BME211HW3 - Homework#3 Solutions P4.3-2 Express the branch...

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Homework #3 Solutions P4.3-2 Express the branch voltage of each voltage source in terms of its node voltages to get: 12 V, 8 a b c d v v v v = - = = + KCL at node b : ( 29 12 0.002 0.002 12 8 4000 4000 4000 b b a b v v v i i v i - - - = + = + + = + KCL at the supernode corresponding to the 8 V source: 0.001 4 4000 4000 d d v i v i = + = + so ( 29 4 4 8 4 4 4 V b d d d d v v v v v + = - + + = - = - Consequently 4 8 4 V and 2 mA 4000 d b c d v v v v i - = = + = = = P4.3-4 Apply KCL to the supernode: ( 29 8 12 8 12 0 500 125 250 500 a a a a v v v v + - + - + + + = Solving yields 4 V a v =
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P4.3-7 Apply KCL at nodes 1 and 2 to get 1 1 1 2 1 2 10 23 3 150 1000 3000 5000 v v v v v v - - = + - = 2 1 3 3 1 3 10 -4 19 50 4000 5000 2000 v v v v v v - - + = + = Solving, e.g. using MATLAB, gives 1 1 1 2 23 3 150 7.06 V and 4.12 V 4 19 50 v v v v � � - = = = � � - � � Then 1 2 b 7.06 4.12 0.588 mA 5000 5000 v v i - - = = = Apply KCL at the top node to get: 1 2 a 10 10 7.06 10 4.12 10 4.41 mA 1000 4000 1000 4000 v v i - - - - = + = + = - P4.4-8 Label the node voltages. First, v 2 = 10 V due to the independent voltage source. Next, express the controlling current of the dependent
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