Question

What is the total impedance of a circuit with a 20 ohm resistor, a 50 ohm capacitive reactance, 30 ohm inductive reactance in parallel?

Answer 1

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

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