In an RLC series circuit, these three elements are connected...

In an RLC series circuit, these three elements are connected in scries: a resistor of $60.0 \Omega,$ a 40.0 -mH inductor, and a $0.0500-\mathrm{F}$ capacitor. The series elements are connected across the terminals of an ac oscillator with an rms voltage of $10.0 \mathrm{V}$. Find the resonant frequency for the circuit.

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Key Concepts

Resonance in RLC Circuits

Resonance in RLC circuits occurs when the inductive and capacitive reactances balance each other, causing the reactive components to cancel out. At this condition, the circuit behaves purely resistively at a specific frequency, known as the resonant frequency, and exhibits maximum current for a given voltage.

Inductive and Capacitive Reactance

Inductive reactance (XL) and capacitive reactance (XC) are frequency-dependent properties of inductors and capacitors respectively. The inductive reactance increases with frequency, while the capacitive reactance decreases. The balance between these two is fundamental in determining the behavior of AC circuits, especially at resonance.

Resonant Frequency Formula

The resonant frequency of a series RLC circuit is determined by the formula f_res = 1/(2??(LC)). This formula encapsulates the relationship between the inductance and capacitance, showing how these two components set the natural frequency at which the reactances cancel, leading to resonance.

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