**Problem:**

Relevant Formulas:

Relevant Formulas:

S = VI*

V = IZ

S = V^2 / Z

**Attempt at Solution:**

I know from my many attempts that my problem is not knowing when to use peak and rms values for current and voltage. I'll show the steps that I follow to get to each solution on the left, and then an explanation of my thought process on the right.

(a) This is quite easy; all I have to do is add up the loads and implement S = VI*

S = 7000 - j1000 Total load

S = (Vrms)(I*rms) Solve for I...

I*rms = (S) / (Vrms)

(I*) / sqrt(2) = (7000 - j1000) / (300 / sqrt(2)) Substitute in values...

I* / sqrt(2) = 33 - j4.714

I = 47.14 A at an angle of 8.13 degrees

I have confirmed that this value is correct.

(b) This is where things start to confuse me. I use the formula S = (I^2)(Z) to find the impedance of Z1

S = (Irms^2)(Z) Solve for Z...

Z = (S) / (Irms^2) Substitute in values....

Z = (5000 - j1000) / ((47.14 / sqrt(2))^2) Calculator....

Z = 4.5 - j2.7 Rectangular Form

Z = 5.25 ohms at and angle of -30.96 degrees Polar Form

I don't know if this is correct; however, I believe I may have made a mistake by using the rms value for the current (I).

(c) In order to find V2, I'll use KVL to get it. I'll find the voltage across the load S1 and subtract it from the source voltage.

S1 = (V1rms) (I*rms)

S1 = (1/2) (V1) (I*) Solve for V1...

V1 = ((2)*(S1)) / (I*) Substitute values in....

V1 = ((2)*(5000-i*3000)) / (47.14) Calculator...

V1 = 247.4 V at an angle of -30.96 degrees

Then I subtract the rms value of this voltage from the rms value of the source voltage to get V2...

V2 = Vrms - V1rms Substitute values in....

V2 = (300) / sqrt(2) - 247.4 / sqrt(2) Calculator....

V2 = 37.19 V at an angle of -30.96 degrees

I'm almost 100% sure that this value in wrong. I can't prove it, but I have a gut feeling it is.

(d) In order to find the impedance Z2, I will use the formula S = V^2 / Z

S2 = (Vrms)^2 / Z2

Z2 = (Vrms)^2 / S2 Solve for Z2

Z2 = (37.19 / sqrt(2))^2 / (-j8000) Sub in values and calculate...

Z2 = j0.08644 ohms

Z2 = 86.4 milli ohms at an angle of 90 degrees

I know for a fact that this is incorrect. The answer should be 900 milli ohms at an angle of -90 degrees. On the bright side, my degrees is similar, just an opposite sign. If I had to guess, I may have dropped a conjugate I* somewhere. However, the amount of milli ohms is way off. If I had to guess what I did wrong, I think I may have accidentally used an rms value when I should've used a peak value perhaps?

(e) I'm not going to post my work for e as my work up until this point would simply result in another wrong answer. I think it'd be best if I start from the beginning and figure what I did wrong first and then continue on.