∙In a series R-L-C circuit, R=400 Ω, L=0.350 H, and C=0.0120 μF (a) What is the resonance angula

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∙In a series R-L-C circuit, R=400 Ω, L=0.350 H, and C=0.0120...

$\bullet$ In a series $R-L-C$ circuit, $R=400 \Omega, L=0.350 \mathrm{H},$ and $C=0.0120 \mu \mathrm{F}$ (a) What is the resonance angular frequency of the circuit? (b) The capacitor can withstand a peak voltage of 550 $\mathrm{V}$ . If the voltage source operates at the resonance frequency, what maximum voltage amplitude can it have if the maximum capacitor voltage is not exceeded?

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Key Concepts

Quality Factor

The quality factor (Q) of a series RLC circuit is a measure of its selectivity or sharpness of resonance. Defined as Q = (1/R)?(L/C), it quantifies the ratio of stored versus dissipated energy per cycle and directly influences the amplitude of voltage across reactive components at resonance.

Voltage Amplification at Resonance

Due to the high quality factor, the voltage across the capacitor (or inductor) in a series RLC circuit operating at resonance can be much larger than the applied source voltage. The amplification factor is essentially Q, meaning that the capacitor voltage equals Q times the source voltage amplitude. This concept is critical when considering maximum voltage ratings for circuit elements.

Resonance in RLC Circuits

In an RLC circuit, resonance occurs when the inductive and capacitive reactances are equal in magnitude and opposite in phase, canceling each other out. At this frequency, the circuit behaves like a purely resistive network and the resonance angular frequency is defined as ?? = 1/?(LC), a key formula for determining the frequency where maximum energy transfer or minimal overall impedance occurs.

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