Understanding capacitance in AC circuits

The in which a capacitor work in AC circuits is widely different from others. Capacitors that are connected to a sinusoidal can produce reactance from the effects of supply frequency and capacitor size. Today you’ll get to know the capacitance of a capacitor in AC circuits. You’ll also learn about capacitive reactance.

Read more: Understanding capacitor

AC capacitor circuit

The capacitors connected across a direct current DC supply voltage cause their plates to charge up until the voltage value across the capacitor is equal to that of the externally applied voltage. This charge is indefinitely held by the capacitor, acting as a temporary storage device as long as the applied voltage is maintained. While the capacitor is charging, an electric current (I) flows into the capacitor causing the plates to hold an electrostatic charge.

This charging process is not linear or instantaneous as the strength of the charging current is at its maximum when the capacitor’s plates are uncharged. Also decreasing exponentially over time until the capacitor is fully charged. This is due to the electrostatic field between the plates opposes any changes to the potential difference across the plates that is equal to the rate of charge of the electrical charge on the plates. Capacitance, C is the property of a capacitor to store a charge on its plates.

Hence, a capacitor charging current is known as i = CdV/dt. The capacitor blocks the flow of any more electrons onto its plates once it’s fully charged. But if an alternating current or AC supply is applied, the capacitor will alternatively charge and discharge at a rate determined by the frequency of the supply. The capacitance in the AC circuit varies with frequency as the capacitor is being constantly charged and discharged.

Read more: Understanding the charge in a capacitor

Since the flow of electrons onto the plates of a capacitor is directly proportional to the rate of change of the voltage across its plates, capacitors in AC circuits like to pass current when the voltage across its plates is constantly changing with respect to time such as in AC signals. However, it does not like to pass current when the applied voltage is of a constant value just like in a DC signal.

Diagram of AC capacitor circuit:

Let take the purely capacitive circuit below, the capacitor is connected directly across the AC supply voltage. The capacitor charges and discharges as the supply voltage increases and decreases. We’ve previously learned that the charging current is directly proportional to the rate of change of the voltage across the plates. This rate of change is at its greatest as the supply voltage crosses over from its positive half cycle to its negative half cycle or vice versa at points, 0⁰ to 180⁰ along with the sine wave.

Therefore, the least voltage rate-of-change occurs when the AC sine wave crosses over at its maximum positive peak (+V_MAX) and its minimum negative peak (-V_MAX). The sinusoidal voltage is constant at these two positions within the cycle, which is why its rate-of-change is zero, so dv/dt is zero. This results in zero current change within the capacitor. Consequently, when dv/dt = 0, the capacitor will act as an open circuit, so i = 0.

AC Capacitor Phasor Diagram

The above diagram explains that at 0⁰ the rate of change of the supply voltage is increasing in a positive direction. This results in a maximum charging current at that instant in time. As the applied voltage reaches its maximum peak value at 90⁰ for a very brief instant in time the supply voltage is not increasing or decreasing so there is no current flowing through the circuit.

Also, as the voltage begins to decrease to zero at 180⁰ the voltage slope will be negative so that the capacitor discharges in the negative direction. At the 180⁰ point along the line, the rate of change of the voltage is at its maximum again so the maximum current flows at that instant and so on. Therefore, the instantaneous value in AC capacitors is at their minimum or zero whenever the applied voltage is at its maximum. Likewise, the instantaneous value of the current is at its maximum or peak value when the applied voltage is at its minimum or zero.

The waveform above shows the current is leading the voltage by ¼ cycle or 90⁰ in the vector diagram. This is why in a purely capacitive circuit; the alternating voltage lags the current by 90⁰. It is obvious that the current flowing through the capacitance in AC circuits is in opposition to the rate of change of the applied voltage. Just like resistors, capacitors also offer some form of resistance against the flow of current through the circuit, but with capacitors in AC circuits, it is known as Reactance or capacitive reactance. In another word, capacitance in AC circuits suffers from capacitive reactance.

Now let get to understand the capacitive reactance!

What is a capacitive reactance?

A capacitive reactance in a purely capacitive circuit is the opposition to current flow in only AC circuits. Just like resistance, reactance is also measured in Ohm’s but its symbol is given in X to distinguish it from a purely resistive value. Reactance is also applied to inductors as well as capacitors, but when used with capacitors it is commonly called Capacitive reactance.

Capacitors in AC circuits, their capacitive reactance is given symbol Xc. The capacitive reactance is a capacitor resistive value that varies with frequency. In addition, capacitive reactance depends on the capacitance of the capacitor in Farads and the frequency of the AC waveform. Below is the formula used to define capacitive resistance:

Where:

F is in Hertz and C is in Farads. 2πƒ can also be expressed collectively as the Greek letter Omega, while ω to define an angular frequency.

From the above formula, when Frequency or capacitance is increased, the overall capacitive reactance would decrease. Also, as the frequency approaches infinity, the capacitor’s reactance would reduce to zero acting like a perfect conductor. But as the frequency approaches zero or DC, the capacitor’s reactance would increase up to infinity, acting like a very large reactance. In another word, the capacitive reactance is inversely proportional to frequency for any given value of capacitance. The capacitive reactance against frequency is shown below:

The above diagram describes how the capacitive reactance of the capacitor decreases as the frequency across it increases. This is why the capacitive reactance is inversely proportional to frequency. In the opposition to current flow, the electrostatic charge on the plates (its AC capacitance value) remains constant. With this, it becomes easier for the capacitor to fully absorb the change in charge on its plates during each half cycle.

Also, as the frequency increases the current flowing through the capacitor increases in value because the rate of voltage change across its plates increases. At this point, we can see that at DC a capacitor has infinite reactance (open-circuit), at very high frequencies a capacitor has zero reactance (short-circuit).

Watch the video below to learn about capacitance and capacitor:

That is all for this article where capacitance in AC and DC circuits have been discussed. We also learned capacitive reactance and look into some examples of AC capacitance. I hope you get enough of the reading, if so, kindly share with other students. Thanks for reading, see you next time!