Chapter 5, Problem 21P

A sinusoidal voltage source V = 110 V of frequency 60 $Hz(\omega =120\pi rad/s)$ is applied to an RLC circuit as shown in Fig. P5.21, where $Z_R=R\Omega$, $Z_L=j\omega L\Omega$ and $Z_C=\frac{1}{j\omega C}\Omega$. Assuming that $R=100\Omega$, $L=\frac{500}{\pi }mH$, $C=\frac{500}{3\pi }\mu F$ and $j^2=-1$ . 

1. Write $Z_R$, $Z_L$ and $Z_C$
2. as complex numbers in both their rectangular and polar forms.
3. If the total impedance is $Z=Z_R+Z_L+Z_C$, write $Z$
4. in both rectangular and polar forms.
5. Determine the complex conjugate of $Z$ and compute the product $Z$ $Z^{*}$.
6. If $V_C=\frac{Z_C}{Z_R+Z_L+Z_C}V$, find the voltage in both rectangular and polar forms.

Figure P5.21 Voltage division for problem P5-21.