Page 107 of the text by Nilsson and Riedel

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Page 107 of the text by Nilsson and Riedel Assessment Problem #4.7 Page 107 of the text by Nilsson and Riedel ECE 201 Circuit Theory I

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

Identify the mesh currents ECE 201 Circuit Theory I

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

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

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

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

Write the equations in matrix form ECE 201 Circuit Theory I

Check for off-diagonal symmetry ECE 201 Circuit Theory I

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

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

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