The resonant frequency of a certain series R L C circuit is 2.84 kHz , and the value of its capa

step 1 Resonance frequency of an RLC circuit would be equaling 1 over 2 pi multiplied by the square roo

The resonant frequency of a certain series R L C circuit is...

The resonant frequency of a certain series $R L C$ circuit is 2.84 $\mathrm{kHz}$ , and the value of its capacitance is 6.50$\mu \mathrm{F}$ . What is the value of the resonant frequency when the capacitance of the circuit is 9.80$\mu \mathrm{F}^{2}$

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Key Concepts

Resonant Frequency

Resonant frequency is the frequency at which the inductive and capacitive reactances in an RLC circuit cancel each other, resulting in a purely resistive impedance. This is a key property in circuits used in filters and oscillators, where maximum power transfer or signal selectivity is desired.

Series RLC Circuit

A series RLC circuit consists of a resistor (R), an inductor (L), and a capacitor (C) connected in series. The circuit exhibits unique frequency-dependent behavior such as resonance, where the circuit’s impedance is minimized, making it critical in applications like tuning and signal processing.

Resonant Frequency Formula

The resonant frequency in a series RLC circuit is given by the formula f = 1/(2??(LC)). This formula shows the inverse relationship between the frequency and the square root of the product of the inductance and capacitance, allowing for calculations of one parameter if the others are known.

Capacitance Effect on Resonance

Changing the capacitance in an RLC circuit directly affects the resonant frequency, as capacitance appears in the denominator of the resonant frequency formula. An increase in capacitance will lower the resonant frequency, while a decrease in capacitance will raise it, which is important for designing circuits with specific frequency responses.

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