(Solved): 5-29. In the current divider circuit shown in Fig. P5.28, the currents flowing through the resistor ...

5-29. In the current divider circuit shown in Fig. P5.28, the currents flowing through the resistor \( I_{1} \) and capacitor \( I_{2} \) are given by \[ \begin{array}{l} I_{1}=\frac{Z_{C}}{Z_{R}+Z_{C}} I \\ I_{2}=\frac{Z_{R}}{Z_{R}+Z_{C}} I \end{array} \] where \( Z_{R}=R \Omega \) is the impedance of the resistor and \( Z_{C}=\frac{X_{C}}{j} \Omega \) is the impedance of the capacitor. (a) If \( R=2 \mathrm{k} \Omega \) and \( X_{C}=10^{3} \Omega \), express \( Z_{R} \) and \( Z_{C} \) as complex numbers in both rectangular and polar forms. (b) If \( I=5 \mathrm{~mA} \), determine \( I_{1} \) and \( I_{2} \) in both rectangular and polar forms. (c) Show \( I=I_{1}+I_{2} \).