For all the circuits lumped elements in which time varying voltages / current exists , we find a relation in which the voltage is proportional to Current . The proportional quantity is in general a complex number and this is called Impedance.
It is a function of frequency of ‘w’ strictly speaking impedance is sum of its real and imaginary parts.
Z= R+ IX
Impedance is equivalent to a Resistance in series with pure imaginary Impedance - called a Reactance.
The voltage drop across the resistance is in phase with the current , while the voltage drop across the purely Reactive part is out of phase with the current.
The average energy loss in an impedance Z= R + iX depends only on real part of ‘Z’ and not on complex part.
There is no energy loss in Reactive part.
GP THOMSON EFFECT - Experimental Verification of Wave nature of Matter
G P Thomson has performed experiments with electrons accelerated from 10000 to 50000 volts.
The high energy beam of electrons is produced by a cathode ‘C’.
The experimental arrangement is as shown
below:
The electron beam is excited with potential upto a maximum of 50,000 volts. A fine beam is obtained by passing it through slit or diaphragm ‘S’.
The accelerating fine beam of electrons now falls on thin gold or Aluminum film (order of 10-6 cm thickness).
The photograph of beam from foil is recorded on photographic plate ‘P’.
After developing the plate, a symmetric pattern consisting of concentric
rings about a central spot is obtained. This pattern resembles that of X- rays.
To know that this pattern is due to electrons or due to x-rays generated
by electrons in their passage through foil, cathode rays in discharge tube are
deflected by magnetic field.
It was observed that beam shifts correspondingly showing there by that
pattern is produced by electrons and not by x-rays. (i.e X – ray pattern is not affected by
electric and magnetic fields).
As diffraction pattern can only be produced by waves and not by
particles, so Thomson concluded that electrons behave like wave.
Thus, Thomson experiment clearly demonstrated the existence of
matter waves.
BCS (Bardeen - Cooper - Schieffer) THEORY
The microscopic theory put forward by Bardeen, Cooper and Schreiffer (BCS), in 1957 provides the better quantum explanation of superconductivity and explains well all the properties exhibited by superconductors.
The basis of formulation of BCS theory are two experimental conclusions namely the isotope effect and variation of specific heat of superconductors.
For isotope effect Tc M^1/2 = constant, one can infer that transition resulting in superconducting state must involve dynamics of ion motions, lattice vibrations and Phonons.
Further we note that Tc attains a value zero when 'M' approaches infinity. This all suggests that the non zero transition temperature is a consequence of finite mass of ions which can contribute Phonons by their vibrations.
Bardeen pointed out that an electron moving through a crystal lattice has a self energy accompanied by virtual Phonons. This means that an electron moving through crystal lattice distorts the lattice and lattice in turn acts on electron by virtue of electrostatic forces between them. The oscillatory distortion of lattice is quantized in terms of Phonons and so one can interpret the interaction between lattice and electron as constant emission and re-absorption of Phonon by latter. These are called virtual Phonons.
BCS showed that basic interaction responsible for responsible for superconductivity appears to be that of a pair of electrons by means of interchange of virtual Phonons.
Suppose an electron approaches a positive ion core . It suffers attractive Coulomb interaction. Due to this attraction ion core is set in motion and consequently distorts the lattice.
Smaller the mass of positive ion core, the greater will be the distortion. Suppose towards that site another electron comes and sees this distorted lattice. Then the interaction between the two, the electron and distorted lattice occurs which in its effect lowers the energy of second electron.
Thus, we interpret that the two electrons interact via the lattice distortion or the Phonon field resulting in lowering of energy for electrons.
The lowering of electron energy implies that force between two electrons is attractive. This type of interaction is called electron-lattice-electron interaction. This interaction is strongest when two electrons have equal and opposite momenta and spins.
Since the oscillator distortion of Lattice is quantized in terms of Phonons, the above interaction can be interpreted as electron-electron interaction through Phonon as mediator.
Let an electron of wave vector K1 emits a virtual phonon 'q' which is absorbed by an electron with wave vector K2. K1 is thus scattered as K1-q and K2+q.
The nature of resulting electron-electron interaction depends on relative magnitudes of electronic energy and phonon energy. If the phonon energy exceeds electronic energy, the interaction is attractive.
When such interaction occurs by phonon exchange by dominating usual repulsive interaction, two such electrons from a pair called as Cooper pair.
The energy of pair of electrons in bound state is less than energy pair in free state. The difference in energy of two states is binding energy of cooper pair.
The energy difference between free state of electron and paired state appears as energy gap at Fermi surface. The normal electron states are above the energy gap and superconducting electron states are below the energy gap at Fermi surface.
What is Meissner Effect?
The Meissner Effect
Superconductors which are resistance less materials have an additional property of exclusion of applied magnetic field on it i.e. inside a superconducting material, we always have B=0.
The property of perfect diamagnetism arises in super conductor because when a magnetic field ‘Ba’ is applied surface screening currents circulate so as to produce a flux density ‘Bi’ which every where inside the metal exactly cancels the flux density due to applied field Bi=-Ba.
The property of perfect diamagnetism arises in super conductor because when a magnetic field ‘Ba’ is applied surface screening currents circulate so as to produce a flux density ‘Bi’ which every where inside the metal exactly cancels the flux density due to applied field Bi=-Ba.
For a Super Conductor μr=0; i.e. B=μrBa=0
TThis property of exhibiting perfect diamagnetism by super conductor is known as Meissner Effect.
What is GM Counter and how does it operate?
The counter is named as GM counter based on its developers ‘Geiger’ and ‘Muller’ in 1928. They are oldest type of gas filled radiation detectors.GM counters were operated in the Geiger discharge region of gas filled ion chambers.
Construction: - The counter is usually a leak tight assembly of two electrodes electrically isolated. The counter is filled to sub atmospheric pressures of few mm of mercury. A high voltage is applied to the anode electrode.
Principle: - This counter also works on the principle of ionization caused by incoming energetic particle in the gas medium filled between anode and cathode. The electron liberated in the primary ionization event would get accelerated towards anode because of its high potential. The electron may gain sufficient energy to cause ionization of other gas molecule. This leads to a chain of ionizing events which is usually referred to as Townsend avalanche. During this process, there may be interactions in which excitation of atoms may occur due to sufficient energy of impinging electrons. Such atoms while de-exciting may emit photons which normally fall in UV or visible region. These photons which are emitted may again lead to photo electrons due to ionization of gas atoms or due to photoelectric interaction with walls of counter. Each photo electron would again cause Townsend effect. Such a series of Townsend avalanches would lead to discharge in the tube called Geiger-discharge. In such a state there is formation of dense envelope of electron-ion pairs distributed on either side of anode.
The voltage applied to anode shall be such that it is enough to trigger the avalanche mechanism and collect total charge (electrons) pertaining to single event leading to Geiger discharge.
Concept of quenching: - Practically the process would not be as simple as above. During the Geiger discharge, there is dense envelope of electrons and ions. The electrons would drift towards anode and positive ions would drift towards cathode. The positive ions which drift towards cathode having ionization potential (E) greater than the work function (W) of cathode material leads to exchange of electron from cathode and becomes neutral. The excess energy may be dissipated in two forms, one by emission of photon or an electron form cathode if excess energy is greater than the work function of the cathode material. This would again initiate another Geiger discharge. The result of this is that the tube would always be in continuous Geiger discharge and hence will not able to measure any radiation.
To overcome this problem, concept of quenching is introduced. There are two types of quenching
i) Organic quenching
ii) Halogen quenching
Organic quenching: -
This involves addition of small quantity of organic gas having complex molecule structure. This prevents the continuous Geiger discharge mechanism by charge transfer collision principle. The positive ions on their path collide with organic molecules to get neutralized. This makes only ions of organic gas reach cathode and gets neutralized. If there is any excess energy released leads to dissociation of organic molecules. Thus multiple Geiger discharges could be avoided.
A typical filling of organic quenched GM tubes is 90% Argon and 10% of ethyl alcohol. When organic gas gets depleted to a sufficient extent there is occurrence of multiple discharges frequently and thus the plateau length gets decreased, with slope increased.
Thus the organic quenched GM tubes are characterized by short life time and thus not suitable for operation in very high fields which leads to large count rate. To overcome this, technique of Halogen quenching is introduced.
Halogen quenching: - This involves the addition of small quantity of Halogen gas such as Chlorine or Bromine. A typical filling is about 0.1% of chlorine to Neon. The quenching action is same as that in Organic quenching process. The diatomic halogen gas molecules too gets dissociated in quenching but gets recombined to replenish the gas molecules and thus counter life gets extended.
Characteristics of GM tubes:-
The important parameters which decide the quality of functioning of Gm tubes are
i) Dead time
ii) Recovery time
iii) Plateau length &Plateau slope
i) Dead time: - As discussed above, the positive ions take considerable time to reach cathode tube compared to electrons. The reason is that the mobility of electrons is about 1000 times greater than that of electrons.
Due to the low drift velocity of positive ions, there is formation of cloud of positive ions which tend to electric field opposite to that of actual field. This reduces the electric field intensity due to anode potential and thus affects gas multiplication factor. This in turn affects the pulse heights.
In high count rates, it is more worse that there is formation of dense positive cloud which makes the electric field intensity in the vicinity of anode wire reduce by great margin thus multiplication goes down by big margin. During this phase of detector, any new ionizing event caused by incoming particle cannot be recorded. Thus the time interval during which any event caused by newly incoming particle would not get counted and called as dead time of the country.
ii) Recovery time: - After certain time, all the positive ions tend to reach cathode wall and thus the electric field begins to restore to actual value. When the electric field goes beyond a critical value there is again formation for pulses. But the process requires some time to give maximum pulse heights. Hence the total time required for GM tube to give maximum pulse height pulses is Recovery time.
iii) Plateau length & Slope: In order to decide the operating voltage of the GM tube, a graph between anode voltage (X axis) and count rate (Y axis) is plotted. After applying minimum voltage to initiate Geiger discharge, the no. of pulses shall remain same in fixed radiation field exposure. But due to formation of short pulses during recovery time there is variation in count rate. Thus one of the quality parameters deciding the operation of GM tube is that plateau slope shall be less. Usually 2-3% plateau slope is a good choice. As we go on applying voltage to the anode, the tube starts entering continuous discharge region. Thus the slope gets worsened. The region or length of voltage region during which the plateau slope remains in desired value is called as plateau length and usually the operating voltage is chosen at the midpoint of plateau length.
Comparison between Frequency Modulation(FM) & Amplitude Modulation(AM)
Frequency Modulation |
Amplitude Modulation |
|
1) The
amplitude of FM signal is constant and in depth of Modulation. |
1) Amplitude of AM signal varies depending on Modulation index. |
|
2) It
requires much wider channel (7-15 times) as compared to AM |
2) Band width, is very small, which is one of the biggest
disadvantages. |
|
3) Transmitters
are complex and hence expensive |
3) Relatively simple and cheap |
|
4) Area
of reception is small since it is limited to line of sight |
4) Area of reception is large |
|
5) Noise
can be easily minimized. Amplitude variations can be eliminated by using
limiter. |
5) More susceptible to noise, interference & low signal to noise
ratio. Difficult to eliminate effects of noise. |
|
6) Average
power in frequency modulated wave is same as contained in un-modulated wave. |
6) Average power in modulated wave is greater than carrier power.
This added power is provided by modulating source. |
|
7) No
restriction is placed on modulated index. |
7) Maximum modulation index is 1 otherwise over modulation would
result in distortion. |
|
8) Possible
to operate several independent transmitters on same frequency. |
8) Not possible to operate out interference. |
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