AC Cirucits - Impedance Values

[Joe85]

Homework Statement

For the circuit given in the power factor is 0.72 lagging and the power dissipated is 375 W.

Determine the:
(1) apparent power
(2) reactive power
(3) the magnitude of the current flowing in the circuit
(4) the value of the impedance Z and state whether circuit is inductive or
capacitive.

(1) Apparent power = True power / Power Factor (S=P/pf)

= 375 / 0.72

= 520.8333 VA

(2) Reactive Power = SQRT (apparent power^2) - (True Power^2)

= SQRT (520.8333^2)-(375^2)

= SQRT (130642.3264)

= 361.4448 VAR

(3) Magnitude of Current

Power= Voltage*Current *Power factor (P=V*I*pf)

375 = 120*I*0.72
I = P/(V*pf)
I = 375/(120*0.72)
I = 4.34 A

(4) Total ohms = Voltage/Current
= 120/4.34
= 27.6498 ohms
Phi= arccos(0.72) = 43.95
R_T = 10 ohms

Z_Total= 27.6498∠43.95

Z = Z_Total - 10 | Cannot subtract complex numbers in polar form.

27.6498(Cos43.95+JSin43.95) = 19.9064 + J19.1898

(19.9064 + J19.1898) - 10 = 9.0964 + J19.1898

Z = SQRT (9.0964^2)+(19.1898^2) = 21.24

Phi = Arctan (19.1898/9.0964) = 64.64

Z = 21.24∠64.64 Lagging

Phase Angle Lagging - Circuit Inductive.

Homework Equations

The Attempt at a Solution

So i borrowed heavily from an older thread as my answers for 1 - 3 are identical. It's part 4 where I'm sturggling a bit. I followed the original thread, went away, refreshed my complex numbers knowledge and have come back with the above.

Would be greatful if someone could validate my answer or tell me if i have completely borked it up and offer some guidence.

 

[cnh1995]

The image you posted is too small to read from. Please upload a larger and clearer circuit diagram.

 

[Joe85]

Updated

 

[cnh1995]

R = SQRT (9.0964^2)+(19.1898^2) = 21.24

Everything looks correct to me, except this typo.

 

[Joe85]

Everything looks correct to me, except this typo.

Corrected and thank you very much.

 

[Joe85]

Slight miscalculations in the OP.

End result should be:

Z = 21.60∠62.7^o