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EE215w03fs

# EE215w03fs - EE215 Winter 2003 Final Exam Solutions Monday...

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EE215 Winter 2003 Final Exam Solutions Monday, March 17, 2003, 2:30 – 4:20pm Name: ______________________________ ID#: ________________ Section: ___ Please show all steps in solving the problem. Clearly mark your final answers and don’t forget the units. Problem 1 (20 points) Consider the wireframe tetrahedron to the right. Each resistor has a value of 1 . What is the equivalent resistance between nodes a and d ? (Note: a tetrahedron is a pyramid with 4 triangular sides.) Answers and grading guide: This is similar but less complicated than Homework 3, Problem 10. We can use the same approach as in the homework solution (node voltage method), by setting v a = 0V and v d = 1V. Then we can write the equations for nodes b and c : c : ( v c v a )+( v c v b ) + ( v c v d ) = 3 v c v b – 1 = 0 b: 3 v b v c – 1 = 0 Solving these equations yields v b = v c = ½V. Thus the currents are i ba = i ca = i db = i dc = ½A, and i da = 1A and i bc = 0A. So the total current is 2A, and the equivalent resistance R eq = ½ . Solution shortcuts: Because of the symmetry of the tetrahedron, it is easy to see that v b = v c = ½V, without using any analysis. Also note that this is essentially a Wheatstone Bridge with equal resistors (plus another resistor R ad in parallel). Alternative solution: It is also possible to use a delta-wye transform, for example on the resistors abc. The three new resistors have the value R 1 = R 2 = R 3 = 1/3 . The resulting circuit can be reduced by serial and parallel transforms: ( R 1 + ( R 2 + R cd )||( R 3 + R bd ))|| R ad = (1/3 + 4/3||4/3)||1 = ½ . If node voltage method is used: Each correct node voltage equation: 5 points. Correct values for v b and v c : 5 points. If circuit transforms are used: Correct delta-wye transform: 10 points. No delta-wye transform: 0 points.

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Problem 1* (20 points) Consider the wireframe tetrahedron to the right. Each resistor has a value of 1 . What is the equivalent resistance between nodes a and b ? (Note: a tetrahedron is a pyramid with 4 triangular sides.) Answers and grading guide: This is similar but less complicated than Homework 3, Problem 10. We can use the same approach as in the
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EE215w03fs - EE215 Winter 2003 Final Exam Solutions Monday...

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