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How to Understand and Solve the Physics of Capacitors in Series

The history of capacitors dates back to the late 1800s. In those days, capacitors were used in parlor demonstrations to teach the public about electricity. They discharged through a line of people holding hands. Eventually, we realized the importance of capacitors in the practical application of electricity. Today, capacitors are present in various electronic devices, including circuit boards and calculators.

Leyden jars were the first high-voltage capacitors

In the mid-1700s, Pieter van Musschenbroek invented the first high-voltage capacitor, the Leyden jar. Typically, the jar has a top electrode connected to the inner surface, a conducting foil wrapped around the outer surface of the jar that matches the internal coated area. We charge the jar using an electrostatic generator—the jar stores opposite charges on its inner and outer surfaces.

A capacitor is a device that stores electrical energy by storing it in an electrostatic field. It consists of two metal plates separated by a dielectric (the substance between the plates). We can make the two metal plates from tantalum, aluminum, silver, or any combination. For example, in 1752, Benjamin Franklin happened to fly a kite during a thunderstorm and managed to collect the ambient electrical charge within a Leyden jar. By doing so, he demonstrated the relationship between electricity and lightning and later invented the lightning rod.

The Leyden jar is one of the oldest types of capacitors. This electrical device is a jar that captures the electricity and then releases it to other components in a circuit. The original Leyden jar, which Pieter van Musschenbroek invented in 1744, contained water in the jar. Typical capacitor designs consist of an electrode and a plate.

Surface-mount capacitor

Franklin Square capacitor

The history of the Franklin Square capacitor began in the mid-18th century when Benjamin Franklin began experimenting with capacitors. After using a Leyden jar, Franklin discovered that an electrified dielectric capacitor could be disassembled and discharged and still produce a spark. He improved this design by using flat glass instead of the jar’s entire interior. This resulted in the capacitor we know today. Benjamin Franklin called his creation a “Franklin Square.”

The earliest electrical capacitors were the Leyden jar. Developed by two Dutch scientists, Pieter van Musschenbroek and Ewald Georg von Kleist, the Leyden jar consisted of two conducting plates separated by an insulator. Gralath had successfully combined several Leyden jars in parallel. The jar proved helpful in Benjamin Franklin’s kite-flying experiments, and he developed the Franklin Square capacitor to overcome this shortcoming.

The Franklin square was not the first capacitor, but it was the first practical one. In 1832, British chemist Michael Faraday made the first practical capacitor and began to develop practical applications for it. The development of capacitors gave us a way to transmit electric power over long distances. Faraday also created the farad, which became the standard unit for measuring capacitors. So while the history of the Franklin Square capacitor is quite interesting, it is also worth exploring its development and application in electrical power.

Mylar capacitor

If you’ve ever had a problem with a capacitor and wondered if you could solve it with a Mylar capacitor, you’re not alone. This special type of capacitor consists of two parallel plates separated by a dielectric material, such as polyester. The plastic used to make Mylar capacitors is polyethylene terephthalate, and it has several unique properties. Learn the history behind the Mylar capacitor and discover its uses.

Dupont first trademarked mylar in 1952, and it was not long before the first one came to the market. The first Mylar capacitor was made in 1954, using 12um-metalized PET. In 1959, they incorporated this plastic material into producing various capacitors, including polyethylene, polystyrene, PET, and polycarbonate. By 1970, electric utilities had switched to film-foil capacitors without the formerly used paper.

Electrons are attracted to the material and try to come together, but the insulator in the middle prevents them, creating an electric field. This tension between the positive and negative sides of the capacitor means that it continues to store charge. And while this is a big advantage, this material is susceptible to moisture and can explode when overloaded. So, while the Mylar capacitor may be an excellent innovation for many industries, its history remains fascinating.

Surface-mount capacitor

Surface Mounting is the fourth generation of electronic interconnection technology, and it has evolved from a very early stage to one that is now a well-established technology. During the 1970s, the field exploded and resulted in a series of developments that are essentially coherent and compatible with other recent innovations. But what is the history of surface mount capacitors? Here are a few essential points to know about this critical technology.

The invention of the surface-mounting process allows Rayming PCB & Assembly to increase the reliability of their devices. This was particularly important when it came to tantalum capacitors. A defect on a tantalum capacitor’s cathode causes local heating. The resulting change causes the nearby MnO 2 to convert into a non-conductive phase of manganese oxide, thus removing the defective part from the circuit. This process allows the MnO 2 cathode to exhibit a decreasing failure rate.

In early designs, capacitors came from mica and copper foils. Because they came from mica, they had air gaps between the two materials. The gaps allowed for oxidation and corrosion and changed the distance between the plates, which affected the device’s capacitance. Today, surface mount capacitors are helpful in nearly all positions in mass-produced electronic equipment. And it was on this day in history, that Benjamin Franklin died in 1790. In addition, the earthquake that hit San Francisco in 1906 left a lot of damage in the region. The space shuttle Apollo 13 also returned to earth after a catastrophic failure.

Aerogel capacitor

The use of carbon aerogels in the production of supercapacitors has a long history, but their use has recently become limited to a few applications. Carbon aerogel electrodes are perfect because of their high surface area, but they also suffer from volumetric capacitance. By contrast, 3D-printed graphene electrodes contain periodic large pores between filaments, sidestepping this problem. Nevertheless, Yat Li, a professor at UCSC and co-author of the Joule journal, says that these materials are a promising option for electrochemical capacitors, especially because they can have high mass loadings without sacrificing their electrochemical performance.

The history of the aerogel capacitor goes back to the 1960s, when the material was helpful as a lightweight, high-capacity capacitor. While the initial versions mainly came from carbon dioxide, a modern version uses inert metal oxide and CRF composites. The main difference between carbon aerogel and other materials is producing these batteries. The process used to create a capacitor from carbon aerogel is called supercritical drying.

How to Calculate the Capacitance of a Network of Capacitors in Series

High-voltage capacitors

We calculate the total capacitance of a network of capacitors connected in series by adding the plate areas and separation distance. Each capacitor stores a similar amount of charge. So, it evenly distributes the total voltage difference from end to end amongst all capacitors. Using a series capacitor in a circuit, you can measure the voltage drop across the entire network of capacitors.

Calculating the total capacitance of a network of capacitors

There are many methods to calculate the total capacitance of a network. In most cases, the network only has two capacitors in series. If this is the case, calculating the total capacitance is straightforward. You can enter the capacitance in Farads, ufarads, nanofarads, or picofarads. The calculator will then provide the answer in the same units as you entered.

The capacitance of a capacitor is directly proportional to its area. Therefore, the larger the plate area, the higher the total capacitance value. If we place the capacitors in parallel, the voltage across each one is the same, resulting in a total capacitance value of the entire network. We can do this using the same procedure as with series resistors.

Distributed decoupling is common on logic boards with many ICs. We place capacitors on each IC and strategically place larger capacitors around the circuit. Distributed decoupling is an excellent example of calculating the total capacitance of a network of capacitors. When capacitors connect in series, the sum of their values will equal the total value of all the capacitors connected in parallel. This method is advantageous because of the flexibility and increased voltage available.

To calculate the total capacitance, we first need to find the voltage and charge across each capacitor. When we have a 12V potential difference across a network of capacitors, we can divide this voltage by two and calculate the total capacitance. This is called the Kirchhoff voltage law. This means that each capacitor in a network has a 50% equal share of the charge.

Characteristics of series capacitors

A series capacitor has two main characteristics. First, their capacity and dielectric properties will change when their temperature varies. This is called its working temperature. Most capacitors will work in the range of -30 to +125 degC. For the plastic-type, the working temperature can reach +700 degC. These two characteristics will influence the working capacity of the series capacitor. This section explains some of the key characteristics of a series capacitor.

The first type of capacitor was the Leyden jar. It was a glass jar lined with metal foil that stored static electrical charges. Benjamin Franklin used one of these devices to prove that lightning was electricity. The capacitance of a series capacitor is proportional to the ratio of its permittivity to its size. This ratio is also the dielectric constant. Two or more plates are connected in parallel to make a series capacitor.

The capacitance of a series capacitor is smaller than the individual capacitors. This property helps to increase the voltage to withstand the power. However, the capacitors are not interchangeable. Therefore, a series capacitor can be helpful for many different applications. Capacitors come in various sizes and types. For instance, a 50-uF capacitor in series is equivalent to 25-uF when connected.

The second type of series capacitors is the radial type. Its metal layer is bridged at both ends, while axial-type capacitors rely on alternate metal and dielectric layers. For surface-mount applications, solder caps bridge the metal and dielectric layers. Finally, the series capacitor circuit model has three passive elements: a dielectric layer and two conducting layers. In this way, it functions as a parallel plate capacitor.

Common values of series capacitors

In many circuits, it is common to connect capacitors in series. In this configuration, they share a common working voltage and charge. As a result, a capacitor connected in series should have a good margin for leakage current. A capacitor that is ten times smaller in capacitance will experience a larger voltage. But it doesn’t have to be this way. The same principle applies when connecting series capacitors in parallel.

If we connect three capacitors in series, their capacitances are 1.000, 5.000, and 8.000 uF. We can calculate the total capacitance of the three capacitors using the equivalent capacitance formula. This formula is the same for any number of capacitors in series. But it is a little bit more complicated than it sounds. Most networks will only use two capacitors in series to make matters simple.

The most common values for series capacitors are E3/E6 and E12. In most applications, capacitors with these numbers are essential as filters in RF circuits. However, when comparing two capacitor series, keep in mind that the preferred values may not always correspond exactly. Fortunately, you can combine two or more of these values to get nearly any value you require. And when comparing series capacitors, remember to take the tolerance level into account.

Charge distribution across a network of capacitors

A capacitor is a device with two parallel conductive plates separated by an insulating material called a dielectric. Electrons pass from one electrode to the other and are distributed equally across each plate. When we apply a voltage to one of the capacitors, it charges the positively-charged plate and the negatively-charged electrode. The same thing happens if we apply a current to a series of capacitors.

In real circuits, the charging of the capacitors doesn’t happen instantly. Instead, there will always be some amount of resistance between the two electrodes, so the current will gradually rise. This is why we place capacitors in series.

Effect of temperature on capacitance

The working voltage of the capacitors determines the effect of temperature on capacitors in series. We express the voltage in parts per million per degree centigrade (ppm/degC) or percent. However, the working voltage is different for different capacitors because some are non-linear in their behavior. As a result, they exhibit an increase in value with temperature, known as a positive “P” coefficient.

In addition, the effect of temperature on capacitors in series depends on the operating temperatures. Therefore, it is essential to know that temperature-dependent capacitance values will vary with frequency and operating temperature. For example, a capacitor under 5V bias will decrease capacity to a minimum of 0.11uF. However, at +85degC, the value will increase to 0.39uF. Therefore, it is important to select the capacitors with a stable C value regardless of operating temperature.

There are two types of capacitors: Class 1 and Class 2. They have non-linear characteristics, while class 2s exhibit positive temperature coefficients. They can exhibit almost any desired characteristic. The dielectric mix used, processing, and assembly methods determine their characteristics. Moreover, the temperature can affect the quality of a capacitor. We will discuss the effects of these factors on the different capacitor parameters in future articles.

The Benefits and Application of Capacitors in Series

A capacitor in series has several advantages, including increased capacitance, higher operating voltage, and low cost. Its capacitance is directly proportional to the distance between its two conductive plates. The dielectric material between these conductive plates provides mechanical support and allows the capacitor to increase its capacitance. In addition, the dielectric’s permittivity increases the capacitance and increases the maximum operating voltage.

High-voltage capacitors

When we connect high-voltage capacitors in series, their charging currents are the same. Because the capacitors share one common path, the charge across their plates is always the same. Therefore, in a series circuit, the same charge will flow through each capacitor, resulting in the same voltage drop. In addition, the capacitors in a series connection have the same reactance and will store the same amount of electrical charge.

Using several high-voltage capacitors in series has several advantages. First, high-voltage capacitors in series can be relatively large with reasonably accurate values. The resulting voltage gradient spreads over several centimeters, which reduces the load on the measurement points. One reasonable compromise is five high-voltage capacitors in series with a capacitance of three picofarads each. This results in a derating frequency of 7.5 MHz, much higher than the highest-voltage probes.

Polypropylene capacitors

The ability to use multiple layers of polypropylene film and plates in series is the hallmark of a polypropylene capacitor. As a result, these capacitors exhibit low dielectric absorption and a low dissipation factor. In addition, because they consist of polypropylene film, their capacitance properties are relatively stable regardless of voltage and time. As a result, polypropylene capacitors have excellent capacitance stability. Therefore, we use them in high-reliability applications.

Polypropylene film capacitors exhibit extremely low dissipation and a narrow operating temperature range as high-quality capacitors. This makes them ideal for applications where long-term exposure to humidity or extreme temperature fluctuation would result in significant capacitor failure. In addition, their low dielectric absorption, high-frequency capability, and low dissipation factor make them particularly suitable for use in the oscillator, RC, and audio circuits.

The capacitor manufacturing process starts with removing a thin plastic film that separates the electrodes. The thinner the film, the higher the capacitance. As the electrode distance decreases, so do the capacitance. Typical values for these capacitors range from 1nF to 30muF.

Power factor correction capacitors

Power factor correction capacitors are essential for reducing power loss, which results in energy savings. Additionally, they improve motor voltage and reduce peak KVA. Unfortunately, inductive loads typically exhibit poor power factors, and we install capacitor banks to correct the problem. Capacitor banks generally provide years of service but should be inspected periodically to maintain proper performance. Failing capacitors, blown fuses, and loose connections can reduce the amount of power correction available. Eventually, these problems can lead to total system failure and even fire.

The power factor is the difference between the total current that a device draws from a source and the total amount of energy it consumes. For example, a load operating at a lagging power factor of 0.7 will dissipate 2 KW of energy if connected to a conventional, two-phase, 60 Hz power line. A power factor of 0.9 would require the use of capacitance. Similarly, a load operating at a lagging power factor of 0.7 will require the use of two capacitors in series.

Tuning inductors

By putting capacitors in series with inductors in parallel, you can tune the circuit to work with a particular frequency. In this way, you can store electrical energy in the magnetic field between the two elements. In the figure below, the capacitors in series form a symmetrical circuit. Each inductor has its magnetic field, and when we place a capacitor in parallel with an inductor, it presents a high impedance.

A series-resonant circuit exhibits a step-up effect. This is when the voltage across the inductor reaches a higher level than the voltage across the capacitor. This resonant phenomenon can be dangerous because the voltage across the inductor and the capacitor are too low. Using the inductive reactance technique to achieve a symmetrical series-resonance circuit is a simple way to get the desired effect.

Small capacitors

Small capacitors are usually fragile and heat resistant. This is because the dielectric material increases the capacitance of a capacitor. The “k” element represents the relative permittivity of the dielectric material. The permittivity of free space is one, whereas that of dielectric material is greater than one. These characteristics make small capacitors an excellent choice for bypassing high-frequency supplies. However, small capacitors are still fragile and heat-resistant despite their heat resistance and fragility.

Moreover, when we connect capacitors in series, the voltage drops across each will be equal. In addition, the coulomb charge across each capacitor plate is equal. Thus, the voltage drop across the capacitors is constant in series-connected circuits. However, the voltage drop across the capacitors in series depends on the individual capacitors’ capacitances. It is important to remember that the lower the capacitance, the smaller its overall capacitance.

KXF series capacitors

KXF series capacitors have several advantages over conventional ones. Their large size is ideal for high-voltage, long-life applications. Their comparatively high thermal conductivity further enhances their long life. The benefits of KXF series capacitors are listed below. They are available in a wide range of voltages. This makes them ideal for many different applications. KXF capacitors are also compatible with other standard capacitors, making them highly flexible.

Mica capacitors have excellent endurance and hardly degrade over time. They are typically coated with epoxy resin to prevent corrosion. Mica capacitors are also highly resistant to high voltages. Though they are expensive and bulky, they are ideal for RF circuits and are comparatively low in the loss. Furthermore, they improve the Q factor of the tuned circuit. Therefore, they have numerous advantages over conventional capacitors. In addition, they can withstand the harshest of conditions.

Despite the high cost of raw materials, mica is a highly stable dielectric. Mica resists most acids, water, and oil. Mica capacitors are made by sandwiching two sheets of mica between two metal sheets. Silver mica capacitors are particularly rare and are helpful in applications where the value needs to be low. In addition, their mechanical strength and longevity are enhanced compared to mica capacitors.