Circuit diagram dealing with capacitor,resistor and zener diode connected in series

Consider a capacitor connected in series with a 5ohm resistor and a zener diode of 20v. The voltage across the 5ohm resistor at time t will be 10e^(-t/5C) and so the current will be 2e^(-t/5C). Since resistance is define as ration between voltage and current the resistance seen by the zener diode by the capacitor at time t will be 10e^(t/5C). So can we say that the resistance seen by the capacitor at time t will be 5+10e^(t/5C)? It is obvious to see that V(t) for the capacitor is 20+10e^(-t/5C). By using I=-Cdv/dt, i try whether i can obtain the same v(t) by using the equation V/5+10e^(t/5C)=-Cdv/dt and i integrate the equation by using integration by substitution method and get back the same answer for v(t) which is 20+10e^(-t/5C).
By using voltage divider formula also, the voltage drop across zener diode
v(t)*R(t)/5+R(t)=20+10e^(-t/5C)*10e^(t/5C)/(10e^(t/5C)+5)=20

At here, can we say that in a circuit diagram which consist a capacitor connected in series with a resistor and a zener diode have the same electrical properties as the circuit diagram which consist of a capacitor connected in series with the same resistor and 20v voltage supply or a "virtual resistor" which has the same parameter as R(t)? Such concept is also applicable to other electrical component right?such as an active regulator?

Replies

  • shreyasm89
    shreyasm89
    Re: Circuit diagram dealing with capacitor,resistor and zener diode connected in seri

    "the resistance seen by the zener diode by the capacitor at time t will be 10e^(t/5C)"..i am not very sure about this statement...and while making the last statement you have already considered the Zener diode as a constant voltage supply in the circuit. I am not able to get your concept about a "virtual resistor" would you please elaborate?
  • chuackl
    chuackl
    Re: Circuit diagram dealing with capacitor,resistor and zener diode connected in seri

    shreyasm89
    "the resistance seen by the zener diode by the capacitor at time t will be 10e^(t/5C)"..i am not very sure about this statement...and while making the last statement you have already considered the Zener diode as a constant voltage supply in the circuit. I am not able to get your concept about a "virtual resistor" would you please elaborate?

    as you can see the voltage acoss the 5ohm resistor will be 10e^(-t/5C) correct? Hence the current flow across the resistor will be 10e^(-t/5C) divided by 5=2e^(-t/5c). Since it is connected in series the current flow should be the same across the components. Assume a constant drop of 20V across the zener diode and resistance is define by v/I so we take 20 divided by 2e^(-t/5C) will get 10e^(t/5C) correct? what i trying to mean here is in circuit diagram rather than draw a zener diode can we replace the zener diode with a resistor which has a parameter of 10e^(t/5C)? I dunno is such components exist maybe a programmable resistor? program it with such parameter than if the parameter of the resistance are known it can be use to replace any component?
  • e2saleh
    e2saleh
    Re: Circuit diagram dealing with capacitor,resistor and zener diode connected in seri

    From your numbers, you are supplying 10v, so how comes u gonna get 20v across the zener diode?! Am sure you are familier with this graph:

    [​IMG]


    So zener diodes maintain their resistance to keep your voltage level constant, after reaching cutoff voltage, but they can not provide voltage on their own.
  • chuackl
    chuackl
    Re: Circuit diagram dealing with capacitor,resistor and zener diode connected in seri

    e2saleh
    From your numbers, you are supplying 10v, so how comes u gonna get 20v across the zener diode?! Am sure you are familier with this graph:

    [​IMG]


    So zener diodes maintain their resistance to keep your voltage level constant, after reaching cutoff voltage, but they can not provide voltage on their own.
    The capacitor has 30v at the beginning when t=0 and it is place in series with a 5ohm resistor and 20v zener diode. I guess i forgotten to mention the initial state of the capacitor at above sorry.
  • chuackl
    chuackl
    Re: Circuit diagram dealing with capacitor,resistor and zener diode connected in seri

    Anyway is zener diode really maintain its resistance in this circuit because if the resistance is maintain a different value of voltage will drop across the 20v zener diode. I have already tested with multisim a constant voltage of 20v will drop across the zener diode if the capacitor initially have 30V.
  • Voltaire
    Voltaire
    Re: Circuit diagram dealing with capacitor,resistor and zener diode connected in seri

    what i trying to mean here is in circuit diagram rather than draw a zener diode can we replace the zener diode with a resistor which has a parameter of 10e^(t/5C)?
    Hey mate
    I think you're right. My reasoning is that the zener maintains the differential voltage and I can see no way of doing this other than by adjusting the resistance. My only concern with this approach is that the mathematical model becomes very complex since this 'new' resistance would feed back to t which will affect discharge rate of the cap which will affect the zener resistance which will again affect t and so on and so on.

    I think you should ignore this feedback resistance and simply use 20V as your baseline. Then make a note to your professor that you have considered this line of thought and ask for clarification.

    Nice one!
  • Voltaire
    Voltaire
    Re: Circuit diagram dealing with capacitor,resistor and zener diode connected in seri

    ...or
    if you are confident that you've got it sussed out then nail it; and good luck!

    PS keep me informed
  • Voltaire
    Voltaire
    Circuit diagram

    How can I get a picture from my computer on here?
  • Kaustubh Katdare
    Kaustubh Katdare
    Re: Circuit diagram

    Voltaire
    How can I get a picture from my computer on here?
    It is not a straightforward process right now. First you will have to upload your image to any free images hosting site like tinypic.com or imageshack.com and then copy-paste the complete image path [ Ex. https:// domain . com / image.jpg , without spaces] in the window that pops up after clicking on [​IMG] icon in the editor.

    PS: Image upload facility will be introduced in near future.
  • chuackl
    chuackl
    Re: Circuit diagram dealing with capacitor,resistor and zener diode connected in seri

    Thank man for pick up my post and finally got someone agree with my point of view😛.My school dun have any professor to help me clarify also so i post up my question at here to see what is people respond. As i mention above you can try using voltage divider formula also and it give u back 20V voltage drop across the 10e^(t/5c) resistance which is the zener diode. While the capacitor treated as a voltage source having a value of 20+10e(-t/5C). From the formula you can see that the voltage drop across the 20v zener diode is independant of time. When t is very big, the capacitor should be discharge and voltage should reach approximately 20V and the zener diode act as a resistor which have a infinite value resistance so the voltage drop will totally drop across the zener diode rather than the 5ohm resistor and because the resistance is big, the current flow is very small which make the capacitor to discharge slower and slower as the zener resistance keep on increase which make a constant of 20v voltage drop across the zener.Every thing is make sense(voltage divider, I=Cdv/dt get back the equation) so i ownself assume it is correct with this concept;-)
  • Voltaire
    Voltaire
    Re: Circuit diagram

    Thanks Biggie
  • Voltaire
    Voltaire
    Re: Circuit diagram dealing with capacitor,resistor and zener diode connected in seri

    I wrote to Professor Shyam Sunder Tiwari and his e-mail response is below:
    ========================
    Hello,

    In this circuit initial discharge peak current of 2A will flow through Zener if it can handle it and then it will be exponential decay up to 20V and current through resistor will also be exponential from 2A to near zero amp. I have ignored capacitor resistance and considered zener as sharp edge zener, which is only an approximation.

    If you consider change in zener voltage with current passing through zener then some amount of correction is required. After zener edge, leakage current through zener will continue discharging the capacitor until capacitor voltage goes to zero volt. Remember that this discharge process is similar to that of a ordinary diode reverse leakage current.

    You can split zener into zener and diode characteristics put together.

    Hope this will help. If you have a question then write to me.

    Prof. (Dr.) Shyam Sunder Tiwari

    Senior Scientist and Managing Director

    Sensors Technology Private Limited

    AM-51, Deen Dayal Nagar, Gwalior, MP 474001, India

    Phone: 0091-751-2470680, Fax: 0091-751-4065716 M:0091-(0)9302146640

    Email: #-Link-Snipped-# Web: #-Link-Snipped-#
  • Voltaire
    Voltaire
    Re: Circuit diagram

    Ladies/Gentlemen
    Please do not contact the Professor directly. I have asked him to join the forum and he may decide to do so. He is very busy and I'm sure he does not want his inbox flooded with stuff we can answer here on the forum. So, let us all respect that
    Thank you for understanding that and for co-operating in this regard
  • chuackl
    chuackl
    Re: Circuit diagram dealing with capacitor,resistor and zener diode connected in seri

    Thank you very much voltaire😁 for your hardwork in answering others people question and mine. So now i do know my concept is partially correct right? I forget to take the leakage current into consideration and thinking that at the end the zener diode will act as if an infinite resistor which is not true. The mathematic equation blinded my thought and the way i accept thing is see whether it make sense or not. Thank to the professor also for point out my mistake. However, the concept that the zener diode acting as a "variable resistor" to ensure there is a constant voltage drop is still correct is it? I guess same thing is also apply to the active regulator installed inside a AC to DC power supply. During rectification the capacitor undergoes charging and discharging process. Hence the voltage across the capacitor is keep changing. By installing an active regulator in series with the load, it can ensure a smooth voltage drop across the load. When the voltage at the capacitor is keep changing but the voltage drop across the load can be constant is also due to the active regulator acting like a "variable resistor" that always varies depend on the voltage of the capacitor to ensure a constant voltage drop across the load am i right about this?
  • Voltaire
    Voltaire
    Re: Circuit diagram dealing with capacitor,resistor and zener diode connected in seri

    Not sure but it sounds good 😀
    You have it right. Now go with your gut
  • Kaustubh Katdare
    Kaustubh Katdare
    Re: Circuit diagram dealing with capacitor,resistor and zener diode connected in seri

    That is awesome, Voltaire! 😀 That was never seen before on CE!
  • shreyasm89
    shreyasm89
    Re: Circuit diagram dealing with capacitor,resistor and zener diode connected in seri

    @chuackl-You have got it right fella!It is a basic property of a Zener diode that the voltage across it remains constant irrespective of the change in the current through it. Refer the V-I characteristics of a typical Zener Diode...you will be able to answer yourself. the "variable resistance" of the ckt which you are referring is actually the 'dynamic impedance' of the Zener. Nevertheless you have got it right..so don't worry.
    @Voltaire-Great work buddy..😁

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