Chapter 5, Problem 24P

In the circuit shown in Fig. P5.24, the impedances of the various components are $Z_R=R\Omega ,Z_L=j{X}_L\Omega ,$ and $Z_C=\frac{1}{j}{X}_C$, where $j=\sqrt{-1}$. Suppose $R=120\Omega ,X_L=120\sqrt{3}\Omega ,$ and $X_C=\frac{1}{50\sqrt{3}}\Omega$.

1. Express the impedance $Z_R,Z_L$ and $Z_C$
2. as complex numbers in both rectangular and polar forms.
3. Now, suppose that the total impedance of the circuit is $Z=Z_C+\frac{Z_R{Z}_L}{Z_R+Z_L}$. Determine the total impedance and express the result in both rectangular and polar forms.
4. Determine the complex conjugate of $Z$ and compute the product $Z$ $Z^{*}$.

Figure P5.24 A capacitor connected in series with a parallel combination of resistor and inductor for problem P5-24.