Question 448: AC fundamentals

Question

In a series LCR circuit, the inductance $$L$$ is $$10 ~\mathrm{mH}$$, capacitance $$C$$ is $$1 ~\mu \mathrm{F}$$ and resistance $$R$$ is $$100 ~\Omega$$. The frequency at which resonance occurs is :-

Accepted Answer

The goal is to find the frequency at which resonance occurs in a series LCR circuit. To achieve resonance, the inductive reactance ($$X_L$$) should equal the capacitive reactance ($$X_C$$).
Given are:
Inductance, $$L = 10 ~\mathrm{mH} = 10 	imes 10^{-3} ~\mathrm{H}$$
Capacitance, $$C = 1 ~\mu\mathrm{F} = 1 	imes 10^{-6} ~\mathrm{F}$$
Resistance, $$R = 100 ~\Omega$$ (which does not directly impact the resonance frequency)
Resonance occurs when the angular frequency ($$\omega$$) meets the condition $$\omega L = \frac{1}{\omega C}$$, leading to the formula for calculating the resonance frequency ($$f$$) as $$f = \frac{\omega}{2\pi} = \frac{1}{2\pi\sqrt{LC}}$$.
Substituting the given values:
$$f = \frac{1}{2\pi\sqrt{10 	imes 10^{-3} \cdot 1 	imes 10^{-6}}} = 1.59 \mathrm{kHz}$$
Thus, the frequency at which resonance occurs in this LCR circuit is 1.59 kHz.

Answer

15.9 kHz

Answer

1.59 rad/s

Answer

1.59 kHz

Answer

15.9 rad/s

AC fundamentals

In a series LCR circuit, the inductance $L is 10 ~\mathrm{mH}, capacitance C is 1 ~\mu \mathrm{F} and resistance R is 100 ~\Omega$. The frequency at which resonance occurs is :-

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