Chapter 5, Problem 18P

A series-parallel electric circuit consists of the components shown in Fig. P5.1K. The values or the impedance of the two components are $Z_1=\frac{-j}{\omega C}$ and $Z_2=j\omega L$, where $C=5\mu F$, $R=100\Omega$, $L=0.15H$, $\omega =120\pi rad/s$ and $j=\sqrt{-1}$.

1. Write $Z_1$ and $Z_2$, as complex numbers in both their rectangular and polar forms.
2. Write down the complex conjugate $Z_2$ and calculate the product $Z_2{Z}_2{}^{*}$.
3. Calculate the total impedance $Z=\frac{Z_1+Z_2}{Z_1+Z_2}$ of the circuit. Write the total impedance in both its rectangular and polar forms

FigureP5.18 Impedance of series-parallel combination of circuit elements for problem P5-18.