32.7
Circuitos en Serie RLC: Impedancia
Cuando el flujo de corriente es opuesto en un circuito de corriente continua (DC) o alterna (AC), se denomina resistencia o impedancia, respectivament…
En los circuitos de CA, la impedancia es una combinación de resistencia y reactancia, medida en ohmios, y está representada por Z.
Recordando los fasores para el circuito RLC y aplicando el teorema de Pitágoras, se puede determinar el voltaje o la amplitud de la corriente.
Al reorganizar los términos, la relación entre la amplitud de voltaje del circuito y la corriente a través del circuito se puede expresar como impedancia.
Recordando la ecuación del ángulo de fase y simplificándola, se obtiene el ángulo de fase entre la corriente y el voltaje.
Considere un circuito de la serie RLC con una resistencia de 10 ohmios, un inductor de 200 micro-henry y un condensador de 100 microfaradios, conectados a una fuente de 36 voltios con una frecuencia de 60 hercios. Determine la impedancia del circuito y el ángulo de fase.
Primero, identifique las cantidades conocidas y desconocidas en el circuito.
A continuación, determine la resistencia, la reactancia inductiva y la reactancia capacitiva. Al sustituir los términos conocidos en la ecuación de impedancia, se puede determinar la impedancia del circuito.
Por último, sustituyendo los términos conocidos en la ecuación del ángulo de fase, se puede determinar el ángulo de fase entre la corriente y el voltaje.
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Q1: What is impedance in an AC circuit?
Impedance, represented by Z, is the total opposition to current flow in an AC circuit, measured in ohms. It combines resistance and reactance, which depend on the angular frequency of the circuit. Unlike DC resistance, impedance accounts for the phase relationships between voltage and current in AC circuits.
Q2: How do you calculate impedance in an RLC series circuit?
Impedance is calculated using the Pythagorean theorem applied to phasors, combining resistance, inductive reactance, and capacitive reactance. The impedance equation yields the magnitude of Z by taking the square root of the sum of resistance squared and the difference between inductive and capacitive reactance squared. This calculation is essential for rlc series circuit problem solving.
Q3: What determines the phase angle between current and voltage?
The phase angle is determined by the relationship between inductive reactance and capacitive reactance. If inductive reactance exceeds capacitive reactance, the phase angle points in a positive direction. If capacitive reactance is greater, the phase angle becomes negative, indicating whether the circuit is inductive or capacitive.
Q4: How does an RLC circuit behave like a car's suspension system?
An RLC circuit is analogous to a car wheel driven over a corrugated road. The voltage source acts like regularly spaced bumps, while resistance functions as the shock absorber, damping oscillations. Energy shifts between the inductor and capacitor, similar to energy moving between kinetic and potential forms in the car's spring system.
Q5: What is bioelectrical impedance analysis used for?
Bioelectrical impedance analysis measures the impedance of the human body to estimate body composition, particularly fat and muscle content. Low impedance indicates higher water content, suggesting more muscle since water is primarily stored in muscle tissue. High impedance suggests greater fat content in the body.
Q6: When is the amplitude of oscillation maximum in an RLC circuit?
The amplitude of oscillation reaches its maximum when the driving frequency matches the resonance in an ac circuit. At this resonant frequency, the inductive and capacitive reactances cancel each other, leaving only resistance to oppose current flow, resulting in maximum current amplitude.
Q7: How do resistance and reactance differ in AC circuits?
Resistance opposes current flow uniformly regardless of frequency, while reactance depends on angular frequency and comes from inductors and capacitors. Impedance combines both: resistance dissipates energy as heat, whereas reactance stores and releases energy. Together, they determine the total opposition to current in AC circuits.