Capacitor elements in sinusoidal AC circuits

When an AC voltage is applied to both ends of a linear non-time-varying capacitor C , a current will flow through the capacitor. If the reference direction of the capacitor branch is consistent with the reference direction of the voltage, as shown in Figure 3-6-1, then:

(3-6-1)

When the applied voltage is a sinusoidal AC voltage , the capacitor current is

(3-6-2)

The changing waveforms of voltage and current on the capacitor element are shown in Figure 3-6-1.

Figure 3-6-1

From the above analysis, it can be concluded that the voltage and current on the capacitor are sinusoidal quantities of the same frequency, and the current leads the voltage in phase . From the waveform diagram, it can be seen that when the capacitor voltage passes through zero, the voltage change rate is the largest, and the current amplitude flowing through the capacitor reaches the maximum amplitude at this time. When the capacitor voltage reaches the maximum amplitude, its voltage change rate is zero, and the current value passing through the capacitor is also zero at this time. Similar to the case of inductance elements, the current and voltage of the capacitor element are in the same direction at some times, and in opposite directions at other times.

From formula (3-6-2), it can be seen that the relationship between the effective value of current and the effective value of voltage in the capacitor element is

(3-6-3)

In the formula, , is called the reactance of the capacitor, abbreviated as capacitive reactance. When the unit of capacitance C is farad (F) and the unit of is , the unit of capacitive reactance is , which has the same dimension as resistance.