Question

Consider a series RLC circuit where the resistance R=345Ω, the capacitance C=2.25μF, and the inductance L=95.0mH Determine the resonance frequency ω 0

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of the circuit. What is the maximum current I max
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when the circuit is at resonance, if the amplitude of the AC driving voltage is 60.0 V ? I max
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Answer 1

To answer the question, we essentially need to carry out two calculations. First, we have to calculate the resonance frequency for the circuit (ω 0), and then we have to figure out the maximum current when the circuit is at resonance (I max).

Let's start with the resonance frequency. For an RLC circuit like the one described in the problem, the resonance frequency is determined by the formula:

ω 0 = 1 / √(LC)

Here, L is the inductance and C is the capacitance. Substituting the given values L = 95.0mH and C = 2.25μF into the formula, we find:

ω 0 = 1 / √((95.0 * 10^-3 H) * (2.25 * 10^-6 F))

Performing this calculation, we find that the resonance frequency ω 0 = 2162.95 rad/s.

Next, we move on to the maximum current. At resonance, the maximum current I max is given by the formula:

I max = V / R

Here, V is the voltage and R is the resistance. Substituting the given values V = 60.0V and R = 345Ω into the formula, we find:

I max = 60.0V / 345Ω

This calculation gives a maximum current I max = 0.174A.

In conclusion, the resonance frequency (ω 0) of the given RLC circuit is approximately 2162.95 rad/s, and the maximum current (I max) at resonance is approximately 0.174A when the AC voltage is 60.0V.