Answer to Question #130550 in Electric Circuits for Sumedh

Question #130550
What is the total impedance of a circuit with a 20 ohm resistor, a 50 ohm capacitive reactance, 30 ohm inductive reactance in parallel?
1
Expert's answer
2020-08-25T11:13:11-0400

For the parallel circuit: 1Z=1R2+1X2\frac{1}{Z}=\sqrt{\frac{1}{R}^2+\frac{1}{X}^2} , where Z is impedance, R - resistance, X - reactance. 1X=1XL1XC.\frac{1}{X}=\frac{1}{X_L}-\frac{1}{X_C}. Hence, 1Z=1R2+(1XL1XC)2=1202+(130150)2=\frac{1}{Z}=\sqrt{\frac{1}{R}^2+(\frac{1}{X_L}-\frac{1}{X_C})^2}=\sqrt{\frac{1}{20}^2+(\frac{1}{30}-\frac{1}{50})^2}=

=(1400+(201500)2=0.052Ohm1=\sqrt{(\frac{1}{400}+(\frac{20}{1500})^2}=0.052 Ohm^{-1}. Thus, the total impedance is Z=10.052=19.23OhmZ=\frac{1}{0.052}=19.23Ohm.


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