Finding Phase Shift in RLC Circuits

AI Thread Summary
The discussion revolves around calculating the phase shift in an RLC circuit with specified resistance, capacitance, and inductance at a given frequency. The initial attempts to find the phase shift using the inverse tangent formula led to results around -1.5 radians, but these were deemed incorrect. A participant confirmed that the current lags the voltage by approximately -1.54 radians, suggesting that the textbook might have rounded the answer prematurely. Another participant recalculated the phase shift to be around -1.44 radians, indicating potential discrepancies in the provided answers. The conversation highlights the complexities of phase shift calculations in RLC circuits and the importance of precise values.
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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 ...
 
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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
 
ehild said:
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!
 
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.
 
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