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.
Applications 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:
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.
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:
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.
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.
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.
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.
In Summary,
Factors Affecting Capacitance
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.
Example1. Find out the capacitance of an isolated spherical conductor of radius R.
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
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.
Test charge moves from high potential to low potential
Simple electric circuit
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,
E = electrical potential difference between two points
W = 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.
Let P be the point at a distance r from the origin O at which the electric potential due to charge +q is required.
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
Small work done in moving the charge through a distance dx from A to B is given by
⇒ dW = Fdx (ii)
Total work done in moving a unit positive charge from P is given by
From the definition of electric potential, this work is equal to the potential at point P.
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. and also the variation of electrostatic field with distance, i.e.
Variation of electrostatic potential V and electric field E with distance r
To find the electric potential at a point P due to multiple point charges located at respective distances from P, we calculate the potential contribution from each charge and then sum them.
A system of charges
The potential at P due to charge q1 is:
Similarly, the potentials due to other charges are:
Using the superposition principle, the total potential V at point P is the algebraic sum of the potentials due to each individual charge:
This can be expressed as:
Or, using summation notation:
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:
Electric potential at point P due to electric dipole
Let O be the centre of the dipole, P be any point near the electric dipole inclined at an angle θ as shown in the figure. Let P be the point at which electric potential is required.
As potential is related to work done by the field, electrostatic potential also follows the superposition principle. Therefore, potential at P due to the dipole,
Now, by geometry,
Similarly,
Putting these values in Eq. (i), we obtain
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.
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 P between the two charges separated by a distance x meter.
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1. What is a capacitor and how does it work? |
2. What factors affect the capacitance of a capacitor? |
3. How is electrostatic potential defined, and why is it important? |
4. How is the electrostatic potential due to a point charge calculated? |
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