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?

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