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Assessment Problem #4.7

Assessment Problem #4.7. Determine the power delivered by the 80 V source and the power dissipated in the 8 Ω resistor using the mesh-current method. Identify the mesh currents. I 3. I 2. I 1. Assign the voltage polarities. +. -. I 3. -. +. -. +. +. -. +. -. -. +. +. I 2.

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Assessment Problem #4.7

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  1. Assessment Problem #4.7 ECE 201 Circuit Theory I

  2. Determine the power delivered by the 80 V source and the power dissipated in the 8 Ω resistor using the mesh-current method. ECE 201 Circuit Theory I

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

  4. Assign the voltage polarities + - I3 - + - + + - + - - + + I2 I1 - - + ECE 201 Circuit Theory I

  5. Write the mesh-current equations (1) + - I3 - + - + + - + - - + + I2 I1 - - + 80 = 31I1 - 26I2 - 5I3 ECE 201 Circuit Theory I

  6. Write the mesh-current equations (2) + - I3 - + - + + - + - - + + I2 I1 - - + 80 = 31I1 - 26I2 - 5I3 0 = -26I1 +124I2 -90I3 ECE 201 Circuit Theory I

  7. Write the mesh-current equations (3) + - 0 = -5I1 -90I2 +125I3 I3 - + - + + - + - - + + I2 I1 - - + 80 = 31I1 - 26I2 - 5I3 0 = -26I1 +124I2 -90I3 ECE 201 Circuit Theory I

  8. Write the equations in matrix form ECE 201 Circuit Theory I

  9. Check for off-diagonal symmetry ECE 201 Circuit Theory I

  10. Solving with TI-89 • Check CATALOG for simult( --- press ENTER • [31,-26,-5;-26,124,-90;-5,-90,125],[80;0;0]) hit ENTER • Resulting column vector is I1 = 5A I2 = 2.5A I3 = 2A ECE 201 Circuit Theory I

  11. Calculate the power delivered by the source Psource = (Vsource)(I1) = (80V)(5A) = 400 W + I1 = 5 A - ECE 201 Circuit Theory I

  12. Calculate the power dissipated in the 8Ω resistor P8Ω = (I2)2R = (2.5)2(8) = 50 W I2 = 2.5 A ECE 201 Circuit Theory I

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