Find the Three Mesh Currents: A Step-by-Step Guide

[xlu2]

Homework Statement

Find the three mesh current.

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!

 

[lewando]

KVL says nothing about power in a loop.

 

[xlu2]

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.

 

[lewando]

Okay, then then power supplied by the active devices should equal the power consumed by the passive devices. What are you getting?

 

[xlu2]

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]

I mean, what, specifically, are you getting for each element?

 

[xlu2]

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!

 

[lewando]

Good work by you!