Finding Phase Shift in RLC Circuits

[jacksonwiley]

Homework Statement

An RLC circuit has a resistance of 2.0 kΩ, a capacitance of 8.0 µF, and an inductance of 9.0 H. If the frequency of the alternating current is 4.0/π kHz, what is the phase shift between the current and the voltage?
A) -1.6 rad
B) -1.5 rad
C) 36 rad
D) 3.1 rad

Homework Equations

Tan-1 (XL-Xc/R)

The Attempt at a Solution

at first i thought that since current phasors lag by 90 degrees that it may be -1.5 rads. but that isn't correct.
then i used the the inverse tangent equation above in hopes of finding the angle which came out to be 88.4 degrees (which is about 1.5 rads)
i then took the 88.4 degrees and subtracted it from 90 degrees, because I thought it might turn out a correct answer because the phasors are perpendicular to each other. but that gives you 1.6 which is not correct either.
I'm not sure what equation to use ...

 

[ehild]

Your work is correct, the current lags the voltage by 1.54 rad. The book might have rounded off too early, so it can be A or B. ehild

 

[jacksonwiley]

Your work is correct, the current lags the voltage by 1.54 rad. The book might have rounded off too early, so it can be A or B.


ehild

yeah that's what i thought, but i submitted both of those and neither is correct but i think that may be a mistake! thanks!

 

[rude man]

I calculated -1.44 rad:
w = 8 rad/s
angle = tan^-1{(8*9 - 1/64e-6)/2e3} = tan^-1(-7.78) = -82.7 deg = -1.443 rad.

 

[HalfLostAndSearching]

The correct equation to use for finding the phase shift between the current and voltage in an RLC circuit is arctan(ωL - 1/ωC)/R, where ω is the angular frequency of the alternating current. In this case, ω = 2πf = 2π(4.0/π) = 8.0 kHz. Plugging in the values for L, C, and R, we get arctan(9.0(8.0 kHz) - 1/(8.0 kHz)(8.0 µF))/2.0 kΩ = arctan(72 - 0.125)/2.0 = arctan(71.875/2.0) = 36.0 degrees. Therefore, the correct answer is C) 36 rad.