32.4
AC 회로의 커패시터
커패시터는 전류를 통과시켜 충전되며, 이로 인해 플레이트에 정전기가 축적되기 시작합니다. 충전 전류의 세기는 커패시터 플레이트가 충전되지 않은 상태에서 최대가 되고 커패시터가 완전히 충전될 때까지 기하급수적으로 점차 감소하므로 충전 과정은 순간적이지도 선형적이지도 않습…
교류 전압 소스를 가로질러 연결된 커패시터를 고려하십시오. Kirchhoff의 루프 규칙을 상기하면 커패시터의 순간 전압과 전하를 결정할 수 있습니다.
전하가 커패시터로 들어오거나 나가는 속도는 회로를 통해 흐르는 전류와 동일하며 삼각 관계를 사용하여 순간 전류를 결정할 수 있습니다.
전압과 전류를 함께 플롯하면 커패시터를 통과하는 전류가 커패시터 양단의 전압을 1/4 사이클로 리드합니다.
순간 전류와 전압 간의 관계는 페이저 다이어그램을 사용하여 나타낼 수 있으며, 두 페이저는 동일한 각도 주파수에서 회전하고 전류 페이저는 전압 페이저를 2 라디안만큼 π 선행합니다.
피크 전압과 피크 전류의 비율은 옴으로 표시되는 커패시터의 용량성 리액턴스를 제공합니다.
커패시터의 용량성 리액턴스는 교류 소스의 주파수에 반비례하며, 여기서 고주파는 낮은 용량성 리액턴스로 이어지고 그 반대의 경우도 마찬가지입니다.
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Q1: Why does current lead voltage in a capacitor connected to an AC circuit?
In an AC capacitor circuit, current leads voltage by 90 degrees because the charging current is maximum when the supply voltage is zero and changing most rapidly. As voltage reaches its peak, the rate of change becomes zero, so current drops to zero. This phase relationship occurs because current depends on the rate of voltage change, not the voltage magnitude itself.
Q2: What is capacitive reactance and how does it relate to frequency?
Capacitive reactance is the opposition to current flow in a purely capacitive circuit, measured in ohms and denoted by XC. It depends inversely on the frequency of the alternating current source: high frequency produces low capacitive reactance, while low frequency produces high capacitive reactance. The ratio of peak voltage to peak current determines the capacitive reactance value.
Q3: How can phasor diagrams represent the relationship between current and voltage in a capacitor?
Phasor diagrams represent instantaneous current and voltage as rotating vectors at the same angular frequency. The current phasor leads the voltage phasor by π/2 radians (90 degrees), visually showing their phase relationship. Both phasors rotate together, maintaining this constant 90-degree separation throughout the AC cycle.
Q4: At what points in the AC cycle does maximum charging current occur in a capacitor?
Maximum charging current occurs at 0 degrees and 180 degrees on the sinusoidal waveform, where the rate of change of supply voltage is greatest. At 0 degrees, voltage increases in the positive direction; at 180 degrees, it decreases most rapidly. Zero current flows at 90 degrees and 270 degrees, when voltage reaches its peak values and stops changing momentarily.
Q5: How does a capacitor respond to changes in AC supply voltage?
A capacitor charges and discharges continuously in response to changes in AC supply voltage. The rate of voltage change across the plates is directly proportional to the charging current. When voltage switches between positive and negative half cycles, the capacitor alternately charges and discharges, with current flow determined by how rapidly the voltage is changing.
Q6: What is the phase difference between voltage and current in a purely capacitive AC circuit?
The phase difference between voltage and current in a purely capacitive circuit is 90 degrees, or a quarter cycle. Current leads voltage by this amount, meaning current reaches its peak value one-quarter of a cycle before voltage does. This phase relationship is fundamental to understanding capacitor behavior in AC circuits and differs from resistor in an ac circuit components.
Q7: How can Kirchhoff's loop rule be applied to determine instantaneous voltage and charge on a capacitor?
Kirchhoff's loop rule states that the sum of voltages around a closed loop equals zero. Applied to a capacitor in an AC circuit, this rule allows determination of instantaneous voltage across the capacitor and the charge on its plates. Trigonometric relationships between voltage and current enable calculation of these values at any moment in the AC cycle.