Chapter 5, Problem 20P

An electric circuit consists of two components as shown in Fig. P5.20. The values of the impedance of the two components are $Z_1=R_1+j{X}_L$, and $Z_2=R_2-j{X}_C$ where $R_1=75\Omega$, $X_L=100\Omega$, $R_2=50\Omega$ and $X_c=125\Omega$ forms.

1. Write $Z_1$ and $Z_2$, as complex numbers in both their rectangular and polar forms.
2. Determine the complex conjugate of $Z_2$ and compute the product $Z_2{Z}_2{}^{*}$.
3. Compute the total impedance of the ¿I Z two components $Z=\frac{Z_1+Z_2}{Z_1+Z_2}$
4. express the result in both rectangular and polar forms.

Figure P5-20 Impedance of elements connected in parallel for problem P5.20