Resonance Circuits: LC Inductor-Capacitor Resonating Circuits

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  • Опубліковано 6 тра 2016
  • How current & voltage oscillate at resonant frequency for both parallel and series inductor-capacitor combinations. My Patreon Page is at / eugenek
  • Наука та технологія

КОМЕНТАРІ • 469

  • @EugeneKhutoryansky
    @EugeneKhutoryansky  5 років тому +19

    To see subtitles in other languages: Click on the gear symbol under the video, then click on "subtitles." Then select the language (You may need to scroll up and down to see all the languages available).
    --To change subtitle appearance: Scroll to the top of the language selection window and click "options." In the options window you can, for example, choose a different font color and background color, and set the "background opacity" to 100% to help make the subtitles more readable.
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    • @jonbigeffortthegoodness7437
      @jonbigeffortthegoodness7437 Рік тому

      Tu parles français ,me abla espagnole muey Beuno, i text home power garage built option with English letters (troi,3, lingual)

  • @EugeneKhutoryansky
    @EugeneKhutoryansky  8 років тому +55

    If you like this video, you can help more people find it in their UA-cam search engine by clicking the like button, and writing a comment. Thanks.

    • @prathameshdusane2619
      @prathameshdusane2619 7 років тому +2

      Thank you for such wonderful knowledge.

    • @santanupanja3350
      @santanupanja3350 5 років тому +1

      sir, which applicaion do you use for animation?

    • @redouanered-one8676
      @redouanered-one8676 5 років тому

      Thanks for helping you are the best.

    • @dilipkn7339
      @dilipkn7339 4 роки тому

      Frequency of voltage source is equal to the resonance frequency which should be said initially

  • @treenelson4063
    @treenelson4063 8 років тому +121

    Its amazing how well you give graphical tangibility to theoretical concepts.
    You often help me get a clear idea of a physic principle that often I'm fuzzy about, or even miss understanding. Thank you so much for your ability.

    • @EugeneKhutoryansky
      @EugeneKhutoryansky  8 років тому +20

      +Tree Nelson, thanks for the compliment. I am glad to hear that my videos have been helpful.

    • @red-baitingswine8816
      @red-baitingswine8816 5 років тому +2

      I wasn't getting the idea in this video, so I went back and looked at the capacitor and inductor videos again - as I was watching the inductor video the first part of this video started to make sense. : ) ... (very enjoyable videos)

    • @rhetoric180c6
      @rhetoric180c6 4 роки тому

      @@EugeneKhutoryansky sir, you are awesome

    • @nishapawar3368
      @nishapawar3368 3 роки тому

      @@EugeneKhutoryansky yes ur videos r very helpful to understand the concept, and it gives ans of almost all my why questions...very satisfying videos :) thank u

  • @tensorbundle
    @tensorbundle 6 років тому +70

    Your videos take us beyond the pages of book..thanks soo much for your videos

    • @EugeneKhutoryansky
      @EugeneKhutoryansky  6 років тому +7

      Thanks.

    • @careereasy9679
      @careereasy9679 6 років тому

      ua-cam.com/video/DYNBxG9xFvQ/v-deo.html WATCH DIS YOUR ALL DOUBTS WILL BE CLEARED AND EXPLAINED IN SIMPLE MANNER

    • @vvxx2287
      @vvxx2287 3 роки тому

      @@EugeneKhutoryansky 谢谢

  • @rajasekarancj8640
    @rajasekarancj8640 7 років тому +7

    you're animations are clear with the concepts u imply on us!! more importantly u guys depicted the potential difference in a nice way!!😄😄😄😄.....

  • @Novous
    @Novous 6 років тому +308

    FACT. Every inductor contains a large wooden log.

    • @spearcheckly2614
      @spearcheckly2614 5 років тому +30

      HA HA! Shit! That's why my circuit wasn't working. I was using a tootsie roll instead of a log! Lol

    • @VoidHalo
      @VoidHalo 5 років тому +6

      Wood actually would work as an inductor core better than air. Although the permeability of wood is only a tiny fraction of a percent more than air. It would make for an interesting experiment to try and measure the difference.

    • @zulusia4140
      @zulusia4140 5 років тому +6

      Now I gotta find some wood for my circuit. Shit

    • @hariohm1415
      @hariohm1415 4 роки тому

      @@VoidHalo 👌

    • @subramanianr7206
      @subramanianr7206 Рік тому

      It's utter nonsense to understand something else when it's said that the inductor is wrapped around a magnetic material; you people must listen carefully rather than to imagine by looking at the colour of the core inside the inductor
      De VU2RZA

  • @4corks
    @4corks 8 років тому +8

    Love your animations, it's impossible to find animations like yours visualizing electronics and it can be really useful to properly understand electricity. Hope you keep it up, I really appreciate your videos!

  • @atari7001
    @atari7001 5 років тому +34

    I think a critical thing to note is that when the magnetic field first begins to collapse across the inductor, its voltage potential spikes to values much much higher than the voltage originally used to first charge the capacitor. Resonant circuits can achieve very high potentials while in operation, because of this phenomenon.
    Also, this explains more concisely why the circuit doesnt just find an equilibrium, rather than resonating. The sudden spike in inductor voltage causes a fierce inrush of current into the capacitor, only when the magnetic field begins to collapse, and not until then. Examples of this spike in voltage can sometimes be seen when a transformer is suddenly disconnected from power, resulting in a surprising high voltage arc from "back EMF".
    I hope this makes it easier to understand resonance. It used to frustrate me in college that most professors really didn't understand the fundamentals of what they were teaching. So, I sought to make this complex phenomenon as simple as possible to visualize.

    • @arthurmead5341
      @arthurmead5341 5 років тому

      Would you be able to see this on an oscilloscope ?

    • @atari7001
      @atari7001 5 років тому +2

      @@arthurmead5341 yes. Pass a dc current through an inductor and interrupt the power supply with a switch. You should be able to see a sharp rise in voltage as the supply is removed.

    • @atari7001
      @atari7001 5 років тому

      @Homo sapiens You're welcome! Glad to help.

    • @uploadJ
      @uploadJ 5 років тому

      re: "thing to note is that when the magnetic field first begins to collapse across the inductor, its voltage potential spikes to values much much higher "
      NO. This would NOT be linear behavior, and an L and C most definitely exhibit LINEAR behavior ...

    • @atari7001
      @atari7001 5 років тому +1

      @@uploadJ The following link is a demonstration of the phenomenon. A neon bulb needs much more than 9 volts to ignite. When a neon bulb is placed across an inductor whose 9 volt power supply is suddenly interrupted, the bulb will flash momentarily from the high voltage that appears across the inductor.
      ua-cam.com/video/T8O8aTO3ea8/v-deo.html

  • @Hugotheman88
    @Hugotheman88 7 років тому +24

    Your videos are great for people with a strong mechanical aptitude like. The math makes so much sense one I've seen it shown to me from a mechanical approach!

    • @careereasy9679
      @careereasy9679 6 років тому

      ua-cam.com/video/DYNBxG9xFvQ/v-deo.html WATCH DIS YOUR ALL DOUBTS WILL BE CLEARED AND EXPLAINED IN SIMPLE MANNER

  • @EugeneKhutoryansky
    @EugeneKhutoryansky  5 років тому +13

    You can help translate this video by adding subtitles in other languages. To add a translation, click on the following link:
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    You will then be able to add translations for all the subtitles. You will also be able to provide a translation for the title of the video. Please remember to hit the submit button for both the title and for the subtitles, as they are submitted separately.
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    Thanks.

    • @GauravKumar-dr2yk
      @GauravKumar-dr2yk 5 років тому

      please make video on collpit oscillator

    • @MEOP589
      @MEOP589 4 роки тому

      thankyou so much

    • @atum7355
      @atum7355 4 роки тому

      What happens if you use a single phase synchronous motor/virtual negative inductor instead?

    • @atum7355
      @atum7355 4 роки тому

      You get overunity.

  • @anthonycalia1317
    @anthonycalia1317 8 років тому +10

    Well, done. Any introductory electronics course should include this video as a practical visual understanding of resonance. Starting young engineers with the equations may be traditional, but a visual presentation such as this will provide a long-lasting practical understanding as well. Something I see lacking in engineers and technicians today. Keep up the good work.

  • @ron6625
    @ron6625 7 років тому +1

    Oh, I love these videos. Makes me think about these things in different terms, and also allows me to verify my understanding (because you can see how the laws are being applied as things are changed and moved around).

  • @akarshchaturvedi2803
    @akarshchaturvedi2803 7 років тому +2

    You put so much effort for making these free educational videos which help us a lot. Thank you, Eugene.

  • @andrevlasblom2411
    @andrevlasblom2411 7 років тому

    Your videos are just totally awesome! For me it cleared up A LOT. Through these representations it is so much easier to understand. Please, keep up the good work.

    • @EugeneKhutoryansky
      @EugeneKhutoryansky  7 років тому

      Thanks. I am glad you like my videos. More are on their way.

  • @ytrew9717
    @ytrew9717 5 років тому

    Amazing how you found a way to illustrate in a clear illustration what people usually try to explain using dark figures and formulas

  • @Fleurlean4
    @Fleurlean4 8 років тому +2

    That's beautiful. I've build many resonant circuits, and never thought to think of them like this. Good work!

    • @EugeneKhutoryansky
      @EugeneKhutoryansky  8 років тому +1

      +luigisf, thanks.

    • @careereasy9679
      @careereasy9679 6 років тому

      ua-cam.com/video/DYNBxG9xFvQ/v-deo.html WATCH DIS YOUR ALL DOUBTS WILL BE CLEARED AND EXPLAINED IN SIMPLE MANNER

  • @slehar
    @slehar 5 років тому +2

    Wow! Awesome visualization! Voltage as slope! That is intuitive! Thanks!

  • @SylwesterKogowski
    @SylwesterKogowski 7 років тому +2

    That was the best explanation I saw, nothing like the standard "capacitor loads the coil and vice versa" without explaining why does it behave this way.

  • @randygraff2825
    @randygraff2825 2 роки тому

    I love the easy to understand animation as well as the strait forward,to the point narrative wich is also easy to follow.Thank you for your well produced production of your great knowledge that you share.

  • @bhartiojha8744
    @bhartiojha8744 6 років тому +2

    Thank you so much for these videos everything is clear after watching them

  • @arnavmishra2155
    @arnavmishra2155 3 роки тому

    I can't express my gratitude for the help I have got from your videos, friend.😊❤️

  • @jnaneshin9282
    @jnaneshin9282 7 років тому

    Really thankful for your efforts with such wonderful videos, please keep them coming !

  • @sinojha1
    @sinojha1 4 роки тому

    Thank you for this great video! Simple yet to the point. Also, the animations are amazing!

  • @johnnyaingel5753
    @johnnyaingel5753 5 років тому +3

    Thank you so much for sharing this incredible story god bless i learned something new today

  • @zdzisawk5198
    @zdzisawk5198 3 роки тому

    The best explanation ever. Just working with resonant circuits. Cannot appreciate more. Thank you.

    • @EugeneKhutoryansky
      @EugeneKhutoryansky  3 роки тому

      Thanks for the compliment about my explanation. I am glad you liked it.

  • @red-baitingswine8816
    @red-baitingswine8816 5 років тому

    I wasn't getting the idea in this video, so I went back and looked at the capacitor and inductor videos again - as I was watching the inductor video the first part of this video started to make sense. : ) ... (very enjoyable videos)

  • @aloeveradrink494
    @aloeveradrink494 8 років тому +14

    Thanks! You help people alot.

  • @raghuchampati4712
    @raghuchampati4712 6 років тому

    Thanks you! That was a very intuitive way to understand resonance in electric circuits.

  • @burningsilicon149
    @burningsilicon149 2 роки тому

    My professor was discussing this circuit and she was using the parallel configuration and she said at resonance the circuit blows up ,but when I went to compute the equivalent impedance of the circuit it seemed the circuit impedance went to infinity at the resonance frequency making it a open circuit and your video made that really clear.

  • @Seaprimate
    @Seaprimate 5 років тому +2

    Excellent work! I'd love it if you were to create videos explaining or comparing slayer-exciter, solid-state, and spark-gap tesla coils.

  • @lrdick
    @lrdick 6 років тому

    These are the best presentations of electrical theory I have ever seen. OUTSTANDING THANK YOU

  • @TalaashDotCom
    @TalaashDotCom 3 роки тому

    a lot of work and effort is put in this animation. Thank you for the good work. Enjoyed it all the way.

  • @mirovskii
    @mirovskii Рік тому

    I have never forget the dancing series RLC circuit with that music :D These are by far the best explanation vidoes ever. Thank you so much!!!

  • @gabrielpotgieter1600
    @gabrielpotgieter1600 6 років тому

    All that I can say to you for all your videos is Thank you.. for all the good information..

  • @seahawkers101
    @seahawkers101 8 років тому

    Just recently learned about the use of these circuits in power line carrier signals. Thanks for the helpful conceptualization.

    • @careereasy9679
      @careereasy9679 6 років тому

      ua-cam.com/video/DYNBxG9xFvQ/v-deo.html WATCH DIS YOUR ALL DOUBTS WILL BE CLEARED AND EXPLAINED IN SIMPLE MANNER

  • @jainesh9181
    @jainesh9181 7 років тому +1

    fantastic... I'm just become fan of u...thanks for helping us.. and serve us more and more knowledge..

  • @Saucepv897
    @Saucepv897 3 роки тому

    Beautiful music. Transitions and changes of music were used well to identify to explain a connecting topic.

  • @parvezquraishi7500
    @parvezquraishi7500 5 років тому

    Your concepts are crystal clear thank you for all these videos

  • @chicomachado
    @chicomachado 6 років тому +1

    Thank you for your videos !

  • @whatsgoing_on8812
    @whatsgoing_on8812 6 років тому

    I've bookmarked a lot of video to help to explain to other what I;m unable to do with words. Thanks for the great animation examples.

    • @careereasy9679
      @careereasy9679 6 років тому

      ua-cam.com/video/DYNBxG9xFvQ/v-deo.html WATCH DIS YOUR ALL DOUBTS WILL BE CLEARED AND EXPLAINED IN SIMPLE MANNER

  • @vucubcaxis
    @vucubcaxis 3 роки тому

    I have made a living working on this field. And this video finally filled the gaps I had in my understanding of the phenomenom.

  • @sky_island
    @sky_island 6 років тому

    AWESOME. Your videos are the best

  • @cphVlwYa
    @cphVlwYa 8 років тому +21

    I don't understand why you only have ~66,500 subscribers, these are by far the best physics videos I have ever seen. Amazing video as always :)

    • @EugeneKhutoryansky
      @EugeneKhutoryansky  8 років тому +8

      +Yextus, thanks for the compliment. Perhaps the number of subscribers will be much higher in the future.

    • @cphVlwYa
      @cphVlwYa 8 років тому +2

      +Physics Videos by Eugene Khutoryansky Im sure it will be

    • @chanakyasinha8046
      @chanakyasinha8046 4 роки тому +1

      Because few percentage of population are interested in curiosity learning.

    • @sparky844
      @sparky844 Рік тому

      963k 6 years later!

  • @ozzymandius666
    @ozzymandius666 8 років тому

    Excellent!
    This is the circuit design at the root of speaker crossovers, and high- and low-pass filters, I believe.

  • @juankaU2
    @juankaU2 2 роки тому

    En el trabajo no tengo más remedio que estar traduciendo y leyendo,cuando veo youtube es para desconectar .
    Saludos,hay millones de hispano hablantes en el planeta

  • @bhyllw
    @bhyllw 4 роки тому

    This is one of my favorite channels.

  • @sinojha1
    @sinojha1 4 роки тому

    You are so amazing!! Thank you for making all these great videos :)

  • @YouKnowMeDuh
    @YouKnowMeDuh 5 років тому +2

    Wow! This is great, thanks! Helps with my electromag physics class! :D

  • @YanLipavsky
    @YanLipavsky 4 роки тому

    Amazing visual explanation - BRAVO !!!

  • @weylin6
    @weylin6 5 років тому +7

    I think inductors and capacitors are well represented by a hydraulic analogue.
    Inductors resemble a turbine which require energy to 'spin up', and in the absence of that energy, maintain their momentum until dissipated.
    Capacitors resemble a diaphragm, allowing a brief flow of current, but resisting it the harder it's pushed.

    • @crisvamc83
      @crisvamc83 4 роки тому +1

      Good analogy ...
      Capacitors are like hydraulic pistons(or rams) (Electric Field ... Potential Energy)...
      Or Capacitors are like Springs (storing Elastic Potential Energy)
      Inductors are like hydraulic motors(or turbines) (Magnetic field ... Kinetic Energy)
      Or Inductors are like Fly Wheels(storing Rotational Kinetic Energy)
      Resistors are like Brakes/Dashpots
      Diodes are like Check valves
      Transistor as a switch is a Gate Valve/clutch
      Transistor as an amplifier/Transformer is a torque converter

    • @dalenassar9152
      @dalenassar9152 2 роки тому

      @@crisvamc83 How would you represent inductor SATURATION with the water analogy??? My search for this continues...

  • @ultravidz
    @ultravidz 8 років тому

    Love this explanation, thanks Eugene!

  • @la7yka
    @la7yka 7 років тому

    A great explaination of the series vs. paralllel resonance.

  • @mnada72
    @mnada72 2 роки тому

    Thank you so much. You know how to clear doubts, magically.

  • @billnye8318
    @billnye8318 8 років тому

    Another video?!? Thanks Eugene!

  • @corneliariasdita715
    @corneliariasdita715 4 роки тому

    Hey, I think it would be very good to add book references (or other source) in case someone wants to know more deeply about the topic in the video. Glad you are still making videos till now :)

  • @davidorr947
    @davidorr947 4 роки тому

    Another excellent video! As a collection all your videos should be used in high schools.

  • @moinshaikh1963
    @moinshaikh1963 2 роки тому

    The way you explain physics is miraculous..!!!

  • @SystemicCreative
    @SystemicCreative Рік тому

    Brilliant, as always 🙂

  • @joannemariebiso860
    @joannemariebiso860 6 років тому

    wow the information was clearly explained plus the good illustration! two thumbs up thanks for this 😊

  • @chitramariappan6788
    @chitramariappan6788 6 років тому

    this video is definitely a master piece for those who study electric al engineering

  • @mubafaw
    @mubafaw 3 роки тому

    Very good explanation and animation. Thanks!

  • @serdar-ors
    @serdar-ors 7 років тому

    These are the best explanations that i have ever seen before. At school before shwing matematical theories of circuits, teachers try to show understanding of how things works. So students may like what they learn so much, otherwise it is just a mess of memorizations of formulas that we see teaching. This is not an ideal way of teaching. Teaching doesnt mean to be writing the book on the board.

  • @abhiramcd
    @abhiramcd 2 роки тому +2

    Not lying. I got emotional at the end. 🙂

  • @Annihilator49
    @Annihilator49 8 років тому

    I have shown your videos to many of my engineering professors and they think these videos are incredible. The philosophy seems to be to make things as easy to understand as possible. Why would you ever want different? One of my professors wants to show some of these to their class!
    All of my friends are subscribing to your channel. Thank you so much for making these incredible videos, and from students and teachers alike, keep on making them!

    • @EugeneKhutoryansky
      @EugeneKhutoryansky  8 років тому

      +Peter Bayley, thanks for the compliment, and thanks for sharing my videos with your friends and professors. I am glad to hear that one of your professors wants to show my videos in his class, and I hope the students enjoy my videos.

    • @Annihilator49
      @Annihilator49 8 років тому

      Yeah! Is there any chance you might eventually make videos about phasors or FPGAs?

    • @EugeneKhutoryansky
      @EugeneKhutoryansky  8 років тому +1

      +Peter Bayley, I would eventually like to make a video on phasor diagrams for AC electric circuits. I am not so sure about a video specifically on FPGAs, but I would like to make additional videos dealing with logic gates. Thanks.

  • @rothenbergt
    @rothenbergt 5 років тому

    Amazing video really helped my understanding!

  • @vamsidharalluri7966
    @vamsidharalluri7966 7 років тому

    the best videos i've ever seen .the concept is so clear after watching this video .please make more videos on op amps .you rock's

    • @EugeneKhutoryansky
      @EugeneKhutoryansky  7 років тому

      Thanks for the compliment about my videos. More videos are on their way.

    • @careereasy9679
      @careereasy9679 6 років тому

      ua-cam.com/video/DYNBxG9xFvQ/v-deo.html WATCH DIS YOUR ALL DOUBTS WILL BE CLEARED AND EXPLAINED IN SIMPLE MANNER

  • @AJ-et3vf
    @AJ-et3vf 2 роки тому

    Awesome video! Thank you!

  • @ForDreamsThatDoComeTrue
    @ForDreamsThatDoComeTrue 5 років тому

    Its indeed the a fantastic explanation...hats off to your hard work....

    • @EugeneKhutoryansky
      @EugeneKhutoryansky  5 років тому +1

      Thanks for the compliment. I am glad you liked my explanation.

  • @markostojiljkovic7100
    @markostojiljkovic7100 8 років тому

    Such a great explanation!

  • @shqipe8894
    @shqipe8894 6 років тому

    Thanks a lot!!Congratulation!!Continue please this amazing work.

  • @chanh-tintruong3083
    @chanh-tintruong3083 6 років тому

    Thanks, very helpful to me.

  • @kylekuil8253
    @kylekuil8253 7 років тому

    This is so easy to understand with the animation.

  • @corneliariasdita715
    @corneliariasdita715 5 років тому

    I like how you match the music with the animation (er... oscillation)
    Anyway, your channel is really helpful :)
    Thanks :)

  • @viniciusfernandes2303
    @viniciusfernandes2303 2 роки тому

    Thanks for the video!

  • @vipinseth1536
    @vipinseth1536 6 років тому

    thankyou so much for this video

  • @animeshjain3013
    @animeshjain3013 5 років тому

    Thanks this helped alot!

  • @ejkitchen
    @ejkitchen 8 років тому

    Excellent video!

  • @TheSharad97
    @TheSharad97 3 роки тому

    Nice video 👍

  • @mahxylim7983
    @mahxylim7983 5 років тому

    I LOVE YOUR VIDEOS!!!!!!!!!!!!!!!!!!

  • @karimsabry2097
    @karimsabry2097 6 років тому

    massive like and thanks to this amazing channel

  • @user-fn5kq1ek2d
    @user-fn5kq1ek2d 3 роки тому

    Thanks for your explanation

  • @alaincesarini5284
    @alaincesarini5284 4 роки тому

    Very helpful vidéo !

  • @milesemanuelpaavola7994
    @milesemanuelpaavola7994 6 років тому +1

    Thank you for sharing, really helps. :-D

  • @ziadamr99
    @ziadamr99 3 роки тому

    This is very helpful. Thank you so much.

  • @raviashokyadav6309
    @raviashokyadav6309 7 років тому

    great explanation

  • @sergiourquijo4000
    @sergiourquijo4000 8 років тому

    great video!

  • @Hya_vaihalxa1123
    @Hya_vaihalxa1123 6 років тому

    This is literally the best youtube channel for study purpose........

  • @muratcosar3873
    @muratcosar3873 4 роки тому

    Awesome contents.

  • @commando340
    @commando340 7 років тому

    excellent video, thank you

  • @bandaruramana2119
    @bandaruramana2119 3 роки тому

    Well said mam rest of all videos are mathematically but you explained practically in detail this is the actual process will going inside superb mam
    Make a video related how capacitor compensates reactive power in this manner

  • @bobdurk5180
    @bobdurk5180 7 років тому

    I like your method and just subscribed to your channel. Thank you !
    Bob D

    • @EugeneKhutoryansky
      @EugeneKhutoryansky  7 років тому

      Thanks. I am glad you like my videos, and I am glad to have you as a subscriber.

  • @denizakyldz9694
    @denizakyldz9694 Рік тому

    Super helpful! Thank you!!! 🙌

  • @alexabadi7458
    @alexabadi7458 5 років тому

    Thanks Kira !

  • @pepesworld2995
    @pepesworld2995 6 років тому

    i love everything about this channel. you are a hero to our species. please propagate.

  • @tanerriffat7963
    @tanerriffat7963 4 роки тому

    Thanks Eugene, another excellent video. It would be nice to see how high pass and low pass filters work (LC, RC, RL, RCL) with an AC signal. I get the idea though from this video.

    • @EugeneKhutoryansky
      @EugeneKhutoryansky  4 роки тому

      I cover that in my video at ua-cam.com/video/zO7RZZW0wSQ/v-deo.html

  • @milzex2082
    @milzex2082 4 роки тому

    I wish all youtubers could explain like this

  • @AKASHL-BLUcomsci
    @AKASHL-BLUcomsci 10 місяців тому +1

    very well explained sir,thanks for this amazing physics video lecture

  • @habtamusium8646
    @habtamusium8646 3 роки тому

    many thanks !

  • @joseaurelianosandovalgarci1884
    @joseaurelianosandovalgarci1884 7 років тому

    excelente explicación...y muy bien expuesto....además de una animación excdpcional

  • @letranquang2862
    @letranquang2862 6 років тому

    great video :)) . Thanks