Reciprocity theorem tutorial of basic electrical circuits course by prof nagendra. Murti, department of electrical engineering,iit madras. Handwritten electricity and magnetism notes pdf lecture download. The circuit should not have any timevarying elements. The reciprocity theorem for the scattered field is the. Nptel, online courses and certification, learn for free. This is how we can find corresponding solutions for the circuit once. In the above figure, the current in the r3 branch is i3 with a single source vs. An antenna or aerial is an electrical device which converts electric power into radio waves, and vice versa. Reciprocity theorem is one of the most important theorems in electromagnetics. Youll also study and analyze the transient and steadystate response of circuits and electric circuits using network theorems and twoport parameters. It is clear from the figure above that the voltage source and current sources are interchanged for solving the network with the.
An antenna or aerial is an electrical device which converts electric power into radio. The shortest known proof also uses a simplified version of double. This page is about reciprocity theorems in classical electromagnetism. With sources j 1 and m 1 turned on, generating elds e 1 and h 1, and j 2 and m 2 turned o, and vice versa. Law of quadratic reciprocity let p and q be distinct odd prime numbers, and define the legendre symbol as. Three applications of the reciprocal theorem by kirsten mckay. Explanation of reciprocity theorem in the above figure, there are three resistances r 1, r 2, and r 3 along with voltage source v which is an excitation for the circuit. Of relatively elementary, combinatorial proofs, there are two which apply types of double counting. Using the reciprocal theorem and the principle of superposition, this dissertation examines three procedures for obtaining the impedance functions and driving force vectors necessary for a soilstructure interaction analysis.
Oct 25, 2020 but every complex reciprocal passive network can be simplified into a simple network. It also tells us what is possible or impossible in the design of many systems. This theorem is used in the bilateral linear network which consists of bilateral components. Two port parameters continued reciprocity in resistive networks. The law of quadratic reciprocity, noticed by euler and legendre and proved by gauss, helps greatly in the computation of the legendre symbol. Jan 17, 2015 for the love of physics walter lewin may 16, 2011 duration. With sources j 1 and m 1 turned on, generating fields e 1 and h 1, and j 2 and m 2 turned off, and vice versa.
If we take an arbitrary point, the potential at that point due to the four charge system is given by the electric field is obtained by taking the gradient of the above. The reciprocity theorem states that the current at one point in a circuit due to a voltage at a second point is the same as the current at the second point due to the same voltage at the first. Nptel syllabus number theory web course course outline division algorithm, euclids algorithm, linear diophantine equations, prime numbers, fundamental theorem of arithmetic, distribution of primes, fermat and mersenne primes, primality testing and factorization. In these circuit theory and network analysis pdf notes, we will study the basic circuit concepts in a systematic manner suitable for analysis and design. Reciprocity theorem for conductors ii an example youtube. Steps for solving a network utilizing reciprocity theorem step 1 firstly, select the branches between which reciprocity has to be established. With it we can develop physical intuition to ascertain if a certain design or experiment is right or wrong. With it we can develop physical intuition to ascertain if a.
In number theory, the law of quadratic reciprocity, like the pythagorean theorem, has lent itself to an unusual number of proofs. Introduction to network theorems free online course alison. Introduction to time varying electrical networks nptel. The reciprocity theorem is explained with the help of the circuit diagram shown below.
Since the system is linear time invariant, it can be written as the. Tellegens theorem is one of the most powerful theorems in network theory. Dirichlet lfunctions and primes in arithmetic progressions pdf 19. Learn for free, pay a small fee for exam and get a certificate. The reciprocity law from euler to eisenstein 69 theorem 1. Circuit theory network theorems exam study material for gate ece. Reciprocity theorem is like \titfortat relationship in humans. The chapter concludes with a brief introduction to millmans theorem and the substitution and reciprocity theorems. Reciprocity in electrical networks is a property of a circuit that relates voltages and currents at two points. The geometry for proving reciprocity theorem when the surface s does not enclose the sources. Gate preparation, nptel video lecture dvd, electronicsandcommunicationengineering, circuittheory, networktheorems, ohms law, kirchoffs laws, direct current circuit, dc circuit, alternating current circuit, ac circuits, resistors in series circuit, series circuit, resistor in parallel circuits, parallel circuits, mesh current method, node voltage method, dc and ac circuits analysis. The theorem can easily be understood by this following example. Bee 301 circuit theory academic course description bharath.
Review of electrical network basics, incidence matrix, tellegens theorem. Circuit theory reciprocity theorem exam study material for gate ece. Modular arithmetic, linear congruences, chinese remainder theorem. Circuit theory network theorems exam study material for. Mcdonald joseph henry laboratories, princeton university, princeton, nj 08544 april 3, 2010 1problem consider any two antennas, labeleda and b, that can be operated as twoterminal devices. The course covers static and dynamic electric and magnetic fields, and the principles of electromagnetic induction.
Several hundred proofs of the law of quadratic reciprocity most of them being variants of previously known proofs have been published. Under basic electrical engineering in many electrical networks it is found that if the positions of voltage source and ammeter are. At the wall x0 the moment felt is the maximum moment or pl, but at the end of the beam, the moment is zero because moments at the locations do not contribute to the overall moments. In this video, i talked about the basic of reciprocity theorem and solved a numerical example. Now, we will find the equivalent circuit for two terminal resistive circuit with sources. Due to its subtlety, it has many formulations, but the most standard statement is. See also reciprocity theorem disambiguation for unrelated reciprocity theorems, and reciprocity disambiguation for more general usages of the term in classical electromagnetism, reciprocity refers to a variety of related theorems involving the interchange of timeharmonic electric current densities sources and the. Castiglianos theorem illinois institute of technology. We will use castiglianos theorem applied for bending to solve for the deflection where m is applied. Electric network theory deals with two primitive quantities, which we will refer to as. The reciprocity theorem for the scattered field is the progenitor of the generalized optical theorem huub doumaa ion geophysicalgxt imaging solutions, 225 east 16th avenue, suite 1200, denver, colorado 80203. Lower and higher pairs, degrees of freedom, various types of mechanisms, their inversions and. Tellegens theorem cntd, its use to prove reciprocity in bilateral networks, reciprocity in networks with controlled sources. Thevenin theorem, norton theorem, superposition theorem, reciprocity theorem, maximum power transfer theorem.
In these electricity and magnetism notes pdf, we will study the concepts of electromagnetism learnt at school from a more advanced perspective and goes on to build new concepts. Basic electrical circuits electronics and communication. Since and are arbitrary numbers, the only possibility for eq. Reciprocity theorem theory and solved example w subtitles. Elements, superposition and reciprocity, thevenins theorem and nortons theorem. Verify the reciprocity theorem for the given network. Nptel provides elearning through online web and video courses various streams. Terminal pairs and ports, network function for the one port and two port, the calculation of network function a ladder network b general networks. The application of the superposition theorem and the concept of duality in electrical circuits will also be covered in this course. Then, this course will teach you how to derive the equations for thevenins theorem, as well as show examples of thevenins theorem with dependent sources. Notice that the primes where 5 is a quadratic residue all have units digits 1 or 9, while the primes where 5 is a nonresidue all have units digits 3 or 7. By uniqueness theorem, these four are the appropriate charges to satisfy the required boundary conditions.
The network where reciprocity theorem is applied should be linear and consist of resistors, inductors, capacitors and coupled circuits. Bettis theorem, also known as maxwellbetti reciprocal work theorem, discovered by enrico betti in. R n is the input or equivalent resistance at the terminals when. Introduction to electromagnetism dvd media storage type. If antenna b is used as a receiver, the opencircuit no load voltagevoc b induced across its terminals by the radiation from antenna a with drive current ia.
In these number theory notes pdf, we will study the micro aptitude of understanding aesthetic aspect of mathematical instructions and gear young minds to ponder upon such problems. Dio1893 problem xiv in book 6, which contains a part of the first complementary law of the quadratic reciprocity. Gate preparation, nptel video lecture dvd, electronicsandcommunicationengineering, circuittheory, reciprocity theorem, ohms law, kirchoffs laws, direct current circuit, dc circuit, alternating current circuit, ac circuits, resistors in series circuit, series circuit, resistor in parallel circuits, parallel circuits, mesh current method, node voltage method, dc and ac circuits. Nov 26, 2020 reciprocity analysed by this new paradigm is called strong reciprocity. Let \p\ be an odd prime and \q\ be some integer coprime to \p\. Reciprocity theorem example with solution electronics tutorials. Most of the energy distribution theorems and extremum principles in network theory can be derived from it. Reciprocity theorem states that in any branch of a network or circuit, the current due to a single source of voltage v in the network is equal to the current through that branch in which the source was originally placed when the source is again put in the branch in which the current was originally obtained.
Lecture 10 thevenin and norton theorem and equivalent circuits. Learn about the types of network theorems used in circuit analysis, as well as the implication of linearity properties in different electrical circuits. In a reciprocal network, the transfer impedance or transfer. Reciprocity theorem an important aspect of reciprocity theorem is that it does not hold for all networks. The various resistances r 1, r 2, r 3 is connected in the circuit diagram above with a voltage source v and a current source i. The geometry for proving reciprocity theorem when the surface sencloses the sources. These gate study material is also useful for other exams like ies, barc. This is known as the multiplicativity of legendre symbol. As per reciprocity theorem, in a linear passive network, supply voltage v and output current i are mutually transferable. Circuit theory and network analysis pdf notes download. Fundamentally, tellegens theorem gives a simple relation between magnitudes that satisfy kirchhoffs laws of electrical circuit theory. The ratio of v and i is called the transfer resistance. The reciprocity theorem can be used to distill and condense the interaction between two antennas over a complex terrain as long as the terrain comprises reciprocal media. The reciprocity theorem for the scattered field is the progenitor of the generalized optical theorem huub doumaa ion geophysicalgxt imaging solutions, 225 east 16th avenue, suite 1200, denver, colorado 80203 ivan vasconcelos school of geosciences, university of.
A twoport network a kind of fourterminal network or quadripole is an electrical network or device with two pairs of terminals to connect to external circuits. The first theorem to be introduced is the superposition theorem, followed by thevenins theorem, nortons theorem, and the maximum power transfer theorem. Electrodiction offers a complete channel of guidance on topics such as analog electronics, microprocessors, digital electronics and circuit theory. This is a hard question, we dont know the answer to. Quadratic reciprocity in number theory, the law of quadratic reciprocity is a theorem about modular arithmetic that gives conditions for the solvability of quadratic equations modulo prime numbers. Show the application of reciprocity theorem in the network given below figure 9. Quadratic reciprocity motivation, iv we can see a few patterns in these results. Network theory study notes handwritten free pdf gate fe. Aoe 3054 notes on maxwells reciprocal theorem page 3 of 5 then the lefthand side is a function of alone, and the righthand side is a function of alone.
If this source is replaced to the r3 branch and shorting the source at the original location, then the current flowing from the original location i1is the same as that of i3. An antenna reciprocity theorem princeton university. Two terminals constitute a port if the currents applied to them satisfy the essential requirement known as the port condition. Mar 16, 2020 using reciprocity theorem, it is possible to conclude whether a network is linear or nonlinear.
Network theorems with circuits used in electrical engineering. Reciprocity theorem the reciprocity theorem states that in a linear passive bilateral network by changing the voltage source from branch 1 to branch2, the current i in the branch 2 appears in branch 1. Riemanns zeta function and the prime number theorem pdf 17. Two port parameters continued reciprocity in resistive networks z parameters. Hence, we observed that when the source was in branch xy as in figure 8a, the ab branch current was 1. Quadratic residues, quadratic reciprocity, lecture 9 notes.
Circuit theory reciprocity theorem exam study material for. Handwritten electricity and magnetism notes pdf lecture. This free online introduction to network theorems course will teach you about. In its simplest form, the reciprocity theorem states that if an emf e in one branch of a reciprocal network produces a current i in another, then if the emf e is moved. Reciprocity theorem example with solution electronics.
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