32.4
AC回路内のコンデンサ
コンデンサは電流を流すことで充電され、プレートに静電荷が蓄積され始めます。 充電電流の強さはコンデンサのプレートが充電されていないときに最大となり、コンデンサが完全に充電されるまで指数関数的に徐々に減少するため、充電プロセスは瞬間的でも線形でもありません。 プレートに電荷を蓄積するコンデンサの特性は…
交流電圧源の両端に接続されたコンデンサについて考えてみましょう。キルヒホッフのループルールを思い出すと、コンデンサの両端の瞬間電圧と電荷を決定できます。
電荷がコンデンサに出入りする速度は、回路を流れる電流と同等であり、三角関数の関係を使用して瞬時電流を決定できます。
電圧と電流を一緒にプロットすると、コンデンサを流れる電流はコンデンサの両端の電圧をサイクルの4分の1だけリードします。
瞬時電流と電圧の関係は、両方のフェーザが同じ角周波数で回転し、電流フェーザが電圧フェーザをπ×2ラジアンリードするフェーザ図を使用して表すことができます。
ピーク電圧とピーク電流の比により、コンデンサの容量性リアクタンスがオームで表されます。
コンデンサの容量性リアクタンスは、交流源の周波数に反比例し、周波数が高いと容量性リアクタンスが低くなり、その逆も同様です。
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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.