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DC Transients cap+resistor in series Theory

Discussion in 'Mathematics and Physics' started by Corky, Jan 8, 2015.

  1. Corky

    Corky Member

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    Hi Everyone,

    I have a theory explination for a cap and resitor in series but the explination dissapears at the point on the photo.

    i understand the theory of all the voltages must add to make the supply

    could someone go through it starting with i=dq/dt im happy to answer any questions as i might know more than i remember

    D.C. Transient.JPG

    Cheers
     
  2. Ratchit

    Ratchit Well-Known Member

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    What is the question? As far as is shown, it looks like standard algebraic substitution. Where or what don't you understand?

    Ratch
     
  3. rumpfy

    rumpfy Active Member

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    the line you just cant read says;
    "integrating both sides of the above equation"
     
  4. dave

    Dave New Member

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  5. Ratchit

    Ratchit Well-Known Member

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    Yes, that will solve the differential equation because the variables are separated. And the question is?

    Ratch
     
  6. Corky

    Corky Member

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    Hi all,

    im ok with algebra but im unsure what the letters represent as they dont state in the question.

    does: dq=a given point of charge
    dt= a given point in time
    Q=CVc = charge is equal to capacitor value x voltage across the cap

    if this is right i think ive got my head around it. its just a simple thing but im trying to get my head around what each letter represents

    Cheers guys, P.S. sorry for the late reply
     
  7. rumpfy

    rumpfy Active Member

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    Electric current is defined as; the rate of flow of charge. So, within an interval of time, if an amount of charge flows, then the current is (amount of charge /time interval). So mathematically, current i = q/t
    For time varying circuit analysis, the time period is mathematically reduced to 'zero' and the incremental current is described as dq/dt and this means the (incremental change of charge/ a small increment of time). Summing the change of charge over time (integration) gives the total charge and hence the capacitor voltage from Vc= Qtot/C as you have said.
     
  8. JimB

    JimB Super Moderator Most Helpful Member

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    Not really.

    I am thinking that you have never studied calculus, defferentiation and integration.

    dv/dt is the rate of change of voltage with time, and similarly
    dq/dt is the rate of change of charge with time.

    The letter d can be thought of as representing "a very small change in".

    JimB
     
  9. Corky

    Corky Member

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    Hi,

    I am terrible at explaining what im thinking, i knew that but i didnt realise d was "a small change in" i thaught it was a sample of a changing number and not a range

    Cheers
     
    Last edited: Jan 12, 2015
  10. Colin

    Colin Member

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    yes. d is called or spoken as: "diddly"
     
  11. MrAl

    MrAl Well-Known Member Most Helpful Member

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    Hi,

    Often the lower case 'd' is taken to be "delta" which is used to indicate a small change in the variable that follows. So a few examples:
    dt: a small change in t
    dq: a small change in q
    dv: a small change in v
    di: a small change in i

    and usually we'll see them in pairs being divided by another like:
    dv/dt
    which means "the change in voltage with respect to time", or more literally, "a small change in voltage as the time changes by a small amount".

    When you integrate one of these by the respective variable you get the top variable as result, plus an as yet undefined constant:
    Integral(dv/dt) with respect to time = v+K
    Integral(di/dt) with respect to time = i+K
     

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