SOLUTION: A series ac circuit has R=3.70 ohms, Xl=5.97 ohms, and Xc=7.90 ohms. Find the impedance,and the phase angle between the current and the voltage.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: A series ac circuit has R=3.70 ohms, Xl=5.97 ohms, and Xc=7.90 ohms. Find the impedance,and the phase angle between the current and the voltage.      Log On


   

Question 177474: A series ac circuit has R=3.70 ohms, Xl=5.97 ohms, and Xc=7.90 ohms. Find the impedance,and the phase angle between the current and the voltage.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The formula for impedance Z is given by,
Z=sqrt%28R%5E2%2B%28X%5Bl%5D-X%5Bc%5D%29%5E2%29
Z=sqrt%283.7%5E2%2B%285.97-7.9%29%5E2%29
Z=sqrt%2813.69%2B3.7249%29
Z=sqrt%2817.4149%29
Z=4.17
The impedance is 4.17 ohms.
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.
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The phase angle alpha is given by,
tan%28alpha%29=%28X%5Bl%5D-X%5Bc%5D%29%2FR
tan%28alpha%29=%28-1.93%2F3.7%29
tan%28alpha%29=-0.522
alpha=-27.5
Voltage lags current by 27.5 degrees.