Did I do the nodal analysis right?

[asdf12312]

can someone confirm i did this rite:

Homework Statement

Find I(x)

Homework Equations

see the next part please

The Attempt at a Solution

using nodal analysis method i have 2 nodes and these are the equations i got for each, after simplification:

V1: (5/2)V1-V2=21
V2: (5/2)V2-V1=10.5

Using cramer's law, this is matrix i got when i plugged in above equations:

| 5 -2 | |V1| = |42|
| -2 5 | |V2| = |21|

V1=[(42*5)-(21*-2)/(5*5)-(-2*-2)]=12V
V2=[(5*21)-(-2*42)/(5*5)-(-2*-2)]=9V

now recognize that I(x)=V2/10, i got I(x)=0.9A.

so my question is two-part: 1st, did i do this rite? 2nd, is there easier way to solve for I(x)?

 

[gneill]

I think you'll want to check the polarity of the 10.5V source, then verify your equations.

With only two equations in two unknowns it may be faster to solve by substitution rather than fire up the Cramer's Rule machinery

 

[asdf12312]

yeah your rite, i didnt see that. since the sign of the 10.5 is opposite all i have to do is negate the 21 in the matrix. so solving i get V1=8 and V2=-1. so I(x)=-0.1A?


and btw i did do substitution to check my answer but i wanted to try out cramer's rule to see that i could do it correctly. and in my 1st try i did get the same answers for both methods.

 

[gneill]

yeah your rite, i didnt see that. since the sign of the 10.5 is opposite all i have to do is negate the 21 in the matrix. so solving i get V1=8 and V2=-1. so I(x)=-0.1A?

That looks better

and btw i did do substitution to check my answer but i wanted to try out cramer's rule to see that i could do it correctly. and in my 1st try i did get the same answers for both methods.

Well that's fine then.

 

[asdf12312]

my teacher wants me to solve I(x) with mesh analysis so i can prove i can use another method to get the same answer, however I'm having trouble. would apreciate if u could tell me what i am doing wrong:

mesh 1: 15(I1)-10(I2)=21
mesh 2: -10(I1)+25(I2)-10(I3)=0
mesh 3: -10(I2)+15(I3)=10.5

i am going under the assumption that I(x) is equal to -I3. my matrix is:

|15 -10 0| |I1)=|21|
|-10 25 -10| |I2|=|0|
|0 -10 15| |I3|=|10.5|

but when i solve this, i get a weird answer, 1.9A for I3. and I know I(x) is supposed to be -0.1A. can u tell me what i am doing wrong??

 

[gneill]

It would appear that the problem lies with your assumption about Ix; Ix is comprised of a suitable sum of the two mesh currents that flow through it.

 

[asdf12312]

thanks your rite, i got it. I(x)=I2-I3=1.8-1.9=-0.1A