(Solved): 8. A series-parallel electric circuit consists of the components shown in Fig. P5.18. The values of ...

8. A series-parallel electric circuit consists of the components shown in Fig. P5.18. The values of the impedance of the two components are \( Z_{1}=\frac{-j}{\omega_{R} C} \) and \( Z_{2}=R+j \omega L \), where \( C=5 \mu \mathrm{F}, R= \) \( 100 \Omega, L=0.15 \mathrm{H}, \omega=120 \pi \mathrm{rad} / \mathrm{s} \), and \( j=\sqrt{-1} \) (a) Write \( Z_{1} \) and \( Z_{2} \) as complex numbers in both their rectangular and polar forms. (b) Write down the complex conjugate of \( Z_{2} \) and calculate the product \( Z_{2} Z_{2}^{*} \). (c) 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. Figure P5.18 Impedance of series-parallel combination of circuit elements for problem P5-18.