Is This Node Voltage Analysis Correct?

[CL1349]

Homework Statement

In the figure, use the node voltage method to find the voltage at point A with respect to ground.

Sorry for the crudely drawn picture.

Homework Equations

Node voltage analysis

The Attempt at a Solution

First I added R3 and R4. Then I tried to find the current equations.

I have I1 - I2 -I34 = 0

then

(30 - VA)/ 82 - (40 - VA)/ 68 - VA/147 = 0 Now, I don't know if this is right. I've only been working simple circuits without a voltage source in the middle branch.

Can someone verify if I've done this right so far? If I haven't, can you push me in the right direction?

Thanks.

 

[vk6kro]

Assume currents flow upwards from batteries.

You have 3 voltages that all equal the voltage Va.

They are:

A: 30 volts minus the voltage across the 82 ohm resistor. I1 * 82

B: 40 volts minus the voltage across the 68 ohm resistor. I2 * 68

C: The total current from the two batteries times the resistance of R3 + R4. (I1 + I2) * 147

So, these voltages are equal to each other.
So, you can say A = B and get an equation involving I1 and I2
and you can say A = C and get another equation involving I1 and I2.

Then solve for these currents and calculate Va.

 

[rudasi]

You seem to be in the right direction. From the way you are assuming current directions though, I34 should be (0-Va)/147. This would give you -Va/147, which you end up subtracting so you should get a +Va/147 in your above equation instead of -Va/147.