Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6 002 Circuits Electronics Spring 2005 Problem Set 2 Issued 2 9 05 Due 2 16 05 Exercise 2 1 In each circuit shown below three light bulbs are driven by a single source In two of the circuits the source is a voltage source and in the other it is a current source Assume that one of the three light bulbs burns out and becomes an open circuit Do the other two light bulbs get brighter get dimmer or exhibit no change in intensity Why Exercise 2 2 Using the node method develop a set of simultaneous equations for the network shown below that can be used to solve for the three unknown node voltages in the network Express these equations in the form e1 G e2 S e3 where G is a 3 3 matrix of conductance terms and S is a 3 1 vector of terms involving the sources You need not solve the set of equations for the node voltages R2 R3 e2 e1 R5 e3 R4 R1 I R6 V Problem 2 1 This problem analyzes the network shown below by two methods superposition and the direct application of the node method You should compare for yourself the work required to analyze the network by these two methods A First use superposition to determine e1 and e2 That is superpose the two partial node voltages obtained with only single sources active to find the total node voltages Remember that a zero valued voltage source is a short circuit and a zero valued current source is an open circuit Hint rather than employing the node method twice once for each partial analysis consider employing alternative simpler analyses involving the use of parallel and series resistor combinations and voltage and current dividers B Second use the node method to directly determine e1 and e2 in total C Compare the solutions to Parts A and B The two solutions should be the same e1 e2 R1 R3 R2 V I R4 Problem 2 2 Two networks N1 and N2 are described graphically in terms of their i v relations and connected together through a single resistor as shown below A Find the Thevenin and Norton equivalents of N1 and N2 B Find the currents i1 and i2 that result from the interconnection of N1 and N2 v V1 N1 R i1 N1 v1 i2 v2 I2 I1 N2 N2 V2 i Problem 2 3 Find the Thevenin and Norton equivalents of the following networks and graph their i v relations as viewed at their ports Network A i v Network B i R1 R2 i R2 v I Network C R1 R1 v V R2 I V Problem 2 4 This problem studies the network shown below The network contains a 2 for v 0 and i 0 for v 0 where nonlinear resistor having the terminal relation iN vN N N N is a constant with units A V2 Assume that and vS are both positive A Analyze the network graphically to determine iN and vN in terms of vS and the network parameters To do so note that the current source and linear resistor together constrain the relation between iN and vN and that the nonlinear resistor also constrains this relation State the two constraints and on a single graph sketch both constraints and identify the solution for iN and vN Within what voltage range will vN lie B Analytically solve for vN in terms of vS Check that this solution is consistent with the graphical solution from Part A C Now let vS VS vs and let vN VN vn where VS and VN are constant large signal voltages which together form an operating point and vs and vn are time varying small signal voltages Using the solution from Part B determine VN in terms of VS Then linearize the solution from Part B around the operating point to determine vn approximately in terms of vs and VS R vS iN Nonlinear Resistor vN
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