31.34. In an L-R-C series circuit, R=400 Ω, L=0.350 H, and C=0.0120 μF . (a) What is the resonan

step 1 Hello friend here it is Kivet LRC circuit, inductor, register and capacitor LRC connected in ser

31.34. In an L-R-C series circuit, R=400 Ω, L=0.350 H, and...

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

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

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Key Concepts

Resonant Frequency

This is the frequency at which the inductive reactance (?L) equals the capacitive reactance (1/?C) in an RLC series circuit. At resonance, the net reactive effects cancel out, leaving only the resistive component to impede the current. The resonant angular frequency is calculated using the formula ?? = 1/?(LC), which is central to analyzing circuit behavior under AC conditions.

Voltage Magnification at Resonance

In a series RLC circuit operating at the resonant frequency, even though the overall impedance is minimized (and equals the resistance R), the voltages across the inductor and capacitor can be significantly larger than the applied source voltage. This phenomenon occurs because energy is alternately stored in the magnetic field of the inductor and the electric field of the capacitor, leading to a voltage magnification effect.

Quality Factor (Q Factor)

The Quality Factor quantifies the degree of voltage magnification and sharpness of the resonance peak in an RLC circuit. It is given by Q = ??L/R (or equivalently Q = 1/(??RC) in a series circuit) and represents the ratio of stored energy to energy dissipated per cycle. A higher Q indicates a stronger voltage amplification across the reactive components and a narrower bandwidth around the resonant frequency.

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