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ECE 201 Circuit Theory I1 Assessment Problem # 4.12 Mesh-Current Method Special Case Current Source in a branch

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ECE 201 Circuit Theory I2 Use the mesh-current method to find the power dissipated in the 1 Ω resistor.

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ECE 201 Circuit Theory I3 Identify the mesh currents I1I1 I2I2 I3I3

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ECE 201 Circuit Theory I4 Assign the voltage polarities Identify the voltage @ the 2A source I1I1 I2I2 I3I3 + - + - +- +- +- +- +- V

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ECE 201 Circuit Theory I5 Write the mesh-current equations (1) I1I1 I2I2 I3I3 + - + - +- +- +- +- +- V V + 2I 1 – 2I 2 = 10

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ECE 201 Circuit Theory I6 Write the mesh-current equations (2) I1I1 I2I2 I3I3 + - + - +- +- +- +- +- V V + 2I 1 – 2I 2 = 10 -2I 1 +5I 2 -2I 3 = 6

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ECE 201 Circuit Theory I7 Write the mesh-current equations (3) I1I1 I2I2 I3I3 + - + - +- +- +- +- +- V V + 2I 1 – 2I 2 = 10 -2I 1 +5I 2 -2I 3 = 6 -V -2I 2 +4I 3 = 0

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ECE 201 Circuit Theory I8 Eliminate V from the equations for meshes 1 and 3

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ECE 201 Circuit Theory I9 Write the equations in matrix form Solving with a TI-89, [6,-4;-4,5],[18;2])ENTER

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ECE 201 Circuit Theory I10 Solving Result looks like I 1 = 7A I 2 = 6A Calculate I 3 I 3 =I 1 – 2 = 5A

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ECE 201 Circuit Theory I11 Find the power dissipated in the 1Ω resistor P 1Ω = (I 2 ) 2 R = (6) 2 (1) = 36 W

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