32.3
Resistor em um Circuito de Corrente Alternada
É necessário existir uma fonte de tensão, ou força eletromotriz, alternada para fornecer uma corrente alternada (AC) a um circuito. Uma bobina de fio…
A fonte de corrente alternada é um dispositivo que fornece uma tensão ou corrente que varia senoidalmente com o tempo.
Uma função pode descrever a tensão ou corrente senoidal, onde V ou I são a tensão ou corrente, respectivamente, no tempo t, V0 ou I0 são a tensão ou corrente de pico, respectivamente, e ω é a frequência angular.
As tensões e correntes que variam senoidalmente são representadas por diagramas vetoriais rotativos.
Esses vetores que giram no sentido anti-horário a uma frequência angular constante são chamados de fasores; os diagramas que os descrevem são conhecidos como diagramas fasoriais.
Considere um resistor conectado a uma fonte de tensão de corrente alternada. Lembrando a regra do loop de Kirchhoff, a tensão instantânea e a corrente que flui através do resistor podem ser determinadas.
Uma vez que os máximos e mínimos de ambas as curvas são alcançados simultaneamente, as curvas são ditas em fase.
Portanto, a relação entre corrente e tensão pode ser representada usando diagramas fasoriais.
As projeções no eixo vertical representam tensão e corrente instantâneas. Como estão em fase e têm a mesma frequência, seus fasores apontam na mesma direção e giram juntos.
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Q1: Why are voltage and current in phase in a resistor connected to an AC circuit?
In a resistor, voltage and current reach their maximum and minimum values simultaneously, meaning they are in phase with each other. This occurs because the resistor's behavior is independent of current direction. Using Kirchhoff's loop rule, both the instantaneous voltage across and current through the resistor follow the same sinusoidal pattern, resulting in a phase angle of zero degrees.
Q2: What is a phasor diagram and how does it represent AC quantities?
A phasor diagram uses rotating vectors called phasors to depict sinusoidally varying voltages and currents. These vectors rotate counterclockwise at a constant angular frequency, with their vertical axis projections representing instantaneous values. Phasors are geometric tools, not physical quantities like velocity or momentum, that help visualize and analyze AC circuit behavior over time.
Q3: How do you calculate total voltage in a purely resistive series AC circuit?
In a purely resistive series AC circuit, all voltage drops across individual resistors are in phase with one another. Since they share the same phase angle, you can add all voltage drops algebraically to determine the circuit's overall voltage. This direct addition works because there is no phase shift between any of the resistive elements.
Q4: What mathematical function describes sinusoidal voltage and current in AC sources?
Sinusoidal voltage or current can be described using a function where V or I represents the instantaneous value, V₀ or I₀ represents the peak amplitude, ω is the angular frequency, and t is time. This mathematical representation allows precise calculation of voltage and current at any moment in the AC cycle.
Q5: How do phasors behave when voltage and current are in phase?
When voltage and current are in phase, their corresponding phasors point in the same direction and rotate together at the same angular frequency. This alignment reflects the simultaneous occurrence of voltage and current maxima and minima, making phasor diagrams an effective tool for analyzing resistive AC circuits.
Q6: What is the relationship between branch currents in a purely resistive parallel AC circuit?
In a purely resistive parallel AC circuit, every branch current is in phase with every other branch current. Because all currents share the same phase angle, you can add all individual branch currents together to determine the total circuit current without accounting for phase differences.
Q7: How does a resistor's behavior differ between DC and AC circuits?
In AC circuits, a resistor's behavior is independent of current direction, unlike considerations in some other circuit elements. The resistor maintains the same relationship between voltage and current regardless of whether current flows forward or backward. This consistent behavior allows resistors to be analyzed using straightforward phasor diagrams in rlc series circuits introduction.