Current phase angle difference (AC circuit)

[gruba]

Note that there should be two candidate angles that will yield the required cosine. One in quadrant 2 and one in quadrant 3.

You are right: $\theta=\frac{3\pi}{4}$ or $\theta=\frac{5\pi}{4}$.

 

[gneill]

Yup, or $\pm \frac{3}{4} \pi$ . Phase angles are conventionally given in the range -180° to +180°.

You should confirm that the resulting total current yields half the power as the original current, say by determining the active power dissipated in Z1.

 

[gruba]

Thanks for the help.

 

[gneill]

You're welcome!