Respuesta :
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
Given Information:
Capacitance = C = 500 μF
Inductance = L = 20 mH
Frequency = ω = 100 rad/sec
Required Information:
Capacitive reactance = Xc = ?
Inductive reactance = XL = ?
Equivalent series impedance = Zseries = ?
Equivalent parallel impedance = Zparallel = ?
Answer:
Capacitive reactance = Xc = -j20 Ω
Inductive reactance = XL = j2 Ω
Equivalent series impedance = Zseries = -j18 Ω
Equivalent parallel impedance = Zparallel = j2.22 Ω
Explanation:
The capacitive reactance is calculated using
Xc = 1/jω*C
Where ω is the frequency in rad/sec and C is the capacitance of the capacitor
Xc = 1/j100*500x10⁻⁶
Xc = -j20 Ω
The inductive reactance is calculated using
XL = jω*L
Where ω is the frequency in rad/sec and L is the inductance of the inductor
XL = j100*0.02
XL = j2 Ω
The equivalent series impedance an can be calculated as
Zseries = XL + Xc
Zseries = j2 - j20 Ω
Zseries = -j18 Ω
The equivalent parallel impedance an can be calculated as
1/Zparallel = 1/XL + 1/Xc
Simplifying the above equation yields,
Zparallel = (XL*Xc) / (XL+ Xc)
Zparallel = (j2*-j20)/(j2-j20) ( j*j = -1)
Zparallel = 40/-j18 (1/-j = j)
Zparallel = j2.22 Ω
