An RLC series circuit has L=0.300 H and C=6.00 μF The source has a peak voltage of 440 V. (a) Wh

step 1 First we will calculate angular resonant frequency of RLC series circuit by using the relation a

An RLC series circuit has L=0.300 H and C=6.00 μF The source...

An RLC series circuit has $L=0.300 \mathrm{H}$ and $C=6.00 \mu \mathrm{F}$ The source has a peak voltage of $440 \mathrm{V}$. (a) What is the angular resonant frequency? (b) When the source is set at the resonant frequency, the peak current in the circuit is $0.560 \mathrm{A}$. What is the resistance in the circuit? (c) What are the peak voltages across the resistor, the inductor, and the capacitor at the resonant frequency?

An RLC series circuit has $L=0.300 \mathrm{H}$ and $C=6.00 \mu \mathrm{F}$ The source has a peak voltage of $440 \mathrm{V}$. (a) What is the angular resonant frequency? (b) When the source is set at the resonant frequency, the peak current in the circuit is $0.560 \mathrm{A}$. What is the resistance in the circuit?
(c) What are the peak voltages across the resistor, the inductor, and the capacitor at the resonant frequency?

Key Concepts

Resonance in RLC Circuits

Resonance in an RLC circuit occurs when the inductive reactance equals the capacitive reactance, meaning that the effects of the inductor and capacitor cancel each other out. At resonance, the circuit behaves as if it were purely resistive, and the overall impedance is minimized. This phenomenon is central to many applications in filtering, tuning, and frequency selection in electronic circuits.

Angular Resonant Frequency

The angular resonant frequency, denoted by ??, is a key parameter in the analysis of RLC circuits. It is defined by the relation ?? = 1/?(LC), where L is the inductance and C is the capacitance. This frequency indicates the natural oscillation rate of the circuit and determines the point at which resonance occurs, making it essential for designing circuits with the desired frequency characteristics.

Impedance in Series AC Circuits

In AC circuit analysis, impedance represents the total opposition that a circuit offers to the flow of alternating current. In a series RLC circuit at resonance, the impedance becomes purely resistive because the inductive and capacitive reactances cancel each other. This simplification allows for the application of Ohm's law to determine the circuit's behavior, such as the relationships between voltage, current, and resistance.

Voltage Distribution Across Circuit Elements

In series RLC circuits, the voltage across each individual component – resistor, inductor, and capacitor – obeys Kirchhoff's voltage law, which states that the sum of the voltage drops equals the total applied voltage. Even when the circuit is at resonance and the overall impedance is minimized, individual components can still have significant voltage drops due to their reactive properties. Understanding how voltage divides among these components is important in the analysis and design of AC circuits.

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