Magical Element

capacitor-
   A capacitor (originally known as a condenser) is a passive two-terminal electrical component used to store electricalenergy temporarily in the form  electrostatic field .The forms of practical capacitors vary widely, but all contain at least two electrical conductors (plates) separated by a dielectric (i.e. an insulator that can store energy by becoming polarized). The conductors can be thin films, foils or sintered beads of metal or conductive electrolyte, etc. The nonconducting dielectric acts to increase the capacitor's charge capacity. Materials commonly used as dielectrics include glass,ceramic, plastic film, air, vacuum, paper, mica, and oxide layers. Capacitors are widely used as parts of electrical circuits in many common electrical devices. Unlike a resistor, an ideal capacitor does not dissipate energy. Instead, a capacitor stores energy in the form of an electrostatic field between its plates.

An ideal capacitor is characterized by a single constant value, its capacitance. Capacitance is defined as the ratio of the electric charge Q on each conductor to the potential difference V between them. The SI unit of capacitance is the farad(F), which is equal to one coulomb per volt (1 C/V). Typical capacitance values range from about 1 pF (10⁻¹² F) to about 1 mF (10⁻³ F).

                               An ideal capacitor is wholly characterized by a constant capacitance C, defined as the ratio of charge ±Q on each conductor to the voltage V between them:^[13]

                                             

                                                            farads

Energy of electric field

Work must be done by an external influence to "move" charge between the conductors in a capacitor. When the external influence is removed, the charge separation persists in the electric field and energy is stored to be released when the charge is allowed to return to its equilibrium position. The work done in establishing the electric field, and hence the amount of energy stored, is

${\displaystyle W=\int _{0}^{Q}V(q)\mathrm {d} q=\int _{0}^{Q}{\frac {q}{C}}\mathrm {d} q={1 \over 2}{Q^{2} \over C}={1 \over 2}CV^{2}={1 \over 2}VQ}$

  

Dielectric

A dielectric material (dielectric for short) is an electrical insulator that can be polarized by an applied electric field. When a dielectric is placed in an electric field, electric charges do not flow through the material as they do in a conductor, but only slightly shift from their average equilibrium positions causing dielectric polarization. Because of dielectric polarization, positive charges are displaced toward the field and negative charges shift in the opposite direction. This creates an internal electric field that reduces the overall field within the dielectric itself.^[1] If a dielectric is composed of weakly bonded molecules, those molecules not only become polarized, but also reorient so that their symmetry axes align to the field.

The study of dielectric properties concerns storage and dissipation of electric and magnetic energy in materials. Dielectrics are important for explaining various phenomena in electronics, optics, and solid-state physics.

When a battery is connected to a series resistor and capacitor, the initial current is high as the battery transports charge from one plate of the capacitor to the other. The charging current asymptotically approaches zero as the capacitor becomes charged up to the battery voltage. Charging the capacitor stores energy in the electric field between the capacitor plates. The rate of charging is typically described in terms of a time constant RC.

 Here are some of the various types of capacitors and how they are used.

• Air - Often used in radio tuning circuits
• Mylar - Most commonly used for timer circuits like clocks, alarms and counters
• Glass - Good for high voltage applications
• Ceramic - Used for high frequency purposes like antennas, X-ray and MRI machines
• Super capacitor - Powers electric and hybrid cars

                                                          Magical Elements


Inductor

Definition of Inductance

If a changing flux is linked with a coil of a conductor there would be an emf induced in it. The property of the coil of inducing emf due to the changing flux linked with it is known as inductance of the coil. Due to this property all electrical coil can be referred as inductor. In other way, an inductor can be defined as an energy storage device which stores energy in form of magnetic field.

An inductor, also called a coil or reactor, is a passive two-terminal electrical component which resists changes inelectric current passing through it. It consists of a conductor such as a wire, usually wound into a coil. Energy is stored in a magnetic field in the coil as long as current flows. When the current flowing through an inductor changes, the time-varying magnetic field induces a voltage in the conductor, according to Faraday’s law of electromagnetic induction.

Lenz law-
Lenz's law states that when an emf is generated by a change in magnetic flux according to Faraday's Law, the polarity of the induced emf is such, that it produces an current that's magnetic field opposes the change which produces it.

The negative sign used in Faraday's law of electromagnetic induction, indicates that the induced emf ( ε ) and the change in magnetic flux ( δΦ_B ) have opposite signs. Where, ε = Induced emf δΦ_B = change in magnetic flux N = No of turns in coil

Explanation of Lenz's Law

For understanding Lenz's law, consider two cases : CASE-I When a magnet is moving towards the coil. When the north pole of the magnet is approaching towards the coil, the magnetic flux linking to the coil increases. According to Faraday's law of electromagnetic induction, when there is change in flux, an emf and hence current is induced in the coil and this current will create its own magnetic field . Now according to Lenz's law, this magnetic field created will oppose its own or we can say opposes the increase in flux through the coil and this is possible only if approaching coil side attains north polarity, as we know similar poles repel each other. Once we know the magnetic polarity of the coil side, we can easily determine the direction of the induced current by applying right hand rule. In this case, the current flows in anticlockwise direction.

CASE-II When a magnet is moving away from the coil When the north pole of the magnet is moving away from the coil, the magnetic flux linking to the coil decreases. According to Faraday's law of electromagnetic induction, an emf and hence current is induced in the coil and this current will create its own magnetic field . Now according to Lenz's law, this magnetic field created will oppose its own or we can say opposes the decrease in flux through the coil and this is possible only if approaching coil side attains south polarity, as we know dissimilar poles attract each other. Once we know the magnetic polarity of the coil side, we can easily determine the direction of the induced current by applying right hand rule. In this case, the current flows in clockwise direction.

NOTE : For finding the directions of magnetic field or current, use right hand thumb rule i.e if the fingers of the right hand are placed around the wire so that the thumb points in the direction of current flow, then the curling of fingers will show the direction of the magnetic field produced by the wire.

Properties of Inductors

The I-V law for a inductor is for the reference directions shown below.

1)  The voltage across an inductor is zero if the current through the inductor is not changing.  i.e. Since di/dt=0 and v=Ldi/dt, then v=0v.

2)  The current through an inductor cannot change instantaneously.  i.e. If di/dt®¥, then v=Ldi/dt®¥ which is not possible.  Therefore i cannot change instantaneously.

3)  In a circuit with only DC sources, an inductor "acts like" a short-circuit after the current through it reaches steady-state. The energy stored is

4)  An inductor is a passive device that stores energy. The energy associated with the inductor is stored in the magnetic field surrounding the device. The energy can be completely recovered by "collapsing" this magnetic field. If discharged through a resistive device the power given off as heat will come from the magnetic field.

Inductor Transient

When a battery is connected to a series resistor and inductor, the inductor resists the change in current and the current therefore builds up slowly. Acting in accordance with Faraday's law and Lenz's law, the amount of impedance to the buildup of current is proportional to the rate of change of the current. That is, the faster you try to make it change, the more it resists. The current builds up toward the value it would have with the resistor alone because once the current is no longer changing, the inductor offers no impedance. The rate of this buildup is characterized by the time constant L/R . Establishing a current in an inductor stores energy in the magnetic field formed by the coils of the inductor.

                                                      Basics for electrical

 Electricity is the presence and flow of electric charge. Its best-known form is the flow of electrons through conductors such as copper wires. Electricity is a form of energy that comes in positive and negative forms, that occur naturally (as in lightning), or is produced (as in a generator).

Inventor of electricity-

Building upon Franklin's work, many other scientists studied electricity and began to understand more about how it works. For example, in 1879, Thomas Edison invented the electric light bulb and our world has been brighter ever since! But was Benjamin Franklin really the first person to discover electricity

                                      (https://en.wikipedia.org/wiki/Benjamin_Franklin)

Electric power is the rate at which electrical energy is transferred by an electric circuit. The SI unit of power is the watt, one joule per second.

Electric powerlike mechanical power, is the rate of doing work, measured in watts, and represented by the letter P. The term wattage is used colloquially to mean "electric power in watts." The electric power in watts produced by an electric current I consisting of a charge of Q coulombs every t seconds passing through an electric potential (voltage) difference of V is

${\displaystyle P={\text{work done per unit time}}={\frac {VQ}{t}}=VI\,}$

where

Q is electric charge in coulombs

t is time in seconds

I is electric current in amperes

V is electric potential or voltage in volts

components of power-

Electric current
Its nothing but the rate of flow of electric charge through a conducting medium with respect to time. It is caused by drift of free electrons through a conductor to a particular direction. As we all know, the measuring unit of electric change is Coulomb and the unit of time is second, the measuring unit of current is Coulombs per second and this logical unit of current has a specific name Ampere after the famous French scientist André-Marie Ampere. If total Q Coulomb charge passes through a conductor by time t, then


current I = Q / t coulomb per second or Ampere

For better understanding, let give an example, suppose total 100 coulombs of charge is transferred through a conductor in 50 seconds.
As the current is nothing but the rate at which charge is transferred per unit of time, it would be ratio of total charge transferred to the required time for that. Hence, here

With electricity, we measure the amount of charge flowing through the circuit over a period of time. Current is measured in Amperes (usually just referred to as “Amps”). An ampere is defined as 6.241*10¹⁸ electrons (1 Coulomb) per second passing through a point in a circuit.

There are two types of electric current: direct current (DC) and alternating current (AC). The electrons in direct current flow in one direction. The current produced by a battery is direct current.

, conventional current is defined as moving in the same direction as the positive charge flow. So, in metals where the charge carriers (electrons) are negative, conventional current is in the opposite direction as the electrons.

voltage

Voltage, also called electromotive force, is a quantitative expression of the potential difference in charge between two points in an electrical field. 

work done in moving a unit negative charge from point of  high potential to low potential with volts as units

    volts

    

    potential

The minimum energy required to move a charge from lower to higher energy level is called potential.

Resistance

The electrical resistance of an electrical conductor is a measure of the difficulty to pass an electric current through that conductor. The inverse quantity is electrical conductance, and is the easy with which an electric current passes. Electrical resistance shares some conceptual parallels with the notion of mechanical friction. The SI unit of electrical resistance is the ohm (Ω), while electrical conductance is measured in siemens (S)

The resistance (R) of an object is defined as the ratio of voltage across it (V) to current through it (I), while the conductance (G) is the inverse:

${\displaystyle R={V \over I},\qquad G={I \over V}={\frac {1}{R}}}$

ohms law

Ohm's law states that the current through a conductor between two points is directly proportional to the voltage across the two points. Introducing the constant of proportionality, the resistance, one arrives at the usual mathematical equation that describes this relationship

${\displaystyle I={\frac {V}{R}},}$ (at constant temperature)

where I is the current through the conductor in units of amperes, V is the voltage measured across the conductor in units of volts, andR is the resistance of the conductor in units of ohms. More specifically, Ohm's law states that the R in this relation is constant, independent of the current.^[

The law was named after the German physicist Georg Ohm

voltage current resistance

 Voltage is the difference in charge between two points. Current is the rate at which charge is flowing. Resistance is a material's tendency to resist the flow of charge (current).