Capacitance

Capacitance is defined as the capacity of any material to store electric charge. The substance that stores the electric charge is called a capacitor, i.e. the ability of the capacitor to hold the electric charge is called capacitance. It is denoted with the symbol C and is defined as the ratio of the electric charge stored inside a capacitor by the voltage applied.

Thus, any material that has a tendency to store electric charge is called a capacitor and the ability of the material to hold electric charge is called the capacitance of the material. In this article, we will learn about capacitance, its formula, capacitor, and others in detail.

Capacitance Definition

The general way of defining the capacitance of any electric device is the ability of that device to hold electric energy in the form of electric charge. The devices that hold electric energy in the form of electric charge are called Capacitors. There are various types of capacitors that are used in electric circuits, they come in various shapes and sizes and are used according to the requirement of the electric circuit. A capacitor is generally made by taking to conducting to plates of conductor and connecting them together.

The charge-holding capacity of the capacitor increases exponentially by inserting dielectric material between to capacitors. The dielectric material is a material that does not allow the current to pass through but increases the strength of the capacitor. Generally, all the insulators behave as dielectric materials.

Capacitor Definition

A two-terminal electric device that can store energy is called the capacitor. A capacitor consists of two electric conductors that are shaped like plates and are connected to different materials and the space between them is filled with a dielectric material that increases the capacity of the capacitor to hold the electric charge. The ability of the capacitor to store electric charge is called capacitance.

A capacitor not only stores electric charge but can store electric energy in the form of electric charge. So one might ask, What is the difference between a capacitor and an electric battery? As a battery also holds electric energy.

So the basic difference between the battery and the electric charge is that a battery stores the electric energy and releases it gradually over a long period of time but a capacitor almost instantaneously releases all its stored energy. A capacitor is sometimes also called a condenser and is an important part of a common electric circuit. We frequently used capacitors to block direct current (dc) while permitting alternating current (ac) to flow in any electrical circuit.

Various types of capacitors are shown in the image below,

Working of Capacitor

The capacitor is a device that holds electrical energy as a form of electric charge. It is made up of two plates that are parallel to each other and are oppositely charged. The positive plates collect some charges and an equal amount of opposite charges is collected in the negative plate. As soon as the circuit is switched on the capacitor holds the energy in the form of the electric charge between the plates of the capacitor.

Switching the circuit off does not make the capacitor lose its charge thus it holds the electric energy as an electric charge between its plates.

The capacitance or the strength of a capacitor is measured in farads (F) unit that is named after famous English Physicist Michael Faraday. A farad is a very large unit of capacitance. Most capacitors are measured in microfarad, (µF), picofarad (pF), etc.

Supercapacitors are specially designed capacitors that can store very large amounts of electrical charges and have a capacitance of thousands of farads.

The parallel plate capacitor is shown in the image below.

How to Increase Capacitance of a Capacitor?

The capacitance of any capacitor can be increased by following the method mentioned below:

• By reducing the space between the two plates of the capacitor.
• By increasing the Area of the plates of the capacitor.
• By inserting a suitable dielectric material between the plates of the capacitor.

Unit of Capacitance

The SI unit to measure the capacitance of the material is Farad. It is denoted by the letter F and is a bigger unit of capacitance, so is not widely used.

Smaller Units of Capacitance

The more common units of capacitance are, 

• Microfarad and its value is, 1 µF = 10^–6 F
• Nano farad and its value is,1 nF = 10^–9 F
• Picofarad and its value is,1 pF = 10^–12 F

Capacitance Dimensions

The formula to calculate the capacitance of any material,

C = Q/V

It is measured in Farad. The dimensions of the Capacitance is,

F = kg^-1m^-2s⁴A² = [M^-1L^-2A²T⁴]

Capacitance Formula

We know that the capacity of any material to hold electric energy in the form of an electric charge is called capacitance. And we can compute the capacitance of any object by taking the ratio of the charge a conductor holds and the potential difference across the conductor. We know that the charge held by a capacitor is directly proportional to the voltage across the end of the capacitor, i.e.

Q ∝ V

Removing the sign of proportionality, and adding C as the constant of proportionality

Q = CV

C = Q / V...(i)

Here, this constant of proportionality is called the Capacitance of the Capacitor. Equation 1 is the required formula for calculating the capacitance of the capacitor and we can say that the capacitance of any capacitor is the ratio of the charge stored by the conductor to the voltage across the conductor.

Another formula for calculating the capacitance of a capacitor is,

C = εA / d

where 
C is the Capacitance of the Capacitor
ε is the Permittivity of the medium Between the Plates
A is the Area of the Plates
d is the distance Between the Plates

Capacitance of Cylindrical Capacitor

A cylindrical capacitor is made by taking two cylinders with similar axis the length of the cylinders is l and the radius of the cylinder is, R₁ and R₂ where R₁ is the radius of the inner cylinder and R₂ is the radius of the outer cylinder.

Now the outer cylinder is Earthned and the inner cylinder is given the charge. The space between them is filled with air. The capacitance of the cylindrical capacitor so formed is,

C = (2πμ_oI) / log(R₂/R₁)

where,
I is the current given to the cylindrical conductor
R₂ and R₁ are outer and inner radii respectively

Factors Affecting Capacitance

There are various factors that affect the capacitance of any material that includes,

• Dielectric Material between Plates of Capacitor
• Spacing Between Plates of Capacitor
• Area of Plates

Now let's learn about each of them in detail,

Dielectric Material between Plates of Capacitor

Dielectric Material between the plates of the capacitor increases the charge-holding capacity of the capacitor and in turn, increases the capacitance of the capacitor.

Spacing Between Plates of Capacitor

The spacing between the plates of the capacitor (d) is inversely proportional to the capacitance of the capacitor, i.e. capacitance of the capacitor increases with the decrease in the space between the plates of the capacitor and vice-versa.

Area of Plates

The area of the plates of the capacitor (A) is directly proportional to the capacitance of the capacitor, i.e. capacitance of the capacitor increases with the increase in the Area of the plates of the capacitor and vice-versa.

Also, Read

• Capacitors in Series and in Parallel
• Energy Stored in a Capacitor
• Electrical Resistance

Solved Examples of Capacitance Formula

Example 1: A spherical capacitor has an inner sphere of radius 12 cm and an outer sphere of radius 13 cm. The outer sphere is Earthed and the inner sphere is given a charge of 2.5 µC. Find the capacitance of the capacitor.

Solution:

Given,

• Radius of Inner Sphere, (r₂) = 12 cm = 0.12 m
• Radius of Outer Sphere, (r₁) = 13 cm = 0.13 m
• Charge on Inner Sphere (q) = 2.5 μC = 2.5 x 10^-6 C

Capacitance of Spherical Capacitor is,

C~=~4\pi\epsilon_0\frac{R_1R_2}{R_2-R_1}

Permittivity of free space is  8.85 x 10^-12 C² N^-1 m^-2.

Substituting the values in the above expression,

C~=~\frac{0.12\times0.13}{9\times10^9\times(0.13-0.12)}\\

C = 2.08×10^-11 F

The required capacitance of the capacitor is 2.08×10^-11 F

Example 2: A capacitor is completely charged with 650 nC by a voltage source that has 275 V. The initial air gap of the capacitor was 7 mm. What is the stored energy if the air gap is now 3 mm?

Solution:

Given,

• Charge on Capacitor (Q) = 650 nC = 650 × 10^-9 V
• Voltage of Source (V) = 275 V
• Initial Air Gap (d₁) = 7 mm
• Final Air Gap (d₂) = 3 mm

Using Capacitance Formula

C = Q / V

C = (650 × 10^-9) / 275

C₁ = 2.36 × 10⁻⁹ F

Gap between the plates changed from 7 mm to 3 mm

C₁d₁ = C₂d₂

C₂ = C₁d₁/d₁

C₂ = [(2.36 × 10⁻⁹) (7 × 10⁻³)] / (3 × 10⁻³)

     =  5.5 × 10⁻⁹ F

Energy stored in the Capacitor is given by the formula,

E = (1/2) C₂V²

Substituting the values in the above expression,

E = 5.5×10⁻⁹× (275)²

    = 207.9 μ J

Thus, the enegry stored in the capacitor is 207.9 μ J