Obtain the voltage of the generator and the phase angle

[cclement524]

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)

 

[gneill]

Numerically your angle looks okay. It's just its sign that I have my suspicions about...

 

[cclement524]

Thank you!