How Do I Correctly Apply Nodal Analysis in This Circuit Problem?

[pat666]

Homework Statement

See attached picture.

Homework Equations

The Attempt at a Solution

I really suck at this and am having trouble understanding the textbook we have. here's my attempt:

I'm calling node 1 v1 and 2 v2.
so
0=(v1-v2)/4k7+v1/10k+(v2-v1)/1k
0=(v2-v1)/1k+v2/470+v2/1

I know I have to do something with the 10V but I'm not sure what?? I've been trying questions with current sources and can sometimes get the answer right with them after ages of playing...

I can solve this equation easily but I'm sure that the setup is wrong. I really need help with this, I know its supposed to be easy but something hasn't clicked and I don't understand these questions yet.

Thanks for any help

 

[gneill]

You might find things to be a bit clearer if you were to label the circuit diagram with some assumed current directions (see attached figure). Then when you write the equation for a given node, you take the voltage difference across the components according to the assumed current directions (current flows from + to -).

The battery fixes the potential at the left end of R1. Treat that point as if it were a neighboring node to NODE 1, but a node that you don't need to write separate equations for (since it already has a completely specified voltage as fixed by the battery).

 

[pat666]

So
0=10/4k7-(v1)/10k-(v2-v1)/1k
0=(v2-v1)/1k-v2/470-v2/1k

Just a guess, I'm still having trouble understanding what I should be doing.

Thanks

 

[gneill]

Using the assumed currents, you can see that the potential difference across R1 would be 10V - V1. So the current entering NODE 1 through R1 would be (10V - V1)/R1.

Similarly, the potential difference across R3 is V1 - 0V (0V because the bottom end of R3 is the "ground" node, which is always assumed to be at 0V potential). So the current leaving NODE 1 via R3 is V1/R3.

The current leaving NODE 1 via R2 is (V1 - V2)/R2.

Sum them up and set equal to zero for the equation for NODE 1. Then do the same for NODE 2.

 

[pat666]

0=(10-V1)/R1-V1/10K-(V1 - V2)/R2
0=(V1 - V2)/R2-V2/470-V2/1k
?
If that is right (?) would you mind telling me how to find the current directions?

Thanks for your help!

 

[gneill]

0=(10-V1)/R1-V1/10K-(V1 - V2)/R2
0=(V1 - V2)/R2-V2/470-V2/1k
?
If that is right (?) would you mind telling me how to find the current directions?

Thanks for your help!

That looks fine.

You can usually make an educated guess about the current directions based upon the values and positions of the sources. In this case, the only source is the 10V supply, so it should have the highest potential in the circuit, and everything should "go downhill" from there.

HOWEVER! It doesn't really matter what directions you assume for the currents! As long as you are consistent about using them as you write the equations, the math will take of everything and you'll arrive at the same results.

 

[pat666]

Thanks for your help.