Node Voltage Analysis: Solve for V1, V2, V3 and V4

[ohdrayray]

Homework Statement

Solve for V1, V2, V3 and V4 (in decimals) using node voltage analysis method for the following:

Homework Equations

:
Node Voltage Analysis

The Attempt at a Solution

:
For Node #1:

V_{1} = 6 V


For Node #4:

V_{4} = 16 V


For Node #2:

\frac{V_{2}-V_{3}}{3300} + \frac{V_{2}}{1000} + \frac{V_{2}-6}{1500} = 0

0.00197V_{2} - 0.000303V_{3}= 0.004 --> equation 1


For Node #3:

\frac{V_{3}-V_{2}}{3300} + \frac{V_{3}}{4700} + \frac{V_{3}-16}{2200} = 0

-0.000303V_{2}+0.00097V_{3} = 0.007273

V_{3}= 0.3124V_{2} + 7.4979 --> equation 2


Solve for V_{2} by substituting V_{3} into equation 1:

0.00197V_{2}-0.000303(0.3124V_{2} + 7.4979) = 0.004

0.001875V_{2} - 0.006272 = 0

V_{2} = 3.3451 V


Solve for V_{3} by substituting V_{2} into equation 2:

V_{3}= 0.3124(3.3451) + 7.4979

V_{3} = 8.5428 V

I mainly just wanted to know if my equations were right, I think that I've done it correctly, but at the same time I'm not sure, haha. Thank you in advance!

 

[gneill]

Hi ohdrayray, welcome to Physics Forums.

Your formulae and methodology are fine. The results are good to two decimal places.