At what frequency does the maximum current flow through a series RLC circuit containing a resistance of \(4.50 \Omega,\) an inductance of \(440 \mathrm{mH},\) and a capacitance of \(520 \mathrm{pF} ?\)

Short Answer

Expert verified
Question: Calculate the frequency at which the maximum current flows through a series RLC circuit with the following values: resistance R = 120 Ω, inductance L = 440 mH, and capacitance C = 520 pF. Answer: The maximum current flows through the series RLC circuit at a frequency of approximately \(1.047 \times 10^{6} \, \text{Hz}\) or \(1.047 \,\text{MHz}\).

Step by step solution

01

Convert given values to SI units

We first need to convert the given values to their proper SI units: Inductance (L) = 440 mH = \(440 \times 10^{-3}\) H Capacitance (C) = 520 pF = \(520 \times 10^{-12}\) F.
02

Calculate the resonant frequency

Apply the formula for resonant frequency, which is \(f_r = \dfrac{1}{2\pi\sqrt{LC}}\). Substitute the given values of L and C: \( f_r = \dfrac{1}{2\pi\sqrt{(440 \times 10^{-3}) \cdot (520 \times 10^{-12})}} \).
03

Calculate the result

Simplify and solve for \(f_r\): \( f_r = \dfrac{1}{2\pi\sqrt{2.288 \times 10^{-10}}} \). \( f_r \approx 1.047 \times 10^{6} \,\text{Hz} \).
04

Present the final answer

The maximum current flows through the series RLC circuit at a frequency of approximately \(1.047 \times 10^{6} \, \text{Hz}\) or \(1.047 \,\text{MHz}\).

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