Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6 002 Circuits Electronics Spring 2006 Problem Set 1 Issued 2 8 06 Due 2 15 06 Find the equivalent resistance as viewed from its port of each resistor network Exercise 1 1 shown below R1 R2 R3 R1 R2 R1 R3 R2 R3 R4 R5 Exercise 1 2 What is the largest valued resistor that can be fabricated by combining a 1 a 2 and a 3 resistor What is the smallest valued resistor By combining these three resistors how can one fabricate a 1 5 resistor Problem 1 1 Each network shown below has several of its branch currents or voltages specified numerically Several other branch currents or voltages are labeled as unknowns Find all labeled unknown branch currents and voltages 2V v1 v2 4V 3V v1 2V i1 i3 1 mA 2 mA 1 mA 3V v2 i2 v3 4V i1 1 mA i3 i2 2 mA Problem 1 2 The circuit shown below has four elements two resistors a current source and a 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 the branch 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 the branch 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 ik plus vk Solve the equations to find all four ik and all four vk Summarize your findings in a table E Find all four branch powers vk ik Show that the sum of the four vk ik is zero and hence that energy 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 v2 i2 1 k i1 3V v1 i3 v2 2 k i4 v4 9A Problem 1 3 Using the node method analyze the network below and find all node voltages and then all branch voltages and currents Note the definition of the reference node e1 5R R R IS e2 e3 5R R Problem 1 4 The following network has two ports and three resistors The resistor values R1 R2 and R3 are unknown Network R1 R2 R3 Using the results of the following two experiments performed on the network find the unknown values of the three resistors Network 1 mA 2V 3V Network 11 V 3 mA
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