Phase angle: 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?

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 resistanceSubstituting the given values into the equation, we get:$$\phi = \arctan\left(\frac{2\pi f L - \frac{1}{2\pi f C}}{R}\right)$$$$\phi = \arctan\left(\frac{2\pi (2.0/π kHz) (23.0 H) - \frac{1}{2\pi (2.0/π kHz) (33.0 μF)}}{4.0 kΩ}\right)$$$$\phi = \arctan\left(\frac{46π - 159.15}{4.0 kΩ}\right)$$$$\phi = \arctan(-1.5)$$$$\phi = -1.5 rad$$Therefore, the correct answer is A.

Phase Angle: a Series LRC Ac Circuit Has a Resistance