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Assessment Problem # 4.12

Assessment Problem # 4.12. Mesh-Current Method Special Case Current Source in a branch. Use the mesh-current method to find the power dissipated in the 1 Ω resistor. Identify the mesh currents. I 3. I 2. I 1. Assign the voltage polarities Identify the voltage @ the 2A source. +. -.

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Assessment Problem # 4.12

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

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

  3. Identify the mesh currents I3 I2 I1 ECE 201 Circuit Theory I

  4. Assign the voltage polaritiesIdentify the voltage @ the 2A source + - I3 - + + - + - V - + I2 I1 + - - + ECE 201 Circuit Theory I

  5. Write the mesh-current equations (1) + - I3 - + + - + - V - + I2 I1 + - V + 2I1 – 2I2 = 10 - + ECE 201 Circuit Theory I

  6. Write the mesh-current equations (2) + - I3 - + + - + - V - + I2 I1 + - -2I1 +5I2 -2I3 = 6 V + 2I1 – 2I2 = 10 - + ECE 201 Circuit Theory I

  7. Write the mesh-current equations (3) + - I3 -V -2I2 +4I3 = 0 - + + - + - V - + I2 I1 + - -2I1 +5I2 -2I3 = 6 V + 2I1 – 2I2 = 10 - + ECE 201 Circuit Theory I

  8. Eliminate V from the equations for meshes 1 and 3 ECE 201 Circuit Theory I

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

  10. Solving • Result looks like I1 = 7A I2 = 6A Calculate I3 I3 =I1 – 2 = 5A ECE 201 Circuit Theory I

  11. Find the power dissipated in the 1Ω resistor • P1Ω = (I2)2R = (6)2(1) = 36 W ECE 201 Circuit Theory I

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