Chapter 5, Problem 30P

In the current divider circuit shown in Fig. P5.30. the sum of the current phasors $I_1$ and $I_2$, is equal to the total current phasor I (i.e., $I=I_1+I_2$ ).

Figure P5.30 A current divider circuit for problem P5-30 and P5-31

Suppose $I_1=\sqrt{2}\angle 45°$ and $I_2=\sqrt{2}\angle -45°$ both measured in mA.

(a) Write $I_1$ and $I_2$ in rectangular form.

(b) Determine the total current phasor $I$ in both rectangular and polar forms.

(c) Suppose $Z_R=1000\Omega$ and $Z_L=j1000\Omega$. Write $V_R$ and $V_L$, as complex numbers in both rectangular and polar forms if $V_R=I_1\times Z_R$ and $V_L=I_2\times Z_L$.