Why Do the Calculated Mesh Currents Not Balance Power in Each Loop?

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xlu2
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Homework Statement



Find the three mesh current.

12.jpg


Homework Equations


KVL

The Attempt at a Solution



I numbered the loop 1 with 2 and 3 ohms, loop 2 with 3, 5, and 212 V, and loop 3 with 3, 122V, and 5. All currents are clockwise.

So for Loop 1: 2i1+3(i1-i2)=0
Loop 2: 3(i2-i1)+5(i2-i3)-212=0
Loop 3: 3i3+122+5(i3-i2)=0

I solve the system and got i1=26.4878 A, i2=44.1463A, i3=12.3415 A.

But when I plug them back in for power, I do not get 0 for every loop. So I know I must doing something wrong here. So would anyone please help me to see where I am doing wrong?

Many thanks in advance!
 
on Phys.org
lewando said:
KVL says nothing about power in a loop.

From my textbook, I learned that if we add the powers for all the elements in the circuit, the result should be zero because energy is neither created nor destroyed.
 
Okay, then then power supplied by the active devices should equal the power consumed by the passive devices. What are you getting?
 
lewando said:
Okay, then then power supplied by the active devices should equal the power consumed by the passive devices. What are you getting?

I get a negative number.
 
lewando said:
I mean, what, specifically, are you getting for each element?

2 ohms: P=i1^2*R=26.49^2*2=1403.44
3 ohms: P=3(i1-i2)^2=3(26.49-44.15)^2=935.6268
5 ohms: P=5(i2-i3)^2=5(44.15-12.34)^2=5059.3805
3 ohms: P=3i3^2=3(12.34)^2=456.8268

122 V: P=IV=122*12.34=1505.48
212 V: P=IV=-212*44.15=-9359.8

I got 0.9541. Unbelievable.

I guess all the numbers are correct!