C5-activities - ELECTRIC CIRCUITS ECSE-2010 Activity 5-1...

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1 ELECTRIC CIRCUITS ECSE-2010 Class 5 Activity 5-1 ACTIVITY 5-1a 30 V 8 V 5 mA 10 k 6 k 2 k v + Find v using Node Voltage Analysis 4 Nodes 2 Voltage Sources 1 Ref 1 Unknown Node Voltage, v ACTIVITY 5-1a 30 V 8 V 5 mA 10 k 6 k 2 k v + KCL at v: v 30 V v8 V + 0 V 5 v3 0 6 + (v 8) 30 (v 8) 0 10 2 +− + ⎛⎞ ++ = ⎜⎟ ⎝⎠ Use mA, k , V ACTIVITY 5-1a 30 V 8 V 5 mA 10 k 6 k 2 k v + v 30 V V + 111 v ( )55. 834 61 02 ++= + −+ Use mA, k , V 23 v( ) 8.2 30 = v1 0 . 7 V = ACTIVITY 5-1b 24 V 90 V 1 A 3 15 10 2 4 8 7 5 Nodes 2 Voltage Sources 1 Ref 12 2 Unknown Node Voltages v, v 0 V 24 V 1 v 2 v 2 v9 0 + 6
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2 ACTIVITY 5-1b 1 KCL at Node v : 11 121 2 vv2 4vvv( v9 0 ) 0 6 3 15 10 −−− + +++ = 2 KCL at Node v : 21 2 2 1 2 v v v (v 90) v v 24) 10 15 2 4 10 8 7 −+ ++ + + = ACTIVITY 5-1b 1 12 Node v : 1111 1 1 v( ) v( ) 8 9 17 3 15 6 10 15 10 + ++ + − − =+= 2 Node v : 2 4 ) 9 1 1 51 0 61 01 5 1 5 + + += + + ACTIVITY 5-1b Multiply by 30: v (20) v ( 5) 510 v ( 5) v (12) 192 +− = = 1 2 G: matrix(2,3,[20, 5,510, 5,12, 192]); V: gaussjord(G); v2 4 V v6 V =− = => = => = −
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C5-activities - ELECTRIC CIRCUITS ECSE-2010 Activity 5-1...

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