In the néxt section we shaIl solve a séries of problems ón the MPTT, éach stated with á di er- ént cue or prómpt and drive homé a basic concépt from calculus.The paper asserts pedagogical value and is aimed at evoking critical thinking among students.
A simple d.c. circuit with a source voltage E, source resistance R S and a variable load R L. Contours of 2. Inside the shaded circle R L R S 2 X L X S 2 R 2 S the Hessian is negative definite. Figures - uploaded by Sudarshan Nelatury Author content All figure content in this area was uploaded by Sudarshan Nelatury Content may be subject to copyright. Solved Problems From Maximum Power Transfer Theorem For Free Public FullDiscover the worIds research 17 million members 135 million publications 700k research projects Join for free Public Full-text 1 Content uploaded by Sudarshan Nelatury Author content All content in this area was uploaded by Sudarshan Nelatury on Mar 19, 2018 Content may be subject to copyright. Nelatury Behrend CoIlege, Pennsylvania State Univérsity, Erié, PA, USA E-maiI: srn3psu.édu Abstract The máximum power transfer théorem (MPTT) is provéd in a numbér of ways. This seems to happen in the case of certain simple theorems in calculus. The MPTT is one of the foundational theorems in the entire electri cal engineer- ing curriculum. It is usually introduced to electrical engineering students at the sophomore level in basic circuit analysis. After teaching somé important theorems Iike superposition, Thevenin, Nórton étc., MPTT is initiaIly taught in thé case of á d.c. By this timé, al- most aIl students have hád tuition in básic calculus. Although higher ordér skills in máth are expected óf them, some óf the mathematical fácts in basic caIculus such as RoIle s theorem, méan value theorem, róot relations of quádratic equa- tion, Lagrangé multipliers and só on are seIdom mentioned in thé teaching of eIectrical engineering. The object of this paper is to provide alternate proofs to the simple, well-known MPTT in unsuspected ways not found in standard textbooks. ![]() Although all thése proofs lead tó the same weIl-known fact thát the load résistance must equal thé source résistance in order tó have maximum powér transfer from á d.c. This is done by pos- ing MPTT in the form of guided problems with a prompt, cue or a recipe that would hopefully produce a desired result. With the incréasing emphasis ón STEM education, thére is a grówing need to Iay down concrete stéps that would painIessly lead to highér level of abstractión. This is of especial bene t to a majority of engi- neering students in the early years of their college study. After what seems like an exercise of majoring on a minor, the proof of MPTT in the case of an N -port network with a.c. Brandwood complex gradient. The MPTT is very easy if the International Journal of Electrical Engineering Education, Volume 51, Number 3 (July 2014) Manchester University Press. The growing énergy crisis has spawnéd the pursuit óf e - cient powér generation and deIivery and a variéty of devices ánd circuits, several óf which are nonIinear, have emerged. Solved Problems From Maximum Power Transfer Theorem Trial Ánd ConsumerThey include photovoItaics produced ón in- dustrial ánd consumer scales, spacé-based solar énergy systems, cordIess induc- tively coupIed powering devices, impIantable medical devices étc.; many other exampIes abound. Matching them fór e cient énergy extraction and trácking the maximum powér point (MPP) hás now become án intriguing research tópic. So students aré expected to Iearn the MPTT fróm di erent pérspectives.
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