Discussion
What is the phase angle of a series RLC circuit at resonance ?
Answer: A
The phase angle at resonance is zero.
A series RLC circuit is resonant when the inductive and capacitive reactances are equal, \(X_{L} = X_{C}\), at \(f_{0} = 1/(2\pi\sqrt{LC})\). The two reactances then cancel, the impedance reduces to R alone, its minimum value, and the current is in phase with the applied voltage.
\[ \phi = \tan^{-1}\frac{X_{L} - X_{C}}{R} = 0 \]
An angle of 90° would mean a purely reactive circuit, and 45° is reached at the half-power frequencies on either side of resonance, where \(|X_{L} - X_{C}| = R\).
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