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inductor capacitor series circuit?
Question:
Cant seem to get my head around this question so any advice would be great
A circuit with an inductor(with both resistance and inductance) Vrl = (200+j300)V connected in series to a capacitor c=150 micraF across a power supply with a 50Hz supply voltage. The supply current is 25<0 degrees
Calculate
a) impedance of the inductor expressed in complex form
b) the values of R and L of the inductor
c) the value of the supply voltage, expressed in polar form
d) the phase angle of the circuit
e) the apparent and active powers of the circuit
f) draw a scaled argand diagram showing the supply current and all voltages
Answer:
Vrl = 200 + j 300
Vrl = √[200² + j300]² = 360.56 Vrms < 56.31 degrees
R = Zr = 200 V / 25A = 8 Ohm
Is = 25A < 0 degrees
Zrl = 360.56 Vrms < 56.31 degrees / 25 A < 0 degrees
Zrl = 14.42 Ohm < 56.31 degrees
Zrl = 8 Ohm + j12 Ohm
f = 50Hz
C = 150 μF
Zc = -1/2πfC
Zc = -1/(100π(.00015))
Zc = -j21.22 Ohm
Zr + Zc = Zrc ==>>
Zr = 8 + j00.00 Ohm
Zc = 0 - j21.22 Ohm
===============
Zrc= 8 - j21.22 Ohm
Zrl - Zrc = Zl ==>>
Zrl= 8 + j12.00 Ohm
Zrc= 8 - j21.22 Ohm
===============
Zl = 0 + j33.22 Ohm
Zl = 33.22 Ohm
Zl = 2 π f L
L = Zl/ 2 π f = 33.22 Ohm /(100 x π) = .105743
L = 105.743 mH
Zt = Zr + Zl + Zc ==>>
Zr = 8 + j00.00 Ohm
Zc = 0 - j21.22 Ohm
Zl = 0 + j33.22 Ohm
===============
Zt = 8 + j12.00 Ohm
Zt = 14.42 < 56.31 degrees
Is = 25A < 0 degrees
Vt = (14.42 < 56.31) x (25A < 0) = 360.5 Vrms < 56.31 degrees
Pt = 360.5 Vrms < 56.31 degrees x 25A < 0 degrees = 9012.5 < 56.31 W
Is² = 25A² < 0 degrees = 625 A² < 0
Pr = 8 Ohm x 625A² = 5000 W
Pc = - j21.22 Ohm x 625A² = -13262.5 VAR
Pl = j33.22 Ohm x 625A² = 20762.5 VAR
Pt = 5000 W + 7500 VAR
Pt = 9013.9 VA < 56.31 degrees
a) impedance of the inductor expressed in complex form
Zl = 0 Ohm + 33.22 j Ohm
b) the values of R and L of the inductor
R = Zr = 200 V / 25A = 8 Ohm
L = 105.743 mH
c) the value of the supply voltage, expressed in polar form
Vt = (14.42 < 56.31) x (25A < 0) = 360.5 Vrms < 56.31 degrees
d) the phase angle of the circuit
φ = 56.31 degrees
e) the apparent and active powers of the circuit
Pr = 8 x 625A² = 5000 W
Pt = 5000 W + 7500 VAR
Pt = 9013.9 VA < 56.31 degrees
f) draw a scaled argand diagram showing the supply current and all voltages
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