A series LRC ac circuit has a resistance of 4.0 kΩ,a capacitance of 33.0 μF,and an inductance of 23.0 H.If the frequency of the alternating current is 2.0/π kHz,what is the phase angle between the voltage and the current?
A) 1.5 rad
B) -1.6 rad
C) 23 rad
D) 3.1 rad

Question

Quizplus · Accepted Answer

The phase angle is given by:$$\phi = \arctan\left(\frac{XL - XC}{R}\right)$$where:* XL is the inductive reactance* XC is the capacitive reactance* R is the resistanceIn this case, we have:$$XL = 2\pi f L = 2\pi (2.0/π kHz)(23.0 H) = 29.9 kΩ$$$$XC = \frac{1}{2\pi f C} = \frac{1}{2\pi (2.0/π kHz)(33.0 μF)} = 12.0 kΩ$$Therefore, the phase angle is:$$\phi = \arctan\left(\frac{29.9 kΩ - 12.0 kΩ}{4.0 kΩ}\right) = 1.5 rad$$

A Series LRC Ac Circuit Has a Resistance of 4