What is Capacitance?
Capacitance is the ability of a material to accumulate electrical charge. Capacitance, a quantity in the SI system of units, is specified as the ratio of Coulombs to the electrostatic energy stored in a unit volume of the material. Capacitance is the electric property most often associated with the two-dimensional conductor, or condenser, or capacitor.
However, this property may also be exhibited by a number of other conductors, including thin-film dielectrics, semiconductors, wires and cables, which form so-called distributed capacitances. In practice, the term capacitor is used to describe any storage device which stores a charge in excess of that required to neutralize it. More often than not, a dielectric is involved. It is the electric part of any capacitor that stores the charge, and the conducting part is the conductor or conductors to which the charge is applied.
A "dielectric" is a material that tends to hold an electric field (electric potential) and can be characterized by a particular permittivity. When a voltage is applied to a dielectric, there are charges (Coulombs) on each side of the dielectric. To remove the charge, the charges have to move to each other, and this is called conduction. If the movement of charges is not free (as it is in a metal), some of the stored energy is converted to heat, and the capacitor will heat up. For that reason, capacitors are often (though not always) of the parallel-plate type: two conductive plates are separated by a dielectric.
An electrical conductor in which movement of the charge carriers is free may store electrical charge without heating up. In such a case, the charges separate from each other, but they are still stored in the material. Such a conductor is not a capacitor: the charge is free to move and the stored energy is the "work done" by the charge on the conductor.
Types
Capacitors can be classified by the type of dielectric and conductors used. The dielectric can be made of a dielectric fluid or a solid. The dielectric can be of any permittivity, positive or negative. The plates are either of metal, or in some cases, can be of the same metal, separated by an insulator. In parallel-plate capacitors, one plate is insulated from the other and the capacitance is the sum of the charges induced at the two plates. If the plates are connected by a wire, the plates are regarded as one plate, and a capacitor-like circuit is formed with a capacitor in series with the wire.
In Practice, Capacitors Fall into One of Three Categories:
Air-Insulated: where there is a separation between the plates, which are separated by a dielectric medium
Oil-Immersed: where the plates are immersed in an oil or another dielectric medium and are separated by a thin membrane
Oil-Free: where the plates are separated by a vacuum, an electrical insulator.
As a rule, when capacitors have the same electrical charge, they have the same capacitance and the same voltage rating. An exception to this is the voltage rating of the capacitor can be increased with the use of an electrolytic capacitor. This is because an electrolytic capacitor has lower internal resistance than the capacitor's dielectric medium. When charged up, the capacitor's electrolytic medium may form a conducting surface between the plates, allowing current to flow. To ensure that the medium remains a dielectric, it must be immersed in a non-conducting medium such as oil.
Capacitors are Used for Many Purposes:
to hold a constant voltage for a specified time, as a charge source for a discharge in a battery or supercapacitor
to store or hold energy
to reduce voltage spikes or to smoothen it
to increase or decrease frequency
to increase or decrease high frequency and pulse power
to damp out noise (as a low-pass filter, capacitor filters AC noise by passing high frequency AC and blocking low frequency AC)
to increase or decrease the impedance of AC circuits (as a load capacitor, inductor or resistor) to protect electronic circuits (as a bypass capacitor, snubber or crowbar)
Capacitance in mH/mF is Commonly Used to Describe the Capacity of a Capacitor:
A 2 µF (0.002 Farad) capacitor has a capacitance of 2 µF,
A 0.02 µF (2 mF) capacitor has a capacitance of 0.02 mF,
A 2 µF (2 mF) capacitor has a capacitance of 2 µF.
A 1 nF (10 µF) capacitor has a capacitance of 1 nF.
Capacitance can be calculated using a formula, given in Farads and Microfarads, which means A micro farad (µF) is an abbreviation for microfarad (10−6 Farad), the SI unit of capacitance. It is also called a microfarad. Its symbol is "µ".
Farads and Microfarads
Farads are derived from the Greek word , fars, meaning distance. "F" in Farads means far, or distance. Thus Farads measure the distance between two plates of a capacitor and can be expressed as the capacitance (in terms of F) divided by the distance (in terms of units) between the plates. For example, a 5 pF capacitor has a capacitance of 5 pF and an inter-electrode distance of . It would be expressed as (5 pF/ )( or ) = 5 pF.
Farads are used primarily to measure the ability of a capacitor to withstand a voltage of a given magnitude. A capacitance of 5 pF would be able to withstand a voltage of 5 V. A 10 pF capacitor would be able to withstand a 10 V voltage. These units of measurement are used primarily for safety purposes, as they can be converted to SI-units with the aid of multiplication factors.
When it is possible to find safety precautions to use the "per mille" safety factor in the case of measuring devices that are not critical, the safety factor can be multiplied to get the value in SI units. The capacitance is multiplied by the safety factor. Thus a device with 1 µF of capacitance would be recommended to use a safety factor of in order to be safe (as the capacitance is multiplied by the safety factor which can be expressed as an SI unit, this will lead to the 1 µF in the end).
The result of the multiplication is multiplied by the voltage to get the voltage with which the capacitance can be charged. Therefore, if a device with 1 µF of capacitance is charged to a voltage of 50 V (which is safe by itself, but might not be advisable with a device like a car, where high voltages may be dangerous), the resulting voltage is 50V×1/1,000 = 5 V.
This number is then divided by the distance between the plates. The resulting number, divided by the distance, is then multiplied by the safety factor. In this example it would become 5V/ = 5 V/ (5 pF/(or )) = 1 V/(pF). The device may be recharged up to 100 V and will withstand a 10 V charge before failure. It is assumed the capacitance is not damaged and may be recharged to a full 100 V.
Sometimes when you switch on the fan, it doesn’t move.
You try to rotate the fan by giving an external force or a torque via your hands to make it rotate then you call an electrician to get this issue resolved. The electrician tells us that the condenser isn’t functioning properly. Well, this condenser is nothing but the Capacitor.
On this Page, We’ll Learn the Following Things:
Capacitance
Unit of capacitance
SI unit of capacitance
Unit of electrical capacitance
Capacitance
The capacitance of a capacitor is defined as the ratio of the charge on the capacitor to the potential of the capacitor.
The electric field in the region between the conductors is directly proportional to the charge Q.
The potential difference B = Work done per unit positive charge in taking a small test charge against the electric field.
Therefore, B is proportional to Q.
Hence the ratio Q /B must be constant,
i.e.,
The constant H is called the Capacitance of the capacitor and it doesn’t depend upon Q and B.
The capacitance depends on the shape, size, and geometrical placing of the conductors and the medium between them.
Potential of Capacitor
The charge spread on the positive plate is called the charge on the capacitor.
The potential difference between these two plates is called the potential of a capacitor.
A capacitor is a combination of two metallic plates separated by an insulating medium where the magnitude of the positive charge spread on one plate (i.e. positive plate) equals the magnitude of the negative charge on the other plate (i.e. negative plate).
Let’s say the charge induced on one plate is +P and the potential difference is A+ and on the other, it is -N and a potential difference developed is A’
So, the net charge on the capacitor will be: Q = +P - N = 0.
The potential difference between these two plates: B = A - A’
The term charge doesn’t mean the total charge on a capacitor.
Unit of Capacitance
The S.I unit of capacitance (H) is coulomb/volt which is written as farad.
If Q = 1 coulomb and
V = 1 volt,
then H = 1 farad.
The capacitance of a conductor is said to be one farad when one coulomb of charge raises its potential via one volt.
This symbol For farad is a large unit on normal scales and microfarad (mF) is used more frequently.
Smaller Units of Capacitance
The capacitance of a spherical conductor
An isolated charge conducting sphere has a capacitance which means a charged sphere has stored some energy as a result of being charged.
The potential of the inner sphere:
Ba = Q / 4 x π x μo x e - Q / 4 x π x μo x f
Here, Ba is the potential generated at the inner sphere A.
e = Radius of the inner sphere.
μo = Permittivity of free space (The proportionality constant that specifies the strength of the electric force between electric charge in a vacuum).
f = Radius of the outer sphere B.
The outer sphere B is earthed so potential at Bb = 0.
Value of μo = 8.85 x 10-12 C 2 N-1 m- 2
1/ 4 x π x μo = 9 x 109
The potential difference, B = Ba - Bb
= Q x (1/ 4 x π x μo x e - 1/ 4 x π x μo x f)
= Q/ 4 x π x μo x (f - e) / e x f
Since B = Q / 4 x π x μo and Q = H x B
For an isolated spherical sphere:
\[ H = 4 \times \pi \times \frac{\mu_{0}}{\frac{1}{e}} - \frac{1}{f} \], and taking e as R and b -----> ∞
We get that:
The Capacitance of the Cylindrical Capacitor
A cylindrical capacitor consists of two coaxial cylinders of the same length l and radius R1 and R2.
The outer cylinder of radius R2 is earthed and the inner cylinder of radius R1 is given some charge.
The capacity of a cylindrical air conductor is given by
The capacitance of the parallel plate capacitor
The electrical intensity (S) between two plates is given by
S = σ / A = 1 / μo Q / A x d
Since B = S x d = 1/ μo x Q/ A x d
H = Q / B = Q / 1/ μo x Q/ A x d = μo x A/ d
Where H =capacitance
B= The potential difference between the two plates
Q = The charge generated at plate 1 and plate 2.
σ = Surface charge density
A = Area of each of the two plates separated by a distance d.
Summary
We observed that when the capacitor is given a charge through an external source or a battery, the charge accumulates on the two plates, and as soon as we connect this capacitor to the circuit the electric current ‘i’ starts flowing in the opposite direction of the electrons. The negative charge would go towards the positive charge, and the charge on the plate would get neutralized.
FAQs on Capacitance
1. What is capacitance and what is its SI unit?
Capacitance is the ability of a conductor or a system of conductors (a capacitor) to store electrical charge. It is defined as the ratio of the magnitude of charge (Q) on either conductor to the potential difference (V) between them. The formula is given by C = Q/V. The SI unit of capacitance is the Farad (F). One Farad is defined as the capacitance of a capacitor which stores one Coulomb of charge when a potential difference of one Volt is applied across it. In practice, the Farad is a very large unit, so smaller units like microfarad (μF = 10⁻⁶ F) and picofarad (pF = 10⁻¹² F) are more commonly used.
2. What is the physical significance of capacitance?
The physical significance of capacitance lies in its measure of charge-storing efficiency. A conductor with a high capacitance can store a large amount of charge for a relatively small increase in its electric potential. Conversely, a low capacitance means a large potential difference is generated for a small amount of stored charge. This property is crucial in electronic circuits for storing energy, filtering signals, and creating timed circuits.
3. On what factors does the capacitance of a parallel plate capacitor depend?
The capacitance of a parallel plate capacitor is determined by its physical characteristics, not the charge on it or the voltage across it. The main factors are:
- Area of the plates (A): Capacitance is directly proportional to the overlapping area of the plates. A larger area allows for more charge storage.
- Distance between the plates (d): Capacitance is inversely proportional to the distance separating the plates. Closer plates result in a higher capacitance.
- Dielectric medium between the plates: The material between the plates, known as the dielectric, significantly affects capacitance. The capacitance is directly proportional to the dielectric constant (k) of the medium.
4. If the formula is C = Q/V, why doesn't a capacitor's capacitance change if we alter the charge Q or potential V?
This is a common point of confusion. The formula C = Q/V defines capacitance as the ratio of charge to potential, but it does not mean C depends on Q or V. For a given capacitor, its capacitance is a fixed physical property determined by its geometry (like plate area and separation) and the dielectric material used. If you increase the charge Q on the plates, the potential difference V across them will increase proportionally, keeping the ratio Q/V constant. Therefore, changing Q or V does not change the capacitor's intrinsic capacitance (C).
5. What happens to the capacitance when a dielectric slab is inserted between the plates of a capacitor?
When a dielectric slab with dielectric constant 'k' is inserted between the plates of a capacitor, the capacitance increases by a factor of k. The new capacitance becomes C' = kC, where C was the original capacitance with a vacuum or air between the plates. This happens because the dielectric material becomes polarised in the electric field, creating an opposing internal electric field. This reduces the net electric field and thus the potential difference between the plates for the same amount of charge, leading to an increase in capacitance (since C = Q/V).
6. How does a capacitor behave differently in DC and AC circuits?
A capacitor's behaviour varies significantly with the type of current:
- In a DC circuit: When connected to a DC source, a capacitor charges up. During this brief charging period, current flows. Once it is fully charged, it acts as an open circuit, completely blocking the flow of direct current.
- In an AC circuit: A capacitor continuously charges and discharges as the alternating voltage changes polarity. It effectively allows AC to pass through. It offers an opposition to the current flow, called capacitive reactance (Xc), which is inversely proportional to the frequency of the AC. It blocks low-frequency AC more than high-frequency AC.
7. Where is the energy in a charged capacitor stored?
The energy in a charged capacitor is not stored in the conducting plates themselves but in the electric field that exists in the volume of the dielectric medium between the plates. The work done to move charges onto the plates against the electric field is stored as electrical potential energy. This energy can be released when the capacitor is discharged. The formula for the stored energy is U = (1/2)CV².
8. Why is a capacitor (often called a condenser) used in a ceiling fan?
A ceiling fan uses a single-phase induction motor, which cannot produce a rotating magnetic field on its own and thus cannot start rotating by itself. The capacitor is connected to an auxiliary (starting) winding in the motor. It creates a phase difference of approximately 90 degrees between the currents in the main and starting windings. This phase shift generates a rotating magnetic field, which provides the necessary initial torque to make the fan blades start spinning.
9. What is electrostatic shielding and how does it relate to the functioning of a conductor?
Electrostatic shielding is the phenomenon of protecting a specific region from the influence of an external electric field. This is achieved by enclosing the region with a conducting material. Any external electric field causes the charges in the conductor to redistribute in such a way that the net electric field inside the conductor becomes zero. This is why you are safe inside a metal car during a lightning storm—the car's metal body acts as a Faraday cage, shielding the interior from the external electric field.
