The resonant frequency of a series circuit consisting of an...

The resonant frequency of a series circuit consisting of an inductance $200 \mu \mathrm{H}$, a capacitance of $0.0005 \mu \mathrm{F}$ and a resistance of $10 \Omega$ is :
(a) $480 \mathrm{kHz}$
(b) $503 \mathrm{kHz}$
(c) $406 \mathrm{kHz}$
(d) $607 \mathrm{kHz}$

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Key Concepts

Series RLC Circuit

A series RLC circuit is composed of a resistor, an inductor, and a capacitor connected in a single path. The circuit's overall impedance and frequency response depend on the interplay of these three components, with the resonant frequency being the point at which the effects of the inductor and capacitor negate each other.

Resonance in RLC Circuits

Resonance in RLC circuits occurs when the inductive reactance and capacitive reactance are equal in magnitude but opposite in phase, causing them to cancel one another. This results in a circuit behavior dominated solely by resistance, which allows for the maximum amplitude of the circuit current at a specific frequency known as the resonant frequency.

Resonant Frequency Calculation

The resonant frequency of a series RLC circuit can be calculated using the formula f = 1/(2??(LC)), where L is the inductance and C is the capacitance. This formula highlights how the energy storage elements (inductor and capacitor) determine the frequency at which the circuit experiences resonance.

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