A capacitor is an electrical component that stores energy in an electric field. It is a fundamental component used in electronic circuits to regulate voltage, filter noise, and control timing. In this article, we will explore the working principle of capacitors, how to calculate capacitance, and its applications.

## What is a Capacitor?

A capacitor is an electrical component that stores energy in an electric field. It consists of two conductive plates separated by a dielectric material. When a voltage is applied across the plates, an electric field is created, causing a charge to build up on each plate. The capacitor's capacitance is the measure of its ability to store charge.

## How Does a Capacitor Work?

When a capacitor is connected to a power source, it charges up to the source voltage. Once fully charged, the capacitor blocks the flow of current. When the capacitor is connected to a load, it discharges, releasing its stored energy to power the load. Capacitors are commonly used in electronic circuits for filtering noise, timing, and voltage regulation.

## How Do You Determine the Value of Capacitance?

The value of capacitance is determined by the physical characteristics of the capacitor, including the surface area of the plates, the distance between the plates, and the permittivity of the dielectric material. The formula for capacitance varies depending on the type of capacitor used.

### Standard Units of Capacitance

The standard unit of capacitance is the farad (F), named after Michael Faraday, a pioneering scientist in electromagnetism. Other units of capacitance include microfarads (μF) and picofarads (pF).

### Capacitance of a Parallel Plate Capacitor

The capacitance of a parallel plate capacitor is given by C = εA/d, where ε is the permittivity of the dielectric material, A is the surface area of the plates, and d is the distance between the plates.

### Capacitance of a Spherical Capacitor

The capacitance of a spherical capacitor is given by C = 4πεab / (b-a), where ε is the permittivity of the dielectric material, a is the radius of the inner sphere, and b is the radius of the outer sphere.

### Factors Affecting Capacitance

The capacitance of a capacitor is affected by the distance between the plates, the surface area of the plates, and the permittivity of the dielectric material. Temperature, humidity, and the frequency of the applied voltage also affect capacitance.

### Applications of Capacitors

Capacitors are used in a wide range of electronic applications, including power supplies, filters, timing circuits, and signal processing. They are also used in electric vehicles, aerospace technology, and medical equipment.

## Capacitor Fundamentals: Capacitance, Voltage, Charge, Reactance, Quality and Dissipation Factors

Capacitors are electronic components used in many different circuits and devices to store electrical energy. They consist of two conductive plates separated by a dielectric material, which can be a vacuum or an insulating material. Capacitors come in various shapes and sizes, and their characteristics are determined by factors such as capacitance, voltage, reactance, quality factor, dissipation factor, and energy storage.

## Capacitance of a Capacitor

The capacitance of a capacitor is defined as the ability of the capacitor to store electrical charge. It is measured in Farads (F) and is determined by the physical characteristics of the capacitor, such as plate area, plate separation distance, and dielectric constant. The capacitance of a capacitor can be calculated using the following formula:

C = Q/V

where C is the capacitance, Q is the charge stored on the capacitor, and V is the voltage across the capacitor.

Charge Stored in a Capacitor

The charge stored in a capacitor is directly proportional to the voltage applied across the capacitor and the capacitance of the capacitor. The formula for the charge stored in a capacitor is:

Q = CV

where Q is the charge stored in the capacitor, C is the capacitance of the capacitor, and V is the voltage applied across the capacitor.

### Voltage of the Capacitor

The voltage of a capacitor is the potential difference between the two plates of the capacitor. When a capacitor is connected to a voltage source, it charges up to the voltage of the source. The voltage of a capacitor can be calculated using the following formula:

V = Q/C

where V is the voltage across the capacitor, Q is the charge stored on the capacitor, and C is the capacitance of the capacitor.

### Reactance of the Capacitor

The reactance of a capacitor is the opposition of the capacitor to the flow of alternating current (AC). It is measured in Ohms and is determined by the frequency of the AC and the capacitance of the capacitor. The formula for the reactance of a capacitor is:

Xc = 1/(2πfC)

where Xc is the reactance of the capacitor, f is the frequency of the AC, and C is the capacitance of the capacitor.

### Quality Factor of Capacitor

The quality factor of a capacitor is a measure of the efficiency of the capacitor. It is defined as the ratio of the energy stored in the capacitor to the energy lost in the capacitor per cycle. The formula for the quality factor of a capacitor is:

Q = 1/(2πfRC)

where Q is the quality factor, f is the frequency of the AC, R is the resistance of the circuit, and C is the capacitance of the capacitor.

#### Dissipation Factor of Capacitor

The dissipation factor of a capacitor is a measure of the losses in the capacitor. It is defined as the ratio of the energy lost in the capacitor to the energy stored in the capacitor per cycle. The formula for the dissipation factor of a capacitor is:

D = tanδ

where D is the dissipation factor and δ is the phase angle between the voltage and current in the capacitor.

## Energy Stored in a Capacitor

The energy stored in a capacitor is the work done to charge the capacitor. It is equal to the product of the capacitance, voltage, and half the square of the voltage. The formula for the energy stored in a capacitor is:

E = 1/2CV²

where E is the energy stored in the capacitor, C is the capacitance of the capacitor, and V is the voltage across the capacitor

### Average Power of Capacitor

The average power of a capacitor is the power dissipated by the capacitor over a period of time. The formula for the average power of a capacitor is:

P = V²/R

where P is the power dissipated by the capacitor, V is the voltage across the capacitor, and R is the resistance of the circuit.

## Capacitor Voltage During Charge / Discharge

When a capacitor is charged or discharged, its voltage changes over time. The voltage of a capacitor during charging and discharging can be calculated using the following formulas:

### During Charging:

V(t) = V₀(1 - e^(-t/RC))

where V(t) is the voltage of the capacitor at time t, V₀ is the initial voltage of the capacitor, R is the resistance of the circuit, C is the capacitance of the capacitor, and e is the natural logarithm base.

#### During Discharging:

V(t) = V₀e^(-t/RC)

where V(t) is the voltage of the capacitor at time t, V₀ is the initial voltage of the capacitor, R is the resistance of the circuit, C is the capacitance of the capacitor, and e is the natural logarithm base.

### Capacitance Formulas

Capacitance of a Plate Capacitor Formula:

C = ε₀A/d

where C is the capacitance of the plate capacitor, ε₀ is the permittivity of free space, A is the area of the plates, and d is the distance between the plates.

### Self Capacitance of a Coil (Medhurst Formula):

C = (π²DL)/(ln(4L/d) - 0.5)

where C is the self capacitance of the coil, D is the diameter of the coil, L is the length of the coil, and d is the wire diameter.

#### Self Capacitance of a Sphere Formula:

C = 4πε₀r

where C is the self capacitance of the sphere, ε₀ is the permittivity of free space, and r is the radius of the sphere.

#### Self Capacitance of a Toroid Inductor Formula:

C = (2π²ε₀h)/(ln(r₂/r₁))

where C is the self capacitance of the toroid inductor, ε₀ is the permittivity of free space, h is the height of the toroid, r₁ is the inner radius of the toroid, and r₂ is the outer radius of the toroid.

## Ohm’s Law for Capacitor

Ohm’s law for a capacitor relates the current flowing through the capacitor to the voltage across the capacitor and the capacitance of the capacitor. The formula for Ohm's law for a capacitor is:

I = C(dV/dt)

where I is the current flowing through the capacitor, C is the capacitance of the capacitor, and dV/dt is the rate of change of voltage with respect to time.

## Conclusion

Capacitors are essential components in many electronic circuits and devices. They store electrical energy, have various characteristics such as capacitance, voltage, reactance, quality factor, and dissipation factor. These characteristics are essential to understand to design circuits and devices that use capacitors efficiently. Understanding the formulas and equations that govern the behavior of capacitors can help in designing circuits and devices that use capacitors effectively.

## FAQs

### What is the formula of the capacitor?

The formula for a capacitor is given by:

C = Q/V

Where C represents capacitance, Q represents charge, and V represents voltage.

#### What is capacitance and its unit?

Capacitance is a measure of a capacitor's ability to store an electrical charge. It is defined as the ratio of the amount of charge stored on each plate to the voltage applied across the plates. The unit of capacitance is the farad (F), named after Michael Faraday.
One farad is defined as the capacitance of a capacitor that will store a charge of one coulomb (C) when a voltage of one volt (V) is applied across it. However, the farad is a very large unit of capacitance, so capacitors are usually measured in smaller units like microfarads (µF), nanofarads (nF), or picofarads (pF).

#### Why capacitance is Q by V?

Capacitance is defined as the ratio of the amount of charge stored on each plate of a capacitor to the voltage applied across the plates. Therefore, the capacitance formula C = Q/V represents this relationship between charge and voltage.
In other words, if you apply a voltage V to a capacitor, it will store a charge Q on each plate, and the amount of charge stored will be directly proportional to the voltage applied. The proportionality constant is the capacitance C, which is a measure of the capacitor's ability to store charge.