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Capacitor

Capacitors are also known as Electric-condensers. A capacitor is a two-terminal electric component. It has the ability or capacity to store energy in the form of electric charge. 

  • The capacitor is an arrangement of two conductors generally carrying charges of equal magnitudes and opposite sign and separated by an insulating medium. 
  • A capacitor is a device that stores electric charge. 
  • Capacitors vary in shape and size, but the basic configuration is two conductors carrying equal but opposite charges.
    Electrostatic Potential & Capacitance | Physics Class 12 - NEET

What are Capacitors Used For?

Applications of CapacitorsApplications of CapacitorsWhen charges are pulled apart, energy is associated with the pulling apart of charges, just like energy is involved in stretching a spring. Thus, some energy is stored in capacitors. In the uncharged state, the charge on either one of the conductors in the capacitor is zero.
During the charging process, a charge, Q, is moved from one conductor to the other one, giving one conductor a charge, Q, and the other one a charge, -Q. A potential difference ΔV is created with the positively charged conductor at a higher potential than the negatively charged conductor. 
Note that whether charged or uncharged, the net charge on the capacitor as a whole is zero.

Note: 

  • The net charge on the capacitor as a whole is zero. When we say that a capacitor has a charge Q, we mean that the positively charged conductor has charge +Q and negatively charged conductor has a charge, -Q.
  • In a circuit a capacitor is represented by the symbol:
    Electrostatic Potential & Capacitance | Physics Class 12 - NEET

Capacitance

The capacitance of the conductor is defined as the charge required to increase the potential of a conductor by one unit. It is a scalar quantity. 
  • Unit of capacitance is farad in SI unis and its dimensional formula is [M-1L-2I2T4]
  • Capacitance is nothing but the ability of a capacitor to store the energy in form of an electric charge. In other words, capacitance is the storing ability of a capacitor. It is measured in farads.
  • 1 Farad: 1 Farad is the capacitance of a conductor for which 1-coulomb charge increases potential by 1 volt.
    1 Farad = Electrostatic Potential & Capacitance | Physics Class 12 - NEET

Electrostatic Potential & Capacitance | Physics Class 12 - NEET

Question for Electrostatic Potential & Capacitance
Try yourself:What is the dimensional formula of capacitance of a capacitor?
View Solution

Applications of Capacitors

1. Capacitors for Energy Storage

Since the late 18th century, capacitors are used to store electrical energy. Individual capacitors do not hold a great deal of energy, providing only enough power for electronic devices to use during temporary power outages or when they need additional power. There are many applications that use capacitors as energy sources and a few of them are as follows:

Electrostatic Potential & Capacitance | Physics Class 12 - NEET

Supercapacitors are capacitors that have high capacitances up to 2 kF. These capacitors store large amounts of energy and offer new technological possibilities in areas such as electric cars, regenerative braking in the automotive industry and industrial electrical motors, computer memory backup during power loss, and many others.

2. Capacitors for Power Conditioning

One of the important applications of capacitors is the conditioning of power supplies. Capacitors allow only AC signals to pass when they are charged blocking DC signals. This effect of a capacitor is majorly used in separating or decoupling different parts of electrical circuits to reduce noise, as a result of improving efficiency. Capacitors are also used in utility substations to counteract inductive loading introduced by transmission lines.

3. Capacitors as Sensors

Capacitors are used as sensors to measure a variety of things including humidity, mechanical strain, and fuel levels. Two aspects of capacitor construction are used in the sensing application – the distance between the parallel plates and the material between them. The former is used to detect mechanical changes such as acceleration and pressure and the latter is used in sensing air humidity.

4. Capacitors for Signal Processing

There are advanced applications of capacitors in information technology. Capacitors are used by Dynamic Random Access Memory (DRAM) devices to represent binary information as bits. Capacitors are also used in conjunction with inductors to tune circuits to particular frequencies, an effect exploited by radio receivers, speakers, and analog equalizers.

Factors Affecting Capacitance

  1. Dielectric


    The effect of dielectric on capacitance is that the greater the permittivity of the dielectric the greater the capacitance, likewise lesser the permittivity of the dielectric the lesser is the capacitance. Some materials offer less opposition to the field flux for a given amount of field force. Materials with greater permittivity allow more field flux, hence greater charge is collected.
  2. Plate Spacing


    The effect of spacing on the capacitance is that it is inversely proportional to the distance between the plates. Mathematically it is given as:
    Electrostatic Potential & Capacitance | Physics Class 12 - NEET
  3. Area of the Plates


    The effect of the area of the plate is that the capacitance is directly proportional to the area. The larger the plate area more is the capacitance value. Mathematically it is given as C∝A

In Summary, 

Factors Affecting CapacitanceFactors Affecting Capacitance

Capacitance of an Isolated Conductor

When a conductor is charged its potential increases. It is found that for an isolated conductor (conductor should be of finite dimension so that potential of infinity can be assumed to be zero) potential of the conductor is proportional to the charge given to it.
q = charge on conductor
V = potential of conductor

⇒ q = CV

Where C is proportionally constant called capacitance of the conductor.
Electrostatic Potential & Capacitance | Physics Class 12 - NEET

Capacitance of an isolated conductor depends on the following factors

  1. Shape and size of the conductor
    On increasing the size, capacitance increase.
  2. On surrounding medium
    With the increase in dielectric constant K, capacitance increases.
  3. Presence of other conductors
    When a neutral conductor is placed near a charged conductor capacitance of conductors increases.

Capacitance of a conductor does not depend on

  1. Charge on the conductor
  2. Potential of the conductor
  3. The potential energy of the conductor

Example1. Find out the capacitance of an isolated spherical conductor of radius R.

Electrostatic Potential & Capacitance | Physics Class 12 - NEET

Sol. Let there is charge Q on the sphere.
Therefore, Potential V = KQ/R
Hence by the formula: Q = CV

Q = CKQ/R
C = 4πε0R

  • If the medium around the conductor is vacuum or air
    Cvacuum = 4πε0R
    R = Radius of the spherical conductor. (maybe solid or hollow)
  • If the medium around the conductor is a dielectric of constant K from the surface of a sphere to infinity then
    Cmedium = 4πε0KR
  • Electrostatic Potential & Capacitance | Physics Class 12 - NEET = K = dielectric constant

 Electrostatic Potential

The electrostatic potential is also known as the electric field potential, electric potential, or potential drop is defined as:

The amount of work that is done in order to move a unit charge from a reference point to a specific point inside the field without producing an acceleration.

  • Electric potential is a scalar property of every point in the region of the electric field. At a point in the electric field, the potential is defined as the interaction energy of a unit positive charge. If at a point in the electric field a charge q0 has potential energy U. then the electric potential at that point can be given as:Electrostatic Potential & Capacitance | Physics Class 12 - NEET
  • The potential energy of a charge in an electric field is defined as the work done in bringing the charge from infinity to the given point in the electric field. Similarly, we can define electric potential as work done in bringing a unit positive charge from infinity to the given point against the electric forces.
  • Potential at a point can be physically interpreted as the work done within the conservative field in displacing a unit (+ve) charge from infinity to that point.Electrostatic Potential & Capacitance | Physics Class 12 - NEET

Potential Energy and Potential Difference

  • Electric Potential is the ‘push’ of electricity through a circuit. It’s easy to confuse electric potential with electric current, so it helps to think of electric current as of the water in our shower and electric potential as the water pressure. Like water pressure, the varying voltage can increase or decrease the flow of electricity.

Test charge moves from high potential to low potentialTest charge moves from high potential to low potential

  • Electric Potential is a scalar quantity denoted by V, equal to the electric potential energy of any charged particle at any location (measured in joules) divided by the charge of that particle (measured in coulombs). By dividing out the charge on the particle a remainder is obtained that is a property of the electric field itself. 
  • This value can be calculated in either a static (time-invariant) or a dynamic (varying with time) electric field at a specific time in units of joules per coulomb, or volts (V). The electric potential at infinity is assumed to be zero. The concept of electric potential is useful in understanding electrical phenomena; only differences in potential energy are measurable.
  • If an electric field is defined as the force per unit charge, then by analogy an electric potential can be thought of as the potential energy per unit charge. Therefore, the work done in moving a unit charge from one point to another (e.g., within an electric circuit) is equal to the difference in potential energies at each point. In the International System of Units (SI), an electric potential is expressed in units of joules per coulomb (i.e., volts), and differences in potential energy are measured with a voltmeter.

Simple electric circuitSimple electric circuit

Electric Potential in Circuits

  • Charge moving through the wires of the circuit will encounter changes in electric potential as it traverses the circuit. Within the electrochemical cells of the battery, there is an electric field established between the two terminals, directed from the positive terminal towards the negative terminal. 
  • As such, the movement of a positive test charge through the cells from the negative terminal to the positive terminal would require work, thus increasing the potential energy of every Coulomb of charge that moves along this path.
    Electric potential movement in circuits
    Electric potential movement in circuits
  • This corresponds to a movement of the positive charge against the electric field. It is for this reason that the positive terminal is described as the high potential terminal. The charge would lose potential energy as moves through the external circuit from the positive terminal to the negative terminal. 
  • The negative terminal is described as the low potential terminal. This assignment of high and low potential to the terminals of an electrochemical cell presumes the traditional convention that electric fields are based on the direction of movement of positive test charges.
  • Chemical energy is transformed into electric potential energy within the internal circuit (i.e., the battery). Once at the high potential terminal, a positive test charge will then move through the external circuit and do work upon the light bulb or the motor or the heater coils, transforming its electric potential energy into useful forms for which the circuit was designed. 
  • The positive test charge returns to the negative terminal at low energy and low potential, ready to repeat the cycle (or should we say circuit) all over again.

Electric Potential Difference

To that position without any acceleration. For any charge, an electric potential is obtained by dividing the electric potential energy by the quantity of charge.

In an electrical circuit, the electric potential between two points is defined as the amount of work done by an external agent in moving a unit charge from one point to another.

Mathematically, E = W/Q

Where,
= electrical potential difference between two points
= Work done in moving a charge from one point to another
Q = the quantity of charge in coulombs
The potential difference is measured by an instrument called a voltmeter. The two terminals of a voltmeter are always connected parallel across the points whose potential is to be measured.

Question for Electrostatic Potential & Capacitance
Try yourself: If a charged body is moved in an electric field against the Coulomb force, then ________
View Solution

Electrostatic Potential due to a Point Charge

Let P be the point at a distance r from the origin O at which the electric potential due to charge +q is required.

Electrostatic Potential & Capacitance | Physics Class 12 - NEET

The electric potential at a point P is the amount of work done in carrying a unit positive charge from ∞ to P. As work done is independent of the path, we choose a convenient path along the radial direction from infinity to the point P without acceleration. Let A be an intermediate point on this path where OA = x. The electrostatic force on a unit positive charge at A is given by

Electrostatic Potential & Capacitance | Physics Class 12 - NEET

Small work done in moving the charge through a distance dxdx from AA to B is given by

Electrostatic Potential & Capacitance | Physics Class 12 - NEET

⇒  dW = Fdx           (ii)

Total work done in moving a unit positive charge from ∞ to the point PP is given by

Electrostatic Potential & Capacitance | Physics Class 12 - NEET

From the definition of electric potential, this work is equal to the potential at point P.

Electrostatic Potential & Capacitance | Physics Class 12 - NEET

A positively charged particle produces a positive electric potential. A negatively charged particle produces a negative electric potential. Here, we assume that electrostatic potential is zero at infinity. Eq.(iv) shows that at equal distances from a point charge q, value of V is same.

Hence, electrostatic potential due to a single charge is spherically symmetric. Figure given below shows the variation of electrostatic potential with distance, i.e. V1rV \propto \frac{1}{r} and also the variation of electrostatic field with distance, i.e. Electrostatic Potential & Capacitance | Physics Class 12 - NEET

Variation of electrostatic potential V and electric field E with distance rVariation of electrostatic potential V and electric field E with distance r

Electrostatic Potential & Capacitance | Physics Class 12 - NEET

Electrostatic Potential Due to a System of Charges

To find the electric potential at a point P due to multiple point charges Electrostatic Potential & Capacitance | Physics Class 12 - NEET  located at respective distances Electrostatic Potential & Capacitance | Physics Class 12 - NEET from P, we calculate the potential contribution from each charge and then sum them.

A system of chargesA system of charges

The potential at P due to charge q1 is:

Electrostatic Potential & Capacitance | Physics Class 12 - NEET

Similarly, the potentials due to other charges are:Electrostatic Potential & Capacitance | Physics Class 12 - NEET

Using the superposition principle, the total potential V at point PP is the algebraic sum of the potentials due to each individual charge:Electrostatic Potential & Capacitance | Physics Class 12 - NEET

This can be expressed as:Electrostatic Potential & Capacitance | Physics Class 12 - NEET

Or, using summation notation:Electrostatic Potential & Capacitance | Physics Class 12 - NEET

Thus, the net electrostatic potential Vnet at a point due to multiple charges is the algebraic sum of the potentials from each individual charge at that location:Electrostatic Potential & Capacitance | Physics Class 12 - NEET

Electrostatic Potential due to an Electric Dipole

Electrostatic Potential & Capacitance | Physics Class 12 - NEET

Electric potential at point P due to electric dipoleElectric potential at point P due to electric dipole

Let OO be the centre of the dipole, PP be any point near the electric dipole inclined at an angle \thetaθ as shown in the figure. Let PP be the point at which electric potential is required.

Electrostatic Potential & Capacitance | Physics Class 12 - NEET

As potential is related to work done by the field, electrostatic potential also follows the superposition principle. Therefore, potential at PP due to the dipole,

Electrostatic Potential & Capacitance | Physics Class 12 - NEET

Now, by geometry,Electrostatic Potential & Capacitance | Physics Class 12 - NEET

Similarly,Electrostatic Potential & Capacitance | Physics Class 12 - NEET

Electrostatic Potential & Capacitance | Physics Class 12 - NEET

Electrostatic Potential & Capacitance | Physics Class 12 - NEET

Putting these values in Eq. (i), we obtainElectrostatic Potential & Capacitance | Physics Class 12 - NEET

Electrostatic Potential & Capacitance | Physics Class 12 - NEET

Electrostatic Potential & Capacitance | Physics Class 12 - NEET

Example 2.  An electric dipole consists of two charges of equal magnitude and opposite signs separated by a distance 2a as shown in figure. The dipole is along the X-axis and is centred at the origin.

Electrostatic Potential & Capacitance | Physics Class 12 - NEET

  1. Calculate the electric potential at point P.
  2. Calculate V at a point far from the dipole.

Electrostatic Potential & Capacitance | Physics Class 12 - NEET

Example 3. Two point charges of 4μC and −2μC are separated by a distance of 1 m in air. Find the location of a point on the line joining the two charges, where the electric potential is zero.

Sol.  Let the electrostatic potential be zero at point PP between the two charges separated by a distance x meter.

Electrostatic Potential & Capacitance | Physics Class 12 - NEET

Electrostatic Potential & Capacitance | Physics Class 12 - NEET

V = \frac{1}{4 \pi \epsilon_0} \sum_{i=1}^{n} \frac{q_i}{r_{iP}}

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FAQs on Electrostatic Potential & Capacitance - Physics Class 12 - NEET

1. What is a capacitor and how does it work?
Ans. A capacitor is an electrical component that stores and releases electrical energy in a circuit. It consists of two conductive plates separated by an insulating material called a dielectric. When a voltage is applied across the plates, an electric field is created, causing positive charge to accumulate on one plate and negative charge on the other. The ability of a capacitor to store charge is quantified by its capacitance, measured in farads (F).
2. What factors affect the capacitance of a capacitor?
Ans. The capacitance of a capacitor depends on three main factors: the surface area of the conductive plates, the distance between the plates, and the type of dielectric material used. Specifically, increasing the plate area or using a dielectric with a higher permittivity increases capacitance, while increasing the distance between the plates decreases it.
3. How is electrostatic potential defined, and why is it important?
Ans. Electrostatic potential, often referred to as electric potential, is defined as the amount of work done per unit charge to move a positive test charge from a reference point to a specific point in an electric field. It is important because it helps to understand how electric fields interact with charged objects and is crucial in calculating the energy stored in electric fields and the behavior of electric circuits.
4. How is the electrostatic potential due to a point charge calculated?
Ans. The electrostatic potential (V) due to a point charge (Q) at a distance (r) from the charge is calculated using the formula: V = k * Q / r, where k is Coulomb's constant (approximately 8.99 x 10^9 N m²/C²). This formula indicates that the potential is directly proportional to the charge and inversely proportional to the distance from the charge.
5. What is the electrostatic potential due to an electric dipole?
Ans. The electrostatic potential (V) due to an electric dipole at a point in space is given by the formula: V = (1/4πε₀) * (p·r) / r³, where p is the dipole moment, r is the position vector from the dipole to the point, and ε₀ is the permittivity of free space. This formula shows that the potential decreases with the cube of the distance from the dipole and depends on the orientation of the dipole moment relative to the position vector.
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