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Solutions: 1. 2.How Can We Check…node voltages? 1. The reference directions of the element currents and voltages are labeled on this circuit drawing. The subscripts suggest a numbering of the 7 elements of this circuit. That numbering has been used to tabulate the values of the voltage and current of each circuit element. Computer analysis of this circuit indicates that the node voltages are abcd e234 V, 222 V, 294 V, 132 V and 12 Vvvvv v==== = where, for example, va denotes the node voltage at node a. a. Check to see if the node voltages satisfy the constitutive equations of the circuit elements. b. Check to see if the node voltages satisfy agree with the tabulated values of the element currents and voltages. c. Verify that power is conserved. v, V i, A p = iv, W 1 −60.0 −6.0 360 2 12.0 6.0 72 3 162.0 −6.0 −972 4 90.0 −7.50 −675 5 222.0 1.50 333 6 −120.0 −1.50 180 7 −12.0 −1.50 182. Computer analysis of this circuit indicates that the node voltages are abc d e1.555 V, 3.778 V, 13.556 V, 5.559 V and 8.889 Vvvv v v=− =− =− =− = where, for example, va denotes the node voltage at node a. The reference directions of the element currents and voltages are labeled on this circuit drawing. The subscripts suggest a numbering of the 7 elements of this circuit. That numbering has been used to set up a table for the values of the voltage and current for each circuit element. Complete the table. v, V i, A p = iv, W 1 2 3 4 5 6 7 2Solutions: 1. For example we can check: Ohm’s law: 4bd4222 1327.5 A12 12 12vvvi−−=− =− =− =− KCL at node d: bd e4767770222 132 12445 5 512 8 12 8vv viiiiii−−⎛⎞−−⎛⎞=+=+= ⇒− = ⇒− =⎜⎟⎜⎟⎝⎠⎝⎠ The constitutive equation of the VCVS: ()()()61 bd ac2 2 12 132 2 243 294vv vv vv=⇒−=−⇒−= − 2. v, V i, A p = iv, W 1 −2.222 0.2222 −0.4937 2 12 −0.2222 −2.6664 3 1.778 −0.2222 −0.3951 4 −8.00 1.333 −10.664 5 −22.44 1.111 −24.933 6 −5.559 1.111 6.176 7 8.889 −1.111 9.8757


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CLARKSON ES 250 - Node Voltages

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