The strange case of phase angles

[ballsystemlord]

Hello,
I was doing some practice problems in my textbook and came upon a parallel RLC circuit. I calculated the phase angle using the impedance but my value differed from the answer key.

Puzzled, I tried obtaining it from the amperage and power vectors successfully. I tried reviewing my math, but can't figure out why my impedance vector doesn't yield the same result as the amperage and power ones. Which is correct? I thought I could try and build a circuit to test this, but the fact that this is a textbook circuit makes it unrealistic so I can't make one.

Attached are images of the problem, my calculator with results, and the answer key.

So, what's the correct phase angle? Why do the impedance and amperage/power vectors differ in their angles?

Thanks!

[strawberry]

simulate in Qspice

[ballsystemlord]

simulate in Qspice

Learning Qspice is in my next book. But I could wait.

EDIT: So far, I've done all calculations for all circuits by hand with a calculator, pen, and pencil.

[Andy Watson]

The impedance of the capacitor should be combined with the impedance of the inductor in parallel; you appear to have combined them in series.

[tooki]

And what that means is that to solve it trigonometrically, you can’t use the impedance (vector addition of resistance and reactance), but rather the admittance (vector addition of conductance and susceptance).

As an aside: as someone who sucks at trigonometry, I just use my calculator’s ability to work with polar complex numbers. So calculating I_T, for example, I just type: 0.02 + 0.008∠-90 + 0.01571∠90 and get 0.02143∠21.1.

[sicco]

The voltage source has an output impedance of zero ohms. It thus dictates a voltage on both the R, the L and the C. No matter what the values are for R, L or C. So no way that L, C, or R can ‘see’ each-other and form a LC resonator or so.
The phase angle from voltage to current through each component leg is zero for R, 90 and -90 for L and C. The current from the source is the sum of I_R, I_C and I_R. So subtract L and C currents because they are 180 deg apart. Then atan the imag and real. So something like atan((I_L - I_C) /I_R) for the phase difference from V_source to I_source.