Okay, so i've got some questions and I seem to be struggling on part of them, mainly the phase angles, real and apparent powers,

1.
Here is the information i know
Inductive reactance = 27.646 ohms
Z = 57.134
Current from power supply = 0.8751 A
Vl = iXl = 24.193 V
VR = 43.755 V

Now the part i got wrong:
I did the square root of 43.755^2 + 24.193^2 which = 49.998
To work out the phase angle i did = cos^-1 (24.193/49.998) which = 61 degrees (wrong)
Apparent power = Vsis = 50x0.8751 = 43.755 (wrong)
Real Power = Vsis x cos(theta) = 43.755 x cos 61.06 = 21.173 (wrong)

Any help with these would be appreciated.

2. Here is the information i know
Xc = 39.7887
Z = 63.899
i = 0.7825 A
Vc = iXc = 31.135
VR = 39.125

Now the parts i got wrong :
I tried to work out the phase angle by doing Cos ^-1 (31.135/50) = 51.488 degrees (wrong)
Apparent power = Vsis = 50x0.7825 = 39.125 (wrong)
Real Power = Vsis x cos(theta) = 30.125 x cos(51.488) (wrong)

The final question:

3.
a)Calculate Power factor of the circuit
b) calculate the value of capacitance needed to bring the circuit to unity power factor

Here is the information given :
Xl = 27.646
Z = 57.134
i=0.8751
VL = 24.193
VR = 43.755
Apparent Power = 43.755
Real Power = 21.173

So here is my working:
Square root of 43.755^2 - 21.173^2 = 38.291

Power factor = real/apparent = 21.173/43.755 = 0.484 (wrong)
Q = E^2/X
X = E^2/Q = 50^2/38.291 = 65.289 ohms (wrong)
C = 1/2 x pi (3.14159) x f x Xc = 1/2 x pi x 200 x 65.289
C = 1.2188496x10^-5
=12.19 uF

Any help with these questions would be appreciated, it is good practice for me

Thank you for your time

 

1.
Since you show no schematic or provide any context I will have to guess what you are trying to do, but if I get it..
the phase angle is = sin^-1 (24.193/49.998) = 28.9 deg.

 

It would be very handy if you would at least tell us if the circuits in question are series or parallel, instead of making us guess.

In the first problem, assuming the components are in series (which seem like they have to be), what is the voltage across the power supply?

If you know the voltage across the supply and the current through the supply, what is the apparent power?

 

You might want to review Volume II, Alternating Current, the ebook at this site.