Obtain the voltage of the generator and the phase angle

AI Thread Summary
The discussion centers on calculating the voltage of an AC generator and the phase angle in a circuit with a resistor and capacitor. The generator operates at a frequency of 4.80 kHz, producing a current of 0.0400 A. The voltage is calculated to be 10.7 V using the impedance of the circuit, which is derived from the resistor and capacitive reactance. The phase angle is determined using the arccosine function, yielding approximately 29.86 degrees, although there are concerns about the sign of the angle. Overall, the calculations for voltage appear correct, but clarification on the phase angle's sign is needed.
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Homework Statement




An ac generator has a frequency of 4.80 kHz and produces a current of 0.0400 A in a series circuit that contains only a 231-Ω resistor and a 0.250-µF capacitor. Obtain the voltage of the generator and the phase angle between the current and the voltage across the resistor/capacitor combination.

I have the voltage correct, I'm just getting an incorrect answer for the angle.


Homework Equations



Capaacitance of the capacitor is C = 0.250 *10^-6 F

resistor is R = 230Ω

phase angle between capacitor and resistor is tan^-1 XC / R

Capcitive reactance is X_C = 1/2 π f C


The Attempt at a Solution



?=2pf = 4.80kHz x 2p = 30.16 x 103rad/s

XC = 1/?C =1/(30.16*103*0.250*10-6) = 132.62 O
Z = 231 - 132.62j

Z = v(2312 + 132.622) =266.36O

V = IZ = 266.36O * 0.0400A = 10.7V (1)

arccos (231/266.36)= 0.5211 (in radian)

0.5211 * 180/p = 29.86 (degrees)
 
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Numerically your angle looks okay. It's just its sign that I have my suspicions about...
 
Thank you!
 
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