Calculate the resonant frequency of a circuit of negligible...

Calculate the resonant frequency of a circuit of negligible resistance containing an inductance of $40.0 \mathrm{mH}$ and a capacitance of $600 \mathrm{pF}$ $$ f_{0}=\frac{1}{2 \pi \sqrt{L C}}=\frac{1}{2 \pi \sqrt{\left(40.0 \times 10^{-3} \mathrm{H}\right)\left(600 \times 10^{-12} \mathrm{~F}\right)}}=32.5 \mathrm{kHz} $$

Calculate the resonant frequency of a circuit of negligible resistance containing an inductance of $40.0 \mathrm{mH}$ and a capacitance of $600 \mathrm{pF}$
$$
f_{0}=\frac{1}{2 \pi \sqrt{L C}}=\frac{1}{2 \pi \sqrt{\left(40.0 \times 10^{-3} \mathrm{H}\right)\left(600 \times 10^{-12} \mathrm{~F}\right)}}=32.5 \mathrm{kHz}
$$

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Key Concepts

LC Circuit

An LC circuit is a basic electrical circuit consisting solely of an inductor (L) and a capacitor (C). In such a circuit, energy oscillates between the magnetic field of the inductor and the electric field of the capacitor, which forms the basis for many applications including filters and oscillators.

Resonant Frequency

The resonant frequency is the frequency at which an LC circuit naturally oscillates when energy is transferred back and forth between the inductor and capacitor. It is determined by the formula f0 = 1/(2??(LC)), where the values of inductance and capacitance set the rate of oscillation.

Inductance

Inductance is a measure of an inductor's ability to store energy in a magnetic field when electrical current flows through it. In an LC circuit, the inductance value, along with the capacitance, directly influences the oscillation frequency, with higher inductance generally leading to lower resonant frequency.

Capacitance

Capacitance is the capacity of a capacitor to store electrical charge in an electric field. In an LC circuit, the capacitance works together with the inductance to determine the circuit's natural resonant frequency, with larger capacitance resulting in lower resonant frequency.

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