itors are like batteries that store electrical energy. The amount they store is measured in Farad. They come in handy because they can release energy whenever it's needed. With other circuit components, capacitors can make a filter that lets some electrical impulses go through while stopping others. A lot of the electronics we use every day, like pacemakers, phones, and computers, depend on capacitors to work.

How does a capacitor charge?

In conductive materials, there are lots of tiny negatively charged particles called electrons that make up the electric current. These electrons can move around easily in the electrical field and separate from atom. But in insulator materials, there are only a few electrons, and they are strongly stuck to the atomic nucleus. So they can't separate from the atom easily.

Knowing this helps us understand how capacitors charge up. Capacitors can store energy because of the electric field that pushes or pulls electrons. When positive and negative charges meet on the opposite capacitor plates, the capacitor gets charged up.

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The plates inside a capacitor have positive and negative charges that attract each other, but they never actually touch. This makes them constantly push and pull in an electric field between the two plates. This is how a capacitor holds onto its charge.

How does a capacitor’s charge behave in AC and DC circuits?

Let us now explore the differences in how a capacitor charges in DC circuits compared to its charging behaviour in AC circuits.

A capacitor’s charging behaviour in DC circuits

To understand how a capacitor works and how its charge behaves in DC circuits, take a look at the basic circuit below.

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When the switch is in position 2, the capacitor is not receiving any voltage and therefore there is no electric field. This means that the electrons in the conductive plates are stationary, and the plates don't have any positive or negative charge. The potential difference between the plates is zero, and the voltmeter will show a value of 0.

However, when you move the switch to position 1, you will notice that the ammeter's pointer moves up and then quickly goes back down. This is because there is an electron movement when the switch is moved to position 1.

The positive pole of the DC supply pulls the electrons in the upper conductive plate, while the negative pole pushes the electrons to the bottom conductive plate. As a result, the top plate becomes positively charged, having lost electrons, and the bottom plate becomes negatively charged, having gained electrons.

Now, there is a potential difference between the two plates of the capacitor, which is in the opposite direction of the DC potential. This change in potential difference is reflected in the readings of the ammeter and voltmeter. You can see how these readings change in the scatter charts below.

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The period during which a capacitor is charging is called the temporary state. It is during this period that the ammeter’s pointer moves up and then back down again. When the capacitor is fully charged, it has reached the steady state. At this point, the voltmeter reads V, which is the value of the DC supply’s voltage.

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The reading of the ammeter value is the opposite of the voltage value. The reason for this is that the capacitor is charging in the temporary state, so the current continues to go through it. As it charges, the potential difference between the capacitor plates rises, approaching the DC supply’s potential difference. As it gets closer, the current begins to decrease because the potential difference between the DC supply and the capacitor is decreasing. When the capacitor is fully charged, it enters the steady state, and the potential differences of the DC supply and the capacitor are the same. The electrical load a capacitor can store in a DC circuit is:

Here:

V = the voltage applied to the capacitor.

C = the capacitance of the capacitor.

Q = the electrical load of the capacitor.

To understand the concept of a capacitor charging in an AC circuit, we need to look at the process in different parts of a charging period.

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We are going to look at the behaviour of the circuit in 4 different parts of a charging period. These parts are for an angle named a between 0 - π/2, π/2 - π, π - 3π/2, and 3π/2 - 2π.

0 < a < π/2

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When you close the switch at the time t = 0, the capacitor begins to charge. Because the voltage is changing at a high rate, there is a high electron flow, which means that the current is at its maximum level. As we get closer to π/2, the capacitor’s voltage is getting closer to Um (the AC source’s peak value), the electron flow is decreasing, and the current is also decreasing.

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π < a < 3π/2

Although it includes differentiation, the explanation is pretty simple. The current going through the capacitor is directly proportional to its capacitance value and how fast the voltage changes in time.

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After the a = π point, the capacitor’s voltage begins to increase as the AC source voltage increases. The electrons in the bottom plate are being pulled by the source, while extra electrons are moving to the upper plate. As we move towards the a = 3π/2 point, because the pace of the change of voltage decreases and the voltage of capacitor approach -Vm, the value of the current decreases.

3π/2 < a < 2π

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In summary, the voltage of a capacitor changes depending on the of the source it is connected to. When the voltage of the source decreases, the voltage of the capacitor also decreases. As the voltage changes more quickly, the current going through the capacitor increases. At the point where the voltage of the AC source is 0, current passing through the capacitor is at its maximum, and the capacitor has fully discharged.

In AC circuits, the current going through a capacitor is directly proportional to its capacitance value and how quickly the voltage changes in time. The equations for finding the maximum voltage and maximum current of a capacitor in an AC circuit involve the peak value of the voltage and the capacitance value. Overall, the behavior of a capacitor is different in DC and AC circuits, with the voltage, current, and load of the capacitor constantly changing in AC circuits.

Capacitor Charge

How long can a capacitor hold a charge?

It depends on the circuit and the quality of the insulator between the two conductive plates because, in practice, there are small leakage currents going through insulators.

When is a capacitor fully charged?

A capacitor is fully charged when it cannot hold any more electric load. We understand when a capacitor is fully charged based upon when it starts not letting any more current go through it.

How do you calculate the charge in a capacitor?

We can calculate the charge in a capacitor by looking at its capacitance and the voltage applied to it according to the equation: Q = CV.

What is charging of capacitor?

Charging of a capacitor occurs when a series resistor and a capacitor is connected to a voltage source. The initial current value going through the capacitor is at its maximum level and steadily decreases all the way down to zero. When you read the current going through the capacitor as zero, it means that the capacitor is charged.

What is the formula for capacitor?

A general formula for finding the capacitance value in a DC circuit can be mathematically expressed as Q=CV. Where V is the voltage applied to the capacitor, C is the capacitance of the capacitor, and Q is the electrical load on the capacitor.

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