In some capacitors like power capacitors used in electrical power circuits, a high resistance will be connected across the capacitor to discharge the capacitor when the circuit is opened. The unit of capacitance is Farads and is denoted by F.
Farad is a large unit and hence, capacitance have values of micro-Farads. The capacitor used in electronic circuits may be denoted by the manufacturer as MF. It should not be mistaken as Mega-Farads, since, Farad itself is a big unit and it should be taken as micro-Farads only. A Farad may be defined as the capacitance of a capacitor between the plates of which there appears a potential difference of one volt when it is charged by one coulomb of electricity.
The electric power lines have charged conductors and hence, there will be capacitance between any two conductors and between a conductor and earth. Since, it is a long line the capacitance will be distributed capacitance and expressed in micro-Farads per kilometer length of line. For precision work, the capacitance between the two ends of a coil and also the capacitance between two turns of the coil should be considered.
The distance between the two plates is 1 cm, Calculate i The electric stress with in the dielectric ii The electric stress on the plate surface iii The charges on the plates Calculate the values i , ii and iii if air dielectric is replaced by paper of relative permittivity 4. This difficulty is overcome by the provision of a Guard Ring around one electrode, as shown in the Fig. Fringing of flux is now confined to the outer edge of the guard ring, while the flux density over the central electrode is uniform.
Parallel - Plate Capacitor with Gaurd Ring 1. Capacitance in Series C1 C2 C3 Fig. Composite Dielectric Capacitors Comparing Eq. A parallel plate capacitor has a plate separation t. The capacitance with air only between the plates is C. The relative permittivities are 2, 3 and 6 and the thicknesses are 0. Calculate the combined capacitance and the electric stress in each material when the applied voltage is V.
Find the capacitance. Take the relative permittivity of paper as 4. Find the total capacitance and the charge on each capacitor when connected in parallel to V supply. Calculate the total capacitance and voltage across each capacitor when connected in series to the same V supply.
Solution : Fig. The charge on each capacitor is the same. Calculate the Potential Difference across the parallel capacitors. The plates must be rigid so that they can move between each other without touching. It follows that the dielectric between the plates in air. Normally one set of plates is fixed and the other made to rotate. The greater the insertion of the movable plates then the greater the capacitance. Most of us know this type of capacitor because it is the device used to tune radios.
This type of capacitor is known as Gang Condenser. The area of each plate is 15 cm2 and separation between opposite plates is 0. These equivalent capacitances are treated to be in series with the remaining capacitances. After solving the circuit, the current in the parallel branches are calculated from the total current. A dielectric slab of width L and thickness d is inserted between the plates, as shown in the figure.
Neglecting edge effects, find expressions for the following: i. The capacitance of the capacitor. The total energy stored in the capacitor. The force tending to draw the dielectric slab into the capacitor. Each part of the problem is examined in order. To find the total energy in the capacitor, use is made of the expression for energy density. To find the force tending to draw the dielectric slab into the capacitor, the work done in moving the slab a distance dl will be calculated.
This work must equal the change in energy in the field. This is the region where we observe a small bit of paper which is a dielectric material and when brought nearer to Nylon or Terylene clothes gets attracted towards the clothes because the cloth gets charged due to the friction with the body. The material will cease to be a nonconductor or dielectric once the field produced exceeds a certain value. The maximum value of field-intensity or potential- gradient that the material can withstand without disruption may be referred to as the Dielectric Strength of the material.
According to Maximum Stress Theory, if the potential difference across the material is raised to such an extent that the electric stress exceeds the above limit, breakdown is sure to occur. Breakdown may also occur due to presence of impurities, lack of homogeneity, surface-irregularities, etc. The high electric field intensity surrounding high voltage power lines accounts for an additional energy loss in the transmission of power. The high voltage gradient at the surface of a wire sometimes accelerates electrons in the air sufficiently to ionize air molecules by collision.
If the voltage gradient at the wire exceeds a certain critical value, the process of ionization becomes cumulative and results in appreciable loss of energy. The ionization is characterized by a faint glow surrounding the wire and is called Corona. This is called Electrostatic Induction.
The charges tend to get distributed at the outer surface of the conductor. The charges get concentrated at sharp points of the conductor. Hence, in the case of lighting arrestors the charged clouds induce opposite charges in the sharp end of arrestor rod which passes the charges to ground, thus, saving the damage to the structure.
Capacitance is generally used in A. The current in a capacitor leads the voltage by 90o. Capacitance stores energy in the form of Electrostatic Energy between the plates. For an ideal capacitor there will be no Power Loss. Capacitance depend upon the dimensions and geometry and also the dielectric medium between the plates.
In the case of D. Thus, the capacitance initially acts as a Short circuit and as an Open Circuit finally. The voltage across a capacitance cannot change all on a sudden. The charged capacitance retains its charge and voltage even after removal of the supply and hence causes an electric shock if touched. Hence, one should be very careful in dealing with capacitance. The charged capacitance has to be discharged by external means before touching. Large Commercial Power Capacitor will have a discharging resistance connected across it.
A lossy capacitance due to the loss in the dielectric can be represented as an ideal capacitor in parallel with a resistance to account for the loss in the capacitor. In resonance circuits to tune and select particular frequency signals as in Radio and TV. In Operational Amplifiers which is used for integration, differentiation, etc. In Wave Shaping Circuits to obtain a desired wave form from a given waveform 5.
In analog circuits, to solve for other systems like Mechanical Systems, Hydraulic System, etc. In Transducers, which convert physical signals into electrical signals as in microphone.
In Power Factor Changing Circuits 8. To improve the Power Factor of Load. To improve the voltage profile of transmission lines. In High Voltage Impulse Generators. In Measurement Circuits. The energy stored in the inductance is in the form of Electromagnetic Field.
Both Inductance can also be used in wave shaping circuits. Inductance is also called as Inductor. Inductance exhibits delay in the rise and fall of currents through it. Hence, it is used to represent a mass possessing inertia in Electrical Analog Circuits used to represent a Mechanical System.
A current flowing through a conductor sets up an electromagnetic field around the conductor. Hence, it will be circular around the conductor as given in the Fig 1.
The cross inside the conductor of Fig. The circle around the conductor along with its direction indicates the direction of the magnetic field setup by the current flowing through this conductor.
If a coil is wound on a soft iron rod, as in Fig. This magnetic field of the electromagnet is represented by the dotted lines and its direction by the arrow heads. The direction of the magnetic field produced by a current in a solenoid may be deduced by applying either the Right Hand Threaded Screw or the Right Hand Grip Rule.
If the axis of the screw is placed along that of the solenoid and if the screw is turned in the direction of the current, it travels in the direction of the magnetic field inside the solenoid, namely towards the right in Fig.
E in the coil or conductor. That means it will try to reduce the current flowing through the conductor which sets up the magnetic field. This reduction in current can be treated as reduction in current due to a parameter called Inductance Parameter L just as the resistance R reduces the current. The inductance is denoted by L and is measured in Henry.
A circuit has an inductance of one henry 1 H if an E. Henry is also a big unit and hence, the coils will generally have inductance of the order of milli-Henrys. In this case, the E. Hence is known as self induced E. The self inductance of a coil is defined as the flux linkages linking that coil for unit current flowing through that coil. Hence, a coil is said to have a self-inductance of one henry if a current of one ampere flowing through it produces flux linkages of one wb-turns in it.
Note : Henry is denoted by symbol H and should not be confused with magnetization force H. Hence, we can also say that a coil or a circuit has an inductance of one henry 1 H if an E.
From Eq. The iron core has a relative permeability of and 8cm2 area of cross- section. Determine the required number of turns of the coil.
Solution : From Eq. Example 2. Calculate the energy in the magnetic field when a current of 2A flows in the Solenoid. With exciting voltage of V, the magnetic flux linking the winding is 0. Calculate the Self Inductance of the winding and the energy stored in the magnetic field. The magnetic flux linkage with the coil is 0.
Calculate the inductance of the coil. If this current is uniformly reversed in 0. Determine i Energy stored in the magnetic circuit ii Voltage applied across the coil.
But the energy stored in the coil remains the same. If a current of 2A flowing in the coil is reversed in 5milli-sec, find the average E. Solution : M. These equivalent inductances are treated to be in series with the remaining series inductances. The direction of the induced E. If the mutual E. If the induced E. Mutual inductance may be defined as the ability of one coil or circuit to produce an E. This action being reciprocal, the second coil can also induce an E.
This ability of reciprocal induction is measured in terms of the coefficient of mutual induction M. M21 denotes the mutual inductance of coil 2 due to current i1 in coil 1. Alternatively, The mutual inductance of a coil of N1 turns is the flux linkages with that coil per unit current flowing through the neighboring coil of N2 turns.
The mutually induced E. F will increase. Then the mutual inductance M is considered to be positive. Similarly, when two current carrying coils are located nearby, if the magnetic flux setup by the coil 2 which links coil 1 aids the magnetic flux setup by coil 1 then, the net flux in coil 1 will be increased and the total E.
Then the mutual inductance M is considered to be negative. Similarly, when two current carrying coils are located nearby, if the magnetic flux setup by the coil 2 which links coil 1 aids the magnetic flux setup by coil 1 then, the net flux in coil 1 will be decrease and the total E. This phenomenon is represented by dot convention as shown in Fig. Referring to Fig. For the second set of coils with mutuals to avoid confusion, instead of dots small triangles or small squares may be used to indicate the mutual inductance as given in Fig.
In general, when two coils mutual coupling are connected in series, the total E. In the Fig. Two coils are said to be magnetically coupled if full or part of the flux produced by one links with the other. Let L1 and L2 be the self inductances of the two coils, M their mutual inductance, and k be the coefficient of mutual coupling between the two coils.
N1 and N2 are the number of turns of coils 1 and 2 respectively. S is the reluctance of the magnetic path. Hence, coefficient of coupling may be defined as the ratio of actual mutual inductance present between the two coils to the maximum possible value of the mutual inductance between the two coils. A pure resistance is denoted by the symbol. It is wound with turns of insulated wire. A second coil of turns in wound on the top of the first.
Assuming that all flux produced by the first coil links with the second, calculate the Mutual Inductance and the coefficient of coupling. If current in one coil is varied from 4A to 1A in 0. Solution : Mutually Induced E. Find the mutual inductance between the two coils if the relative permeability of iron core is If current in coil A grows from zero to 10 Amperes in 0.
Coil S is open circuited. Coil P carries a current of 4A resulting in flux 0. Determine a Mutual Inductance between the coil and b The Voltage induced in open circuited coil S when the current in coil P changes at the rate of 1.
Hence, the current through out the inductance cannot change all on a sudden. In this case, the inductance of each coil is increased by M1 i. In this case, the inductance of each coil is decreased by M, i. If one of the coils when isolated has a self inductance of 0. These equivalent inductances are treated to be in series with the remaining inductances along with their mutuals if any.
If the core material is a magnetic material of high permeability then, the flux linking with the coil will be maximum and hence, the inductance self or mutual will be maximum. For that purpose, an iron core is used instead of air core for the coil. As we draw the core inside into the coil or away from the coil by means of linear motion or screwed motion by means of a dial or wheel, the inductance of the coil will increase or decrease accordingly. Now the inductance consists of two parts which are equivalent two partial coils, one with air core and the other with magnetic core.
By varying the length of the magnetic core, the inductance is varied. To reduce the noise the magnetic core should be fixed tightly.
Inductance is generally used in A. The current in a inductor lags the voltage by 90o. Inductance stores energy in the form of Electromagnetic Energy in the core. If the current in an inductive circuit like a coil, motor or fan is broken by opening a switch, the stored magnetic energy gets dissipated in the form of an arc across the switch.
Hence special care has to be taken in opening of inductive circuits like opening of the circuit breakers of electric power circuits. The arc should be quenched by proper means if necessary. For an ideal inductor there will be no Power Loss. Inductance depend upon the dimensions, geometry and material of the magnetic core. If the resistance of the coil is less as is generally the case, the coil will get burnt away.
The current through an inductance cannot change all on a sudden. So, for a system with constant inductance the current through the inductance, before the change will be the same just immediately after the change like closing of a switch or opening of a switch. This principle is used in Pulse and Digital Circuits. The Unit of inductance Henry is a large unit. Hence, inductance is expressed in milli-Henries.
Normally, the inductance should have very low resistance. But the coils used in electronic circuits because of their low current capacity and smaller area of cross-section will have fairly good resistance.
The core of an inductance can be an air core or iron core. For large inductances iron core is implied so that the inductance will be more. The magnetic core of the inductance should be fixed very tightly otherwise there will be magnetic hum creating noise.
Inductance is setup by a coil when A. A coil will also have a resistance equal to the resistance of the wire constituting the coil. However, if this resistance is negligible then the coil exhibits only inductance and is called a pure inductance. The principle of constant flux linkages states that the flux linkages cannot change instantaneously in a given system.
The inductance should have very less or negligible resistance or on the other hand, the coils used in electronic circuits will have more resistance since the area of cross-section of the conductor of the coil will be very small.
In electrical transmission lines, because of the time varying magnetic field setup by the A. The electric power lines will also exhibit inductance and since it is a long line the inductance will be distributed and is expressed as milli-Henries per kilometer length of line. Inductors are used in the form of Solenoids for operating Gate Valves to control the fluid flow etc. The inductance coils are used in Electromagnetic relays for opening and closing the control circuits.
The principle of Mutual Induction is used in Transformers in which Electrical Energy at certain voltage in one circuit can be transferred magnetically to another circuit at a different voltage with out actual connection between the two circuits.
Transformers are used in Electric Power Transmission and Distribution. Extra High Voltage EHV Lines will have large capacitance due to its long length and will cause higher receiving and voltage than the sending end voltage of the transmission line. It will also cause High Voltage Oscillations when the line is switched off. To overcome this, Large Inductors are used between the transmission lines and the Earth to compensate for the line capacitance. Inductors can also be used in tuning.
But since the inductance will be heavy, instead of inductors, capacitors are used to tune and select particular frequency signals as in Radio and TV. The coils used in Electronic Circuits Ferrite Rods for tuning will have resistance also. Norton current is the short circuit current flowing through the load, and it is shown in the below figure.
It is based on the conservation of charge. Where i n represents the n th current. Additional Information. It is based on the conservation of energy. Where V n represents the n th Voltage. Let the current I 1 is current flows through the resistor R when only one source is active and I 2 is the current flow through the resistor R when only the other source is active. Here Maximum Power Transfer theorem is not applicable as the load resistor is not variable. Properties of maximum power tran sfer theorem:.
Key Points. Reciprocity theorem is applicable to a network. Containing R, L and C elements. Which is initially not a relaxed system. Having both dependent and independent sources. Reciprocity theorem: It states that the current I in any branch of a network, due to single voltage source E anywhere in the network is equal to the current of the branch in which source was placed originally and when the source is again put in the branch in which current is obtained originally.
Limitations of reciprocity theorem:. Con cept:. To find R th :. Place a voltage source of 1V across the terminal and find the current I T flowing through it. Place a current source of 1A across the terminals and find the voltage V t across the current source. As the given circuit contains a dependent source, then place a current source of 1A across the terminals and find the voltage V x across the current source.
Case 1: Circuits with independent Sources only. If the network has no dependent sources, we turn off all independent sources.
R th is the input resistance of the network looking between terminals a and b. Case 2: Circuit with Both Dependent and independent sources.
We apply a voltage source V 0 at terminals a and b and determine the resulting current I 0. To evaluate the Thevenin voltage, we evaluate the open-circuit voltage. The circuit is redrawn as:. Note : The current source in parallel to resistance is replaced by a voltage source in series with the same resistance using source transformation.
Determine the load resistance R L that will result in maximum power delivered to the load for the given circuit. Also, determine the maximum power P max delivered to the load resistor. The effects of various magnitudes of bias voltage on the device 11 can best be understood by reference to Figs.
In the following discussion it is assumed that the side of the P-N junction to which Va is connected, here shown as a dot 23, is equipotential. This is essentially true in practice since the dot 23 is made of a good electrically conducting material.
In referring to Figs. Attention is first directed to the circuit illustrated by Fig. For this relation of voltages, the P-type region 25 is positive relative to the N-type region immediately below the junction 27 because the voltage impressed in P-type region 25 from battery 35 is positive and is greater than the positive voltage existing in the bar 12 at all points below the junction 27 due to the battery This is a forward bias for the junction 27 and the area of the entire junction 27 consequently emits holes.
The non-linearity results from the flow of current into the bar 12 from the junction As can be seen from Fig. In the circuit shown in Fig. For this relation of V0 to V0, the junction 27 is biased in the reverse direction over its entire area because the region of P-type semiconductive material 25 is negative relative to the voltage of the area of the bar 12 directly beneath the junction This reverse bias prevents hole current flow into the body of N-type semiconductor, and space charge collects along side of the junction barrier.
The entire area of the junc tion 27 thus is biased in the reverse direction. This condition is illustrated by the graph of Fig. When this voltage relationship exists, the potential of the P-type semiconductive region 25 is intermediate the values of the potentials of the N-type semiconductive region adjacent it.
Thus, because of the potential gradient existing in the bar 12, the value of the voltage at the left side of the P-type region 25 is greater than the voltage of an N-type semiconductive region 37 adjacent it. In this area 37, therefore, the N-type region is negative with respect to the P-type region 25 and the left side of the junction 27 acts as an emitter, i.
This is indicated in Fig. However, the voltage V0 applied to the dot 23 is less than the voltage existing in a N-type region 39 adjacent the right side of the P-type semiconductive region Since the voltage V0 is less than the potential existing in the N-type region 39 of the bar 12, the junction of the N-type region 39 and the P-type region 25 is biased in the reverse direction, i.
Therefore, when the value of the voltage Vc applied to the dot 23 is intermediate the value of voltage existing in the bar 12 at the sides of the region 25, the N-type region 37 and the P-type region 25 form an emitter junction and the N-type region 39 and the P-type region 25 form a collector junction. When this condition exists, the relation between current Ic flowing through the junction 27 and the voltage V0, applied between the dot 23 and the contact 13, exhibits non-linear properties including a negative resistance region.
The region AC of the voltage-current curve is the negative resistance region. Thus, the device 11 is extremely sensitive to a small change in voltage and is adapted to relay operation. As in Fig. The magnitude Vc, the potential of battery 29, is set at a value slightly less than C Fig. The marginal relay 43 is adjusted so that it is insensitive to the normal flow of current through the coil A source of controlling voltage 45 is connected to terminals 47 and 49 in series with the battery 29 so that the voltages are additive.
When a controlling voltage pulse V is applied to the terminals and 49 from the source 45, the pulse voltage adds to the voltage Vc and because of the negative resistance region AC Fig. This electrical contact between terminals 51 and As a result of the shorting of terminals 51 and 52, current from a source of potential 55 flows, through a device to be controlled 57 thereby energizing it.
If desired, the normally open marginal relay. In this modification the controlling voltage pulse Vp from source 45 is applied to terminals and 61, the polarity of Vp being as shown and is such as to subtract from the voltage V0 of battery When a controlling pulse is impressed between terminals 59 and 61, the voltage between contacts 13 and of the device 11 is decreased. This decrease in voltage lowers the value of the unidirectional field in device 11 to a point where the voltage Va is intermediate the values of axial voltage at the sides of dot
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