AC Capacitance and Capacitive Reactance – Working Principle with Sinusoidal Supply

Introduction

Electrical charge is a form of energy that capacitors store on their conducting plates. The voltage applied across the plates of a capacitor directly affects the amount of charge (Q) that can be stored.

When a capacitor is connected to a DC supply, it charges up to the value of the applied voltage at a rate determined by its time constant. As long as the supply voltage remains connected, the capacitor continues to store this charge. During the charging process, a current flows into the capacitor, opposing any change in voltage. The relationship between the charging current and the rate of change of voltage is given by:

I = C (dv / dt)

where C is the capacitance in farads and dv/dt is the rate of change of voltage with respect to time. Once the capacitor is fully charged, no more electrons can enter the plates, and it behaves like a temporary energy storage device. Even after the DC supply is removed, an ideal capacitor will retain the stored charge.

However, in an AC circuit, the capacitor continuously charges and discharges as the polarity of the supply voltage keeps changing. This is known as AC capacitance. The rate at which the charge changes depends on the frequency of the AC supply. When an alternating sinusoidal voltage is applied to a capacitor, the capacitor first charges in one direction and then in the opposite direction. This continuous charging and discharging results in opposition to the change in voltage, which is known as capacitive reactance.

AC Capacitance with a Sinusoidal Supply

Consider a capacitor with no initial charge on its plates at time t = 0. When the switch is closed, a strong current begins to flow into the capacitor. At 0° on the sinusoidal waveform, the applied voltage is increasing at its maximum rate as it crosses the zero reference line. Therefore, the current flowing into the capacitor is also at its maximum value because the rate of change of voltage is greatest.

As the supply voltage approaches 90°, the rate of change of voltage gradually decreases. For a brief moment, the voltage becomes almost constant. Since there is no change in voltage, the current reduces to zero.

At exactly 90°, the capacitor reaches its maximum voltage (V_max). At this point, the capacitor is fully charged and no current flows because the plates are saturated. After this point, the supply voltage begins to decrease towards the 180° position. Although the voltage is still positive, the capacitor starts to discharge. The charging direction is reversed as the AC cycle continues, and the process repeats itself in every cycle.

Conclusion

In an AC circuit, a capacitor does not store a constant charge as it does in a DC circuit. Instead, it continuously alternates between charging and discharging. This behavior creates capacitive reactance, which opposes the change in voltage and depends on the frequency of the AC supply. Understanding AC capacitance is essential in analyzing AC circuits, filters, and signal processing systems.