Node Voltage Analysis for Finding V1 in a Circuit

[jdawg]

Homework Statement

Find V₁. I attached a picture for the circuit.

Homework Equations

The Attempt at a Solution

This is what I did (Refer to Fig. 1):

-2A + (V₁)/(50) +(V₁-45)/(1) = 0

But when I looked at the solution my professor posted this is what he did (Redrew Fig.1 as Fig.2):

-2A + (V₁)/(50) +(V₁-45)/(1+4) = 0

I thought you were finding the potential difference between V₁ and the voltage source? I don't understand why he included the 4Ω resistor. Any help is appreciated!

 

[gneill]

Each term of a node equation represents a branch current. A branch is a series-connected set of components lying between two nodes. The current flows through the entire branch. For the branch in question there are two resistors and one voltage supply stretching between node V1 and the reference node.

Edit: I should mention that rearranging the components in a series circuit does not change the current or end-to-end potential drop. It's like rearranging the terms of a sum of terms in math; they add up to the same value no matter the order.

 

[jdawg]

Thanks for clearing that up!