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26 December, 17:05

Calculate the impedance of a 20 mH inductor at a frequency of 100 radians/s. Calculate the impedance of a 500 µF inductor at a frequency of 100 radians/s. What is the equivalent impedance of the inductor and capacitor connected in series? What is the equivalent impedance of the inductor and capacitor connected in parallel?

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  1. 26 December, 18:14
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    a) Zinductor = j2 Ohm

    b) Zcapacitor = - j20 Ohm

    c) Zseries = - j18 Ohm

    d) Zparallel = - j2.22 Ohm

    Explanation:

    The inductor impedance is directly proportional to the frequency, therefore:

    a) frequency = 100 rad/s inductor = 20mH

    Zinductor = j*frequency*inductor = j*100*20*10^ (-3) = j2 Ohm

    b) The capacitor inductance is inversely proportional to the frequency and it's also negative, therefore:

    frequency = 100 rad/s capacitor = 500 uF

    Zcapacitor = j*frequency*capacitor = - j / (100*500*10^ (-6)) = - j / (0.05) = - j20 Ohm

    c) The equivalent impedance of these two components in series is the sum of each part, wich goes as follow:

    Zseries = Zinductor + Zcapacitor = j2 - j20 = - j18 Ohm

    d) The equivalent impedance of these two components in parallel is given by the following equation:

    Zparallel = (Zinductor*Zcapacitor) / (Zinductor+Zcapacitor)

    Zparallel = [j2 * (-j20) ] / (j2-j20)

    Zparallel = [-40] / (-j18) = 2.22/j = - j2.22 Ohm
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