[@ABHIRAMR1]

4:36 where is Vc in 4ac

[@thirumal1086]

Thank you very much sir for making the video ..it makes subject simple Please also do videos for AC excitation & series & parallel resonance circuits

[@ALLABOUTELECTRONICS]

The videos are already there. Please check the network analysis playlist. You will get all the videos. Here is the link: kzbin.info/www/bejne/sIaqkohqoL-jl8k

[@thirumal1086]

@@ALLABOUTELECTRONICS thank you sir

[@ganeshambati5789]

Explanation super Sirr

[@shashankcholleti8855]

sir pls confirm whether the roots are D1 ,D2 are -D1,-D2 ....i mean after 20:25

[@ribofen]

Excellent lesson.

[@samradnigomkar7952]

while explaining the concept, it was mentioned in the series rlc ckt overdamped final equation is of v(t). However, while solving the example you took it as i(t). How exactly did you use that?

[@ALLABOUTELECTRONICS]

If the roots of the system are real and negative, then the response of the circuit will be overdamped. And same is true for circuits. So, it doesn't matter if it is voltage or current if the roots for voltage or current equation are real and negative then the response will be overdamped. I hope it will clear your doubt.

[@fatinamirah4426]

Thankyou sir. very good and detail explanation :)

[@secondjar]

Can you add annotations to fix case 1? I got a bad grade on my midterm because I had D1, and D2 as negative (this question was worth half the points on the exam), you won't get the correct answer using this, and I verified multiple times with a circuit solver. Your videos have been super helpful to me, but it seems like you aren't willing to fix your mistakes, which makes it a potential risk for me to use your videos going forward.

[@ALLABOUTELECTRONICS]

Thanks for pointing it out and sorry to hear that ( about mid- term grading). Yes, I will definitely add that remark in the description and in the pinned comments. In the some of the videos, where there is some mistake, I have already done that.

[@ugursoydan8187]

why this circuits oscillates in underdamped case?

[@12jodyt29]

8.04 Vc(t)=C1 e^-D1t + C2 e^-D2t 👈 If D1=-Alpha+Beta D2=-A-B Then Vc(t)= C1 e^(A-B)t + C2 e^(A+B)t👈 Sir please explain.

[@ALLABOUTELECTRONICS]

I have provided the PDF link in the description for that. Please check the description for more info.

[@12jodyt29]

@@ALLABOUTELECTRONICS 👍 I'm stuck in this topic. Your explanation is simple and easy to understand. If you've the pdf for over damped response I would be thankfu to you.

[@12jodyt29]

Sir The said equation is for over damped response b2>4ac.

[@ugursoydan8187]

thank you very much. Very benefitfull

[@insaneeeeeeeeeeeeeeeee]

Is steady state and transient response same ?

[@DurgaPrasad-im3lb]

Best explaination ever

[@aamir99204]

Sir while solving for first RLC Series example circuit why didnt you add the Particular Integral Value to the solution

[@ALLABOUTELECTRONICS]

Particular integral value represents the steady state value of the circuit. In this case, in steady state ( t = ∞), current i (t) will be 0. So, its not included in the final solution.

[@aamir99204]

But you were solving for voltage Vc(t) and not current. So shouldn’t it be included? For example if we follow critically damped case for Vc(t) the entire equation will become zero at t = infinity. However since capacitor will be open at t= infinity Vc should be Vin and not zero. Please could you explain this. V was also included in the RC circuit so it should be included here as well right?

[@ALLABOUTELECTRONICS]

@@aamir99204 If you closely observe at 23:26, we got the expression for the current i(t).

[@aamir99204]

@@ALLABOUTELECTRONICS sorry Sir I meant in the derivation of RLC circuit you derived expression for Vc (T)

[@MOMODOUALPHAJALLOW]

well explained thanks

[@sreenathmukherjee4564]

Awesome sala

[@saeedmalhi6883]

Respected, as u said that the supply is dc. But capacitor blocks dc, so, then where from current across capacitor?? Plz elaborate

[@noweare1]

Capacitor is uncharged initially so it acts like a short circuit untill is charges up. So there is a current through it initially.

[@vishalkokare5188]

Very much usefull..............

[@IrfanUllahKhanVlogs]

sir how the capacitor act as a short circuit (at time t=0) when it is fully charged .If i am not wrong it should act as open circuit while inductor act as short circuit . Please guide me about this...

[@ALLABOUTELECTRONICS]

The capacitor opposes the instantaneous change in the voltage. So, if it is fully uncharged before t= 0, it will act same at t=0+. That means it will act as short circuit. If it has some finite voltage V at t=0-, then it will have the same voltage V at t=0+. On the other end, the inductor opposes the instantaneous change in the current. That means if no current is flowing through the inductor at t=0-, at t=0+, the current through the inductor will remain zero. If some finite current I is flowing through the inductor before t=0-, then the same current will flow through it at t=0+. I hope it will clear your doubt.

[@karthikraju9068]

if r=0 in case 4 ( parallel rlc circuit) shouldn't the D1 and D2 be infinity?? HELP ME GUYSS

[@hemanthm6015]

At 18:15 ,when R=0 that means (1/RC) become infinity ,then how roots become imaginary.

[@avinandanpal6562]

at 14.40 why differentiation of I is zero??? Can't get it...plz help

[@ALLABOUTELECTRONICS]

Current I is constant. It is not changing with the time. That means dI/dt will be zero.

[@sonujss]

how roots can be jw in 4th case of parallel R L C ckt if R =0 then it will give infinity value no solution

[@ALLABOUTELECTRONICS]

In the fourth case, the value of R will be equal to infinity and not zero. If it's zero then L and C will also be get shorted. That's a valid point and it has been already discussed in comments earlier. But good you pointed out.

[@mayankraj8645]

sir, you didn't mention about force response in rlc circuit

[@silversharky3258]

Can someone please tell how did he write the equations at 8:55 and 10:05.... I'm kinda lost here...it'd be nicer if they could have shown how that equation is derived..

[@ALLABOUTELECTRONICS]

The Link of the PDF File (For Derivation) is already provided in the description. Anyway here is the link: drive.google.com/file/d/0B3FOmN0FcD6Oa3lSWnVtbUx2YTQ/view

[@mohanentertains9242]

The expression at 4:20 ( Vc kyun aaya) kya Vc ko common le ke zero Kar diya.

[@hillarymutegi355]

Excellent

[@shrijithmjain2137]

Can the same method be used for finding voltage? Also

[@avinandanpal6562]

at 18.38, will not we assume value of R as infinite ( very large) ?

[@ALLABOUTELECTRONICS]

Yes, true R should be very large or ideally infinite for that case.

[@sameeppoudel8883]

Plz make video on Mixed (parallel and series) of transient response of RLC Circuit

[@mayurshah9131]

Very good!!!

[@chamanthavijay2001]

pretty good explaination..

[@ishaberry5837]

What will be its response in sinusoidal excitation?

[@crazymatthew2010]

how do we solve this if we have a resistor in series with either the capacitor or inductor?

[@ALLABOUTELECTRONICS]

For RC and RL circuit, there is a seperate video. Please check this video. kzbin.info/www/bejne/garPe2WsZsSWY9E

[@crazymatthew2010]

@@ALLABOUTELECTRONICS Thanks for the reply, I meant with it still being a second order circuit. A series-parallel example perhaps with an antiresonant frequency?

[@rakshitks7850]

You are awesome...... ..

[@studyaccount8189]

Is there an explanation for impulse input?

[@mayankgupta1280]

Sir, what is time response of R LC circuit?

[@ALLABOUTELECTRONICS]

I have already shown the graph of time response at 24:08. And then for the next example, I have shown the time response at 29:03. Please go through it, You will get it. 😀

[@noweare1]

One question: In solving for transient response of series LRC the term V/(LC) was zero because you said V was zero. Can you clear that up for me ?

[@ALLABOUTELECTRONICS]

Would you please provide the timestamp where you are referring to? So, that I can easily answer your question.

[@noweare1]

ALL ABOUT ELECTRONICS 3:50

[@ALLABOUTELECTRONICS]

Like I mentioned, the solution of the linear differential equation contains two terms (C.F - Complementary function and P.I- Particular Integral) The C.F represents the transient response of the circuit while the particular integral represents the steady state response. Here we want to find the transient response. Which means in the differential equation it has been assumed that there is no excitation. Hence Voltage V on the right-hand side of the equation is assumed zero. I hope it will clear your doubt.

[@noweare1]

ALL ABOUT ELECTRONICS Ok, Thank you

[@Fun_explorer_UAE]

At time 3:04 i think the auxillary equation is wrong it will D2+RD/L+1/LC N plss make me correct if m wrong!

[@shyamyadav3163]

@@lavarthan3298 Thanks dude, I was confused over there.

[@polalasindhu6668]

Why transient effect is more severe for DC compared to ac

[@ahinsasoni8236]

Is it important for jee advanced?

[@aaryanrs5795]

Not this topic .... but yes previous topic in this playlist of transient analysis are important