Chapter 5, Problem 27P

A resistor, capacitor, and inductor are connected in series as shown in Fig. P5.27. The total impedance of the circuit is $Z=Z_R+Z_L+Z_C$, where $Z_R=R\Omega ,Z_L=j\omega L\Omega$ and $Z_C=\frac{1}{j\omega C}\Omega$. For a particular design, $R=100\Omega ,L=500mH,C=25\mu F$ and $\omega =120\pi rad/s$.

 

FigureP5.27 RLC circuit for problem P5-27

1. Express the impedances $Z_R,Z_{L}and{Z}_C$
2. as complex numbers in both rect4inuIar and polar forms.
3. Determine the total impedance $Z$
4. in both its rectangular and polar forms.
5. If $V=100\angle 0°V$, find the current $I=\frac{V}{Z}$
6. as a complex number in both rectangular and polar forms.
7. Show that the KVL is satisfied for the circuit shown in Fig. P5.27 (i.e., show $V=V_R+V_L+V_C$
8. ).