Problem 4-35


Find the power dissipated in the 8 W resistor.


First define is in terms of mesh currents.

is = I1

KVL around mesh 1.

7 I1 + 4 I1 - 4 I3 + 16 I1 - 16 I2 = 0

27 I1 - 16 I2 - 4 I3 = 0 (Eq. 1)

KVL around mesh 2.

16 I2 - 16 I1 + 7 I2 - 7 I3 + 8 I2 - 80 = 0

- 16 I1 + 31 I2 - 7 I3 = 80 (Eq. 2)

KVL around mesh 3.

4 I3 - 4 I1 - 24 is + 20 I3 + 7 I3 - 7 I2 = 0

4 I3 - 4 I1 - 24 i1 + 20 I3 + 7 I3 - 7 I2 = 0

- 28 I1 - 7 I2 + 31 I3 = 0 (Eq. 3)

Solving the three equations yields:

I1 = 4.352 A

I2 = 6.022 A

I3 = 5.291A

Finally, the power dissipated in the 8 W resistor is

P = I2R = I22R = 6.0222 (8) = 290 W

and yet again, the book's answer is incorrect. (This is getting ridiculous!)


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