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MIT 6 002 - Problem Set 1

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Massachusetts Institute of TechnologyDepartment of Electrical Engineering and Computer Science6.002 – Circuits & ElectronicsSpring 2005Problem Set #1Issued 2/2/05 – Due 2/9/05Exercise 1.1: Find the equivalent resistance, as viewed from its port, of each resistor networkshown below.R1R2R3R1R2R3R1R3R2R5R4Exercise 1.2: Beginning with 1-Ω resistors, synthesize a resistor of 0.75 Ω and a resistor of1.5 Ω. Use no more than four 1-Ω resistors in each case.Problem 1.1: Each network shown below has several of its branch currents or voltages specifiednumerically. Several other branch currents or voltages are labeled as unknowns. Find all labeledunknown branch currents and voltages.+1V−− 1V+− v1++3V−+v2−i12Ai2i31A+1V−− 2V+− v1++3V−+v2−+ v3−i12Ai2i31A2AProblem 1.2: The circuit shown below has four elements: two resistors, a current source anda voltage source. The resistance of the resistors and the strengths of the sources are all given.Branch currents (ik) and voltages (vk) are also defined for each element.(A) How many nodes are there in the circuit? Write a KCL equation for each node in terms of thebranch currents ik. How many of the KCL equations are independent?(B) How many loops are there in the circuit? Write a KVL equation for each loop in terms of thebranch voltages vk. How many of the KVL equations are independent?(C) Write an expression for the v-i constitutive law for each element.(D) By combining the independent equations from Parts (A) and (B) with the equations from Part(C), you should have a set of eight linear equations, matching in number the set of ikplus vk.Solve the equations to find all four ikand all four vk. Summarize your findings in a table.(E) Find all four branch powers vkik. Show that the sum of the four vkikis zero, and hence thatenergy is conserved in the circuit. (If energy is not conserved, then you made a mistake.)Which branch elements source power and which branch elements sink power?8A+v1−i1i3+ v3−3Ωi4+v4−4V+v2−1Ωi2Problem 1.3: Using the node method, analyze the network below and find all node voltagesand then all branch currents. Note the definition of the reference node.ISR2RR2RRProblem 1.4: The following network has two ports and three resistors. The resistor valuesR1, R2and R3are unknown.NetworkR1R2R3Using the results of the following two experiments performed on the network, find the unknownvalues of the three


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MIT 6 002 - Problem Set 1

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