How does the phase angle change with frequency in an RLC circuit?

The impedance (Z) of an RLC circuit is given by the vector sum of the resistance (R), inductive reactance (XL), and capacitive reactance (XC). Mathematically, impedance is represented as:

Z = R + j(XL - XC)

where j is the imaginary unit (√(-1)).

The inductive reactance (XL) and capacitive reactance (XC) are frequency-dependent. Inductive reactance is given by:

XL = 2πfL

where f is the frequency and L is the inductance of the inductor. Inductive reactance increases linearly with frequency.

Capacitive reactance is given by:

XC = 1 / (2πfC)

where f is the frequency and C is the capacitance of the capacitor. Capacitive reactance decreases inversely with frequency.

As the frequency changes, the inductive reactance and capacitive reactance change in opposite directions. When the frequency is low, the inductive reactance dominates, causing the phase angle to be positive. As the frequency increases, the capacitive reactance becomes more significant, causing the phase angle to become negative.

At a certain frequency, called the resonant frequency, the inductive reactance and capacitive reactance are equal in magnitude but opposite in sign, resulting in their cancellation, and the impedance becomes purely resistive. At this point, the phase angle is zero.

Overall, the phase angle in an RLC circuit changes from positive to zero to negative as the frequency increases from low to resonant to high frequencies.