Introduction to Electronics - Capacitors

Capacitors are fundamental electronic components, widely used in circuits to store and release electrical energy. They are used in a variety of functions, such as signal filtering in power supplies, coupling and decoupling signals in audio and radio circuits, as well as smoothing voltage variations.

Capacitors also play a crucial role in timers, oscillators, and even energy storage systems. Thanks to their properties, they are indispensable components in the operation of devices such as smartphones, computers, audio systems, and telecommunications equipment.

Capacitors consist of two conductive plates separated by an insulating material known as a dielectric. The main characteristic of capacitors is their ability to accumulate electric charge when subjected to a potential difference (voltage), and release it when necessary.

The fact that the capacitor is separated by a dielectric means that there is effectively no current flow between its terminals. However, when a potential difference is applied to a capacitor, charge accumulates on one of its plates, generating an electric field. This field also affects the other plate of the capacitor. With the accumulation of charge on one side of the component, an electromagnetic force is generated on the other side, causing the charge to flow.

This behavior gives the capacitor the ability to accumulate charge. Additionally, this accumulation of charge can take a certain amount of time. Therefore, the electrical variables of capacitors, such as current and voltage, are not constant as in a purely resistive circuit, but instead vary over time.

Capacitor Formulas

The variable used for capacitors is called Capacitance. This quantity refers to the amount of electric charge the component is capable of storing. Its unit of measurement in the SI system is Farad (F). The formula for capacitance is:

Where:

• C - Capacitance, measured in F (Farad).

• Q - Stored electric charge, measured in C (Coulomb).

• U - Applied voltage, measured in V (Volt).

In other words, 1 Farad represents the component's ability to store 1 Coulomb for each Volt applied.

As mentioned above, capacitors do not have a constant behavior over time. The current consumed by a capacitor is given as a function of the rate of change of the voltage. In other words, the current depends on the derivative of the voltage. This behavior is explained by the formula below, where Ic represents the capacitor's current, Uc its voltage, and C the capacitance.

To better understand, let's simulate a simple capacitive circuit, which consists of a voltage source, a resistor, and a capacitor.

When 10V is applied to the circuit, the capacitor begins to charge. It takes about 7 seconds to fully charge. The graph below shows the voltage across the capacitor over time.

The current through the capacitor is shown in the graph below. Right at the beginning, the current is at its maximum, with a value of 10mA. But as the capacitor charges, the current decreases until it reaches zero.

The maximum voltage of the circuit is 10mA, because a voltage of 10V was applied and there is a 1kΩ resistor. So, the voltage at the beginning is given by:

In other words, at the beginning of the process, the capacitor acts like a short circuit, as if it were not present. Its voltage is 0V, and it does not interfere with the current.

After some time, the current reaches zero, and the voltage across the capacitor reaches the maximum value of 10V. At this stage, the capacitor acts like an open circuit, blocking the flow of current.

Real Capacitors

There are various types of capacitors, made from different materials and with different shapes. One of the most common types is the electrolytic capacitor, shown in the figure below. This type of capacitor consists of two sheets of aluminum separated by a very thin layer of aluminum oxide, which acts as the dielectric. This component is also immersed in a liquid electrolyte.

Electrolytic capacitors have a high capacitance compared to other types, but they cannot withstand very high voltages. These components have polarity, meaning they have positive and negative terminals, unlike other types of capacitors. The negative side has the shorter terminal and is marked with a white band and negative signs.

Capacitors Association

Just like with resistors, it is possible to make associations of capacitors in series and in parallel.

Parallel Connection

When capacitors are connected in parallel, their capacitance is added together. Therefore, the equivalent capacitance of the circuit above is:

Series Connection

When capacitors are connected in series, their equivalent capacitance follows the formula below.

It is noted that capacitors have the opposite relationships of resistors, decreasing their capacitance when connected in series and increasing it when connected in parallel.

Conclusions

In conclusion, capacitors play an essential role in the field of electronics, being fundamental components in a wide range of circuits and devices. Their ability to store and release energy in a controlled manner allows them to perform crucial functions, such as filtering, signal smoothing, temporary energy storage, and voltage stabilization.

Furthermore, capacitors are indispensable in coupling and decoupling systems, optimizing the operation and efficiency of electronic circuits. Their versatility and importance are evident in virtually all modern electronic devices, from the simplest to the most complex, making them indispensable components for the advancement of technology.