Massachusetts Institute of TechnologyDepartment of Electrical Engineering and Computer Science6.002 – Circuits and ElectronicsSpring 2003Handout S03-016 - Homework #3Issued: Thurs. Feb 20Due: Fri. Feb 28Problem 3.1: This problem is concerned with nodal analysis and the superposition theorem.A linear circuit containing two sources is shown below. Conductance values are in mhos (Ω−1).+−V I0.2Ω−10.2Ω−10.1Ω−10.1Ω−1iAA(A) Write node equations which enable the complete determination of the voltages and currents inthe circuit.(B) Solve these equations for the node to reference voltages (in terms of V and I ) and calculatethe value of the current iA(also in terms of V and I ) in the resistor marked A. Pay attentionto the polarity of iA!(C) Sketch the circuit when the voltage source is acting alone and the current source is dead.(D) By inspection, and the use of series-parallel relationships, determine the component of iAthatresults from the voltage source alone.(E) Sketch the circuit when the current source is acting alone and the voltage source is dead.(F) As in Part (D), determine the component of iAthat results from the current source alone.(G) Add the components determined in (D) and (F) together. Compare this result for iAwith thatyou obtained in Part (B).If the results are not the same, check your answer.Problem 3.2: This problem is concerned with equivalent circuits. Two gray boxes are con-nected as shown.BOXAaa’BOXBbb’iaib3kΩv+-As shown the voltage v across the 3kΩ resistor is 6V.When the 3kΩ resistor is replaced by a short circuit, the currents at the terminals of the boxes areia= −6mA and ib= 2mA.(A) What is the value of v when the 3kΩ resistor is replaced by an open circuit (i.e., the resistoris removed)?(B) Is there sufficient information to determine the Norton equivalent circuits of each box? Explain.(C) You are now free to cut the connections between the boxes. What singlemeasurement wouldyou make on either (but not both) boxes to determine the Norton equivalents of both boxes?(D) Assume a value for that measurement and specify the equivalent circuits of each box.Problem 3.3: Determine the Thevenin equivalent circuit at the terminals indicated of thecircuit shown below. Label the terminals and indicate element values and source polarity.+−12V2kΩ4kΩ6kΩ1mΑ3kΩa bProblem 3.4: This problem concerns Thevenin and Norton equivalents.A gray box has the terminal characteristics shown. Devise both Thevenin and Norton equivalentcircuits which represent the terminal characteristics of the box. Be sure to show element valuesand source polarities and label the terminals.BOXiv+-GRAYabi (milliamperes)v (Volts)-25Problem 3.5: A network has the Norton equivalent circuit shown below:0.5kΩab10mAIt is connected to the following circuit: terminal a to a0, terminal b to b0.+−1kΩ2kΩ0.5kΩ6Va’b’Determine the power provided by or absorbed by the 6V source. Make clear in your answersdirection of power flow at the voltage
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