Chapter 5, Problem 29P

In the current divider circuit shown in Fig. P5.28. the currents flowing through the resistor ¡ and capacitor I₂ are given by

$I_1=\frac{Z_C}{Z_R+Z_C}I$ $I_2=\frac{Z_R}{Z_R+Z_C}I$ 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.

1. If $R=1K\Omega$ and $X_C=10H^3\Omega$, express 1R and Z as complex numbers in both rectangular and polar form,.
2. If $I=1mA$, determine $I_1$ and $I_2$, in both rectangular and polar forms.
3. Show $I=I_1+I_2$.