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Math Help - determining current in LR circuit

  1. #1
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    Post determining current in LR circuit

    A 30-volt electromotive force is applied to an-LR series circuit in which the inductance is 0.1 henry and the resistance is 50 ohms. Find the current i(t)
    if i(0)=0 Determine the current as t--> infinity.

    V=IR
    I=V/R,

    but i don't really understand what the question wants. can anyone help?
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by bleu90 View Post
    A 30-volt electromotive force is applied to an-LR series circuit in which the inductance is 0.1 henry and the resistance is 50 ohms. Find the current i(t)
    if i(0)=0 Determine the current as t--> infinity.

    V=IR
    I=V/R,

    but i don't really understand what the question wants. can anyone help?
    Since we are dealing with an LR circuit, the proper differential equation set up is L\frac{\,dI}{\,dt}+RI=30\implies 0.1\frac{\,dI}{\,dt}+50I=30

    Solve this linear DE, and then apply the initial condition I(0)=0 to find C, once you have solved the DE for I(t).

    Then take \lim_{t\to\infty}I(t) to answer the last part of the question.

    --Chris
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    after dividing the equation by 0.1 and getting the integrating factor,

    integrating e^500t*y = 300e^500t

    i'm getting confused here. how can i proceed?
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  4. #4
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by bleu90 View Post
    after dividing the equation by 0.1 and getting the integrating factor,

    integrating e^500t*y = 300e^500t

    i'm getting confused here. how can i proceed?
    Note that once you multiply through by the integrating factor, you get \frac{d}{\,dt}\bigg[e^{500 t}I\bigg]=300e^{500t}

    Integrating both sides, you get e^{500 t}I=\tfrac{3}{5}e^{500 t}+C\implies I(t)=\tfrac{3}{5}+Ce^{-500t}

    Now apply the initial condition I(0)=0 to find C:

    0=\tfrac{3}{5}+C\implies C=-\tfrac{3}{5}

    Therefore, I(t)=\tfrac{3}{5}\left(1-e^{-500t}\right)

    Now find \lim_{t\to\infty}I(t)

    Does this make sense now?

    --Chris
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    i got my final answer as 15. is this correct?
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  6. #6
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by bleu90 View Post
    i got my final answer as 15. is this correct?
    \lim_{t\to\infty}\tfrac{3}{5}\left(1-e^{-500t}\right)=\tfrac{3}{5}\lim_{t\to\infty} \left(1-e^{-500t}\right)=\tfrac{3}{5}\cdot\left(1\right)=\colo  r{red}\boxed{\tfrac{3}{5}}

    --Chris
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