Kerns, JR. David Irwin Pearson. A1: Ohms law — At constant temperature, the current flowing through a conductor is directly proportional to the potential difference p. An electrical iron carrying 2A at V. Find resistance of the device? Average rating 4. Vote count: No votes so far!
Be the first to rate this post. Your email address will not be published. How useful was this post? Circuit Concepts and Circuit Elements-I 3 The work done in moving a unit positive charge from one point in the electric field to another field in the electric field is known as the potential difference between the two points and is measured in volts.
The voltage rise from point B to point A is generally denoted by the letter E. Continuous flow of electrons constitute a current flow from negative potential to positive potential of the field. This current is known as electron current. The conventional current flow is opposite to that of the electron current in direction.
The conventional current flow which is in opposite direction to electron current flow, will be flowing from a point of higher potential to a point of lower potential. In metals conducting materials , a large number of free electrons are available which move from one atom to the other at random when a potential difference is applied between two points of the conducting material and the current starts flowing.
Current is expressed in terms of amperes. Hence, one ampere is the current which flows when a charge of one coulomb moves across the cross-section of a conductor in one second. Active elements are the sources that supply electrical energy to the circuit causing current flow through it. The energy sources can be independent or dependent sources.
They may be voltage or current sources. An ideal voltage source is expected to deliver a constant voltage to the outside circuit whatever be the amount of current drawn from the voltage source. The voltage of the source is called the Electro-Motive Force E. It is denoted by the symbol E. In practice the terminal voltage of the voltage source will be decreasing as the current drawn from it is increased due to the voltage drop in the internal resistance of the voltage source.
The internal resistance has to be very small in order that the voltage drop inside the source will be very small and maximum voltage may be available to the load.
Note : For any D. For Time Varying Sources to polarities indicate the polarities at different terminals at any particular instant of time. An ideal current source is expected to deliver a constant current to the outside circuit whatever be the circuit. The internal resistance of the current source should be as high as possible so that maximum current will be delivered to the load connected across the current source with the current through the internal resistance being very very small.
For the model of 1. Sources If the voltage or current supplied by an electrical energy source is constant with respect to time as shown in Fig. Source has two terminals from which energy is supplied to the outside load. They are known as Positive Terminal which supplies the positive ions and Negative Terminal which receives the returning current or which can be assumed as supplying negative charges called electrons in the direction opposite to the conventional current direction. The battery converts chemical energy into electrical energy.
The generator converts mechanical energy into electrical energy. If the voltage or current is varying with respect to time but, has the same polarity as shown in Fig. If the polarity is positive, it is known as Positive Source. If the polarity is negative, it is known as Negative Source. If the voltage or current supplied by an electrical energy source varies in both magnitude and polarity with respect to time as shown in Fig. Voltage Source or Alternating Current Source.
Voltage Source ii D. Current Source a D. Voltage or Current b A. C and D. In general, the instantaneous values may also be denoted as v or i. Generally no polarities will be marked for A. If at all polarities are marked for A. Unilateral and Bilateral Elements : Elements in which current flow is in only one direction are called unilateral elements.
Elements in which current flow can be in both directions are called bilateral elements. Resistance, Inductance, Capacitance etc. While moving through the material, these electrons collide with other atoms and molecules. They oppose this flow of electrons or current through it. This opposition is called Resistance. Heat is produced because of the collisions of moving electrons with the other atoms and molecules.
Thus whenever a current flows through a conductor, heat is produced in the conductor and this heat has to be dissipated fully.
Otherwise, the insulation of the conductor the Sheath made of insulating material covering the conductor will get damaged. The opposition offered to the flow of current free electrons is called Resistance. They will be made of carbon resistors and will have color codes for different digits. For higher wattages of 5 or 8 or 10 Watts etc. In the case of carbon resistors, it is usual to identify the ratings by means of rings painted around the resistors, as shown in Fig. One of the bands is always placed near to the end of the resistor and should be taken as the first band.
The first, second and third bands are used to indicate the resistance of the resistor by means of a color code which is also given in Fig. In the code the first two bands are orange and blue which, from the table are 3 and 6 respectively. Therefore we are being told that the resistance has a numerical value of The third band tells us how many zeroes to put after that number.
In this case, the third band is green and there should be five zeroes, i. The resistance R of a conductor depends on 1. Since Copper and Aluminium have good electrical conductivity and cheaper compared to Silver, they are used for conductors. The resistivity of copper is 0. The colour codes for the bands are given in Table 1. Not only conductors, but a coil wound with a conductor or any other electrical equipment offers resistance to current flow. A wire wound coil with two fixed terminals is called a resistor or resistance.
A coil with two fixed terminals and a variable contact terminal which makes contact with the body of the coil is called a Rheostat or Variable Resistor.
A rheostat can be connected in two ways as, 1. Series Resistance as shown in Fig. Circuit Concepts and Circuit Elements-I 11 offered will be the resistance of the remaining part of the winding. As the moving contact is varied the resistance offered by this part will be varying, as the moving contact is moved away from or towards the second terminal. If the moving contact is towards the starting terminal then the resistance offered by the rheostat will be less. R R1 R2 R1 Fig.
Potential Divider as shown in Fig. The output is tapped between the moving contact and one of the end terminals, in which case, part of the input voltage will be the output voltage.
Vin Vout R Fig. Effect of Temperature on Resistance As temperature increases the resistance of most of the conducting materials increase while for some material like Carbon, electrolytes, insulators the resistance decreases as the temperature increases. The change in resistance depends upon the temperature-coefficient of resistance, which will be positive if the resistance increases with temperature and negative if the resistance decreases with temperature.
Calculate the value of temperature-coefficient of resistance of the material of the coil at 0oC. Find the resistance at 0oC. If the conductance or conductivity is less the current flowing will be less. The constant of proportionality is R, the resistance. Note : While writing the equations for Volt-Ampere relationships in matrix form the second form i. Circuits or to circuits with Unidirectional Source in Laplace Transform domain for instantaneous values.
For steady state conditions of A. Those resistances for which the current through them does not vary in direct proportion are called Non-Linear Resistances. For nonlinear resistances the v-i characteristics will be nonlinear. Hence, it is used in Lightning Arrestors. In certain other nonlinear resistances like Semiconductors, Thermistors, the current decreases as the voltage across increases like in curve 3 of Fig. Hence, thermistor is used in over current protection in Motors, etc.
Example 1. What is the length of the wire? What is the conductivity and conductance of the wire? It is called copper loss, even though the conductor material is not made of copper. The power loss or copper loss appears in the form of heat. This heat has to be dissipated properly or else the insulation of the conductor or the insulation coating varnish of the coil will get damaged and there will be short circuits between turns of the coil and the coil may get burnt away in the case of machines and other equipments using coils.
Circuit Concepts and Circuit Elements-I 19 1. As such energy calculations are very important. Of late to have good efficiency in getting the work done and to have good economy Energy Auditing is resorted to in Industries and because energy charges are recurring charges involving expenditure. According to the Law of Conservation of Energy, energy can neither be created nor destroyed. As such energy can atmost be converted from one form of energy into another form like converting mechanical energy into electrical energy and vice versa, converting electrical energy into heat energy and vice versa, etc.
In this process the efficiency of the equipment used in conversion plays an important role. Also the constants of conversion are to be considered. It is denoted by W. By convention, the E. For eg. By convention, a currents entering the junction are taken to be positive and currents leaving the junction are taken to be negative.
The currents of the current sources entering the junction are positive. Circuits or to circuits with Unidirectional Source using instantaneous values for Voltages and currents. Find the power delivered by the battery and the energy supplied by the battery for a period of half an hour. Let it be I2. Also find the current through 0.
Applying KCL for node B, the current through 0. Current through 0. Circuit Concepts and Circuit Elements-I 27 In series circuits, the elements in the series can be connected in any order. For example, R2, R3, R1, etc. In series circuits, the same current will flow through all the elements in series. Positive polarities of the meters or the equipments should always be connected to the positive of the supply point and the negative terminals should be connected to the negative of the supply point.
While two equipments are connected in series, the positive of the first equipment should be connected to the positive terminal of the supply point. Negative terminal of the first equipment should be connected to the positive terminal of the second equipment and the negative terminal of the second equipment should be connected to the positive terminal of the third equipment and so on.
Ammeters are used to measure the currents. The ammeters should always be connected in series in the circuit so that the current to be measured flows through the ammeters. In order that, the voltage drop across the ammeter to be very very small so that full current flows through the circuit, the resistance of the ammeter should be very very small. Hence, if the ammeter is connected across the supply or across two points having large voltage drop, very heavy current will flow through the ammeter and the ammeter will get burnt.
If the voltmeter is connected in series, it causes high voltage drop across it and the voltage supplied to the remaining circuit will be less.
Hence, voltmeters should be connected only in parallel and not in series. Find the value of the resistor to be connected in series with the lamp. What is the power lost in the resistance.
A parallel element may also be known as a Shunt Element. In the parallel circuit given in the Fig. All resistances are in Ohms. After finding the current flowing through this equivalent series circuit again the parallel equivalent resistance may be replaced with the corresponding parallel circuit and the current in the parallel paths are calculated as given in the Section 1.
Find the current through the Galvanometer. Solution : The circuit is shown in the figure. A voltage source of 30V is connected to this circuit. Solution: The circuit is as shown in the figure given below. Circuit Concepts and Circuit Elements-I 41 1. If one end of the resistances R1, R2, R3, are all connected together and the other ends of the three resistances are connected to different points of the circuits, as given in the Fig.
In general, more than three resistances can also be connected in Mesh. In some cases, the circuits cannot be solved by means of simple series, parallel or parallel combinations but by finding the equivalent Delta for the given Star connection or equivalent Star connection for the given Delta connection of resistances, the circuit can be resolved into simple Series, Parallel or Series-Parallel combinations.
The same statement can be extended to more than three resistances connected in Mesh and its equivalent Star!! A 1 3 3 1 1 B C 3 Solution: The given combination of resistances between the terminals B and C is neither series combinations nor parallel combination.
If, the star connection between A, B and C is converted into equivalent Delta, we will have a known combination which can be simplified by series parallel simplification. There is Delta and Star connection. Find the current supplied by a 10V Batter connected to PQ.
The two 1. For steady state calculations of A. Resistance is used in both D. The current in resistance will be in phase with the voltage i. Resistance causes Power Loss and loss appears in the form of heat. Hence, sufficient provision should be made to dissipate this loss. Resistance depends upon the dimensions and material of the resistance conductor.
In the case of resistance, the current is setup instantaneously when the voltage is applied and is cutoff instantaneously when the voltage is removed.
The resistance which is in the form of a coil, when used in an A. In precision work, the contact resistance, when the resistance is connected to a terminal should also be taken into account.
The resistance of the electrical transmission lines will have to be very small in order to cause negligible voltage drop across the resistance as it has to carry heavy currents. Thus, the resistance of the transmission lines is generally neglected in calculations.
Resistance is used in any circuit to limit the current. Resistance is used in series resonance circuits to limit the currents at resonance point. Resistance will be used in Wave Shaping Circuits to obtain a different wave form from a given wave form.
Resistance can be used in analog circuits, to solve for other systems like Mechanical Systems, Hydraulic System, etc. Resistance will be used in Filter Circuits to select or reject certain frequencies. Change of resistances as obtained in Resistance Strain Gauges, which convert physical signals like temperature, strain, load, force etc.
Resistance can also be used in Power Factor changing circuits but because it causes Power Loss and additional real power to be supplied, the power factor changing circuits generally do not employ change of resistances.
Resistances are used in quenching the arcs extinguishing the arcs in the case of circuit breakers, while breaking heavy current circuits in electrical transmission and distribution.
Resistance can be used in Measurement Circuits. For example, Variable Resistance is used to balance the bridge networks. Resistance shunt is used to extend the range of an ammeter or galvanometer, by diverting a major part of the circuit current through the shunt resistance so that only the allowable current flows through the ammeter or galvanometer.
The actual current is calculated from the reading of the ammeter or galvanometer using a factor in terms of resistance of the galvanometer and the resistance of the shunt as in the case of parallel circuit. Resistance shunt can also be used as a series resistance causing a small voltage drop across it, so that this voltage drop can be used in CRO Cathode Ray Oscilloscope to trace the current waveform which will be proportional to the voltage waveform across the resistance shunt.
Circuit Concepts and Circuit Elements-I 51 1. In electrical circuits, the cross over of two wires are shown as , whereas in electronic circuits, the cross over is shown as.
In electrical circuits, the junction of wires is shown as , whereas in electronic circuits, the junction is shown is shown as. In electrical circuits, the circuit is given completely including sources and elements whereas in electronic circuits, the circuit will not be shown completely. A pointing arrow with voltage along with its polarity marked indicates the connection to the voltage source of that polarity. The return path is assumed to be through ground by indicating the ground connections at the required places as shown in Fig.
A common ground wire will be run to which all the grounding points will be connected. In electronic circuits like a transistor amplifier, the biasing of the transistor will not be shown separately. Only the input signal and the output load will be shown as in Fig. In such cases, the biasing circuit is assumed to be present. Here resistances R1 and R2 are used for biasing to fix up the operating point in the characteristics of the transistor.
The signal will make an excursion about the operating point. A separate wire for power supply to which power supply points will be connected and a separate grounded earthwire to which the grounding points will be connected, while rigging up the circuit have to be provided. While connecting the circuit the biasing circuit should also be connected. The direction of the conventional current will be opposite to that of electron current. Resistance is a bilateral element and it can be linear or non-linear.
Generally linear resistances are widely used. Resistance is an element which will be used in both D. Capacitance and Inductance elements are generally used in A.
They are used in D. They are also used in filter circuits for allowing or rejecting currents or voltages of certain frequencies. Inductance and capacitance can be used in resonance circuits to select or reject the particular frequency voltage or current.
They can also be used in narrow band filters based on resonance to select or reject a narrow band of frequencies. In the case of resistance parameter, the resistance reduces the current and at the same time causes Power Loss in the resistance. Just like resistance, the capacitance and also the inductance reduce the current, but they store energy in them. The energy stored in the case of capacitance will be in the form of Electrostatic Energy and the energy stored in the case of inductance will be in the form of Electromagnetic Energy.
For an ideal capacitor and for an ideal inductor there will be no power loss. Just like the resistance, the capacitance and also the inductance depend upon the dimensions and geometry.
Capacitance also depends on the dielectric medium between the capacitance plates and the inductance depends up the core material of the inductor. Capacitor is also called Condenser. The electric field E will exists between charged conductors of any arbitrary shape also. If the capacitor is connected in an A. Note : 1. This principle is made use in designing of Pulse and Digital Circuits. The Capacitors used in electronic circuits will have Paper or Ceramic or an electrolyte as the dielectric medium.
The electrolytic capacitors will have polarities marked and they have to be connected — to the same polarities of the supply else the capacitor will burst. The symbol for the electrolytic capacitor is given in Fig. A pure capacitance will have no resistance. The capacitance gets charged to its full value and the voltage across the capacitance remains the same when the capacitor circuit is opened, since, the charge of the capacitance cannot be discharged.
Hence the capacitance gives an electric shock when touched after the circuit is opened. To prevent the shock, the capacitor has to be discharged by connecting a wire across the two terminals of the capacitor. 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.
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