Can someone help me with this ECE problem?

[iamtrout]

Here's the problem:

http://img117.imageshack.us/img117/6602/ece18vk.jpg

I can't figure out how to do part b. I got everything else.

The answer's supposed to be Vb = -12.5V but I can't figure out how the teacher got it.

 

[ColdFusion718]

I don't know how your teacher got -12.5V either, I got -12.8333V

When you tie Va to -2V, re-analyze the circuit because the current changes. I got -2V = 20(I) + 10V + 5(I) - 15V + 5(I) +2V

I=1/30A, now Vb = -15V + 5(I) +2V Vb = -12.83333V, the only way you can get Vb = -12.5V is if the new current is 0.1A. Try that, I know I probably messed up the math somewhere. I hope that helps.

 

[Analog]

The answer is -12.5V. Look at it this way. If you ground the top node, it is like connecting it to the (-) terminal of the 2V source at the bottom, so you have a 'loop'. The sum of the voltages around the loop is -3V (10-15+2). The total resistance in the loop is 30 ohms. The current through the loop is 100mA, going down. Therefore, start at ground and work your way up to Vb. We have 2V, +0.5V across the 5 ohm resistor, which is 2.5V, then a negative 15V. So the total is -12.5V.