Chapter 5, Problem 25P

In the RC circuit shown in Fig. P5.25, the impedances of R and C are given as $Z_R=R\Omega$ and $Z_C=-j{X}_C\Omega$, where $j=\sqrt{-1}$. Suppose $R=100\Omega$ and $X_C=50\Omega$ . 

1. Express the impedances $Z_R$ and $Z_C$
2. as complex numbers in both rectangular and polar forms.
3. Find the total impedance $Z=Z_R+Z_C$, as a complex number in both rectangular and polar forms.
4. If $V=100\angle 0°V$
5. find the current $I=\frac{V}{Z}$
6. as a complex number in both rectangular and polar forms.
7. Knowing the Current in part (c), find the voltage, phasors $V_R=I{Z}_R$ and $V_C=I{Z}_C$
8. in both rectangular and polar forms.
9. Show that the KVL is satisfied for the circuit shown in Fig. P5.25; in other words, show $V=V_R+V_C$.

Figure P5.25 An RC circuit for problem P5-25.