Complex impedance

Electricity and Magnetism Level 3

What is the magnitude of complex impedance between points A and B(in Ohms)?


The answer is 20.

Novak Radivojević by Novak Radivojević , 23, Serbia

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1 solution

Steven Chase
Jul 23, 2019

Use the delta-wye transform and then simplify. Specific steps are shown in the attached code: 

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import math

######################################################

# Given impedances

R = 50.0
L = 50.0 * (10.0**-3.0)
C = 20.0 * (10.0**-6.0)
w = 1000.0

XL = w*L
XC = 1.0/(w*C)

ZR = complex(R,0.0)
ZL = complex(0.0,XL)
ZC = complex(0.0,-XC)

######################################################

# Derived Impedances - Delta/wye transform

Zsum = ZR + ZC + ZL

ZB1 = ZR*ZC/Zsum
ZB2 = ZR*ZL/Zsum
ZB3 = ZL*ZC/Zsum

ZP1 = ZR*ZL/Zsum
ZP2 = ZR*ZC/Zsum
ZP3 = ZL*ZC/Zsum

######################################################

# ZR, ZB1, and ZP1 in series

ZS1 = ZB1 + ZR + ZP1

######################################################

# ZB3 and ZP3 in series

ZS2 = ZB3 + ZP3

######################################################

# ZS1 and ZS2 in parallel

ZPar1 = ZS1*ZS2/(ZS1+ZS2)

######################################################

# ZB2, ZPar1, and ZP2 in series

ZS3 = ZB2 + ZPar1 + ZP2

######################################################

# ZAB = ZR in parallel with ZS3

ZAB = ZR*ZS3/(ZR+ZS3)

######################################################

print ZAB       
print abs(ZAB)

#(20-2.55795384874e-15j)   # equivalent impedance is 20 ohms, purely resistive
#20.0

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