Chapter 5, Problem 31P

In the current divider circuit shown in Fig. P5.30. the currents flowing through the resistor $I_1$ and inductor $I_2$, are given by

$I_1=\frac{Z_L}{Z_R+Z_L}I$ $I_2=\frac{Z_R}{Z_R+Z_L}I$ where $Z_R=R\Omega$ is the impedance of the resistor and $Z_L=-j{X}_L\Omega$ is the impedance of the inductor.

1. If $R=1K\Omega$ and $X_L=10H^3\Omega$, express $Z_R$ and $Z_L$
2. as complex numbers in both rectangular and polar forms.
3. If $I=1mA$, determine I₁ and I₂ in both rectangular and polar forms.
4. Show $I=I_1+I_2$.