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Math Help - Finding values from two equations

  1. #1
    Junior Member froodles01's Avatar
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    Finding values from two equations

    A transmission line is designed so it has self inductance, L = 7.0x10^-7 Hm^-1 & signal speed 70% of c 9speed of light)
    Find characteristic impedance

    Now
    Z = √L/C (where C is capacitance, but shouldn't really matter just for the maths bit)
    also
    v = 1/ √LC


    remembering
    L = 7.0x10^-7 Hm^-1
    v = 0.7c
    (c = 3x10^8 ms^-1)

    7(3x10^8)/10 = 1/√7.0x10^-7 * C
    so
    C = √((10(7.0x10^-7))/(7*3x10^8))
    C = √ 3.33x10^-15
    C = 5.77x10^-8 F

    Z = √L/C
    Z = √7.0x10^-7/5.77x10^-8
    Z = 3.4 Ω

    Which isn't in the park as far as expected result goes, so AGAIN, please could you show me where I went wrong.
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  2. #2
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    earboth's Avatar
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    Re: Finding values from two equations

    Quote Originally Posted by froodles01 View Post
    A transmission line is designed so it has self inductance, L = 7.0x10^-7 Hm^-1 & signal speed 70% of c 9speed of light)
    Find characteristic impedance

    Now
    Z = √(L/C) (where C is capacitance, but shouldn't really matter just for the maths bit)
    also
    v = 1/ √LC


    remembering
    L = 7.0x10^-7 Hm^-1
    v = 0.7c
    (c = 3x10^8 ms^-1)

    7(3x10^8)/10 = 1/√(7.0x10^-7 * C )
    so
    C = √((10(7.0x10^-7))/(7*3x10^8))
    C = √ 3.33x10^-15
    C = 5.77x10^-8 F

    Z = √L/C
    Z = √7.0x10^-7/5.77x10^-8
    Z = 3.4 Ω

    Which isn't in the park as far as expected result goes, so AGAIN, please could you show me where I went wrong.
    __________________
    Just trying to keep up.
    As far as I understand your calculations:

    1. You've forgotten to use parantheses (added in red)

    2. To get the value of C you have to square both sides of the equation first.
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  3. #3
    Junior Member froodles01's Avatar
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    Re: Finding values from two equations

    A fresh pair of eyes has it every time.
    Thanks. X
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