Power dissipated in circuit: What is the total power dissipated in this circuit?

[zealeth]

Homework Statement

Use the node-voltage method to find the total power dissipated in the circuit in the figure if i1 = 2A , i2 = 3A and v1=16V

Homework Equations

P = iv
v = iR
P = v^2/R

G = 1/R

\sumG connected to node 1 * v_1 - \sumG between node 1 and 2 * v_2 = Current source into node 1

\sumG connected to node 2 * v_2 - \sumG between node 1 and 2 * v_1 = Current source into node 2

The Attempt at a Solution

Nodal analysis. Going clockwise from the node above the voltage source, each node is labeled 1 through 5.

1:
v_1 = -16

2:
-2 = v_2(1/12+12/25+1/20) - v_3(1/20) - v_4(1/25) + 16(1/12)

3:
5 = -v_2(1/20) + v_3(1/20+1/40) - 0 - v_5(1/40)

4:
0 = 0 - v_2(1/25) + 0 + v_4(1/25+1/40) - v_5(1/40)

5:
-3 = 0 - v_3(1/40) - v_4(1/40) + v_5(1/40+1/40)

Solving, v_2 = -10.8, v_3 = 43.7, v_4 = -18.1, v_5 = -47.2

Power dissipated:
P = \sum(v_a - v_b)^2/R
P = (-16+10.8)^2/12 + (-10.8-43.7)^2/20 + (-10.8+18.1)^2/25 + (43.7+47.2)^2/40 + (-18.1+47.2)^2/40
P = 380.6 W (incorrect obviously)

Feedback: "Not quite. Check through your calculations; you may have made a rounding error or used the wrong number of significant figures."

 

[NascentOxygen]

Hi zealeth! http://img96.imageshack.us/img96/5725/red5e5etimes5e5e45e5e25.gif

Check your equation for node 2.

You started by saying let V1=-16, so this means V4 must be 0v, fixed at 0v. You can't later determine V4 to be -18.1v.

 

[zealeth]

Hi zealeth! http://img96.imageshack.us/img96/5725/red5e5etimes5e5e45e5e25.gif

Check your equation for node 2.

You started by saying let V1=-16, so this means V4 must be 0v, fixed at 0v. You can't later determine V4 to be -18.1v.

Node 2 was just a typo I think, but nonetheless I got it (P dissipated = 389 Watts). V_4 being 0 was indeed the problem I was having. Thanks.