12Spring_hw02_solns

12Spring_hw02_solns - Problem 1 a Use the node voltage...

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a) Use the node voltage method to find v 1 , v 2 , and v 3 . Node 1 equation: v 1 " V o Node 2 equation: % v 2 # v 1 & 2 \$ v 2 2 " I o Node 3 equation: % v 3 # v 2 & 2 " I o Solve the three equations simultaneously, using the fact that V o =8V and I o =2A, to find that v 1 = 8V, v 2 =6V, and V 3 =16V. b) Use the loop current method to find i 1 , and v 2 . Loop 1 equation: # V o \$ 2 i 1 \$ 2 % i 1 # i 2 &" 0 Loop 2 equation: i 2 "# I o Solve the three equations simultaneously to find that i 1 =1A, and i 2 =-2A, remembering that V o =8V and I o =2A. c) Use the properties of linearity/superposition to find v 2 and i 1 , imagining, of course, that you have not already computed these quantities. Assume that v 2 =AV o + BI o and i 1 =CV o +DI o and use SOURCE SUPRESSION to find A, B, C, and D. Problem 1

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Find v 2 - I) first suppress the voltage source V o by setting V o =0 thereby causing V 1 =0. The node voltage v 2 = I o under this condition (substitute v 1 =0 into the node 2 equation). This means that I o =A*0 + Bi o ! B=1.
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