Answer:
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