# Supernodes with Constant Current & Voltage Sources: Voltage = Current

I am a technologist trying to improve my understanding of electricity by reading a textbook. I am reading Fundamentals of Electric Circuits and something that keeps popping up when solving the problems he proposes requires me to say voltage equals current. I cannot solve a few of his problems without dropping my units and just going with it so there is something fundamentally flawed with my understanding. Here is one example (there are a few going through chapter 3) (excerpt from PP 3.4).

The logic required to get one of his equations (according to the solutions manual I have) is that that the voltage across the constant current source of the supernode can be defined as V3 - V2 (that makes sense) but then he says this equals

$$\5i (V3-V2 = 5i)\$$.

He then solves for 5i (i = V1/R1) so V3-V2 = 5*(V1/R1). On the left hand side of the equation my units are voltage, and on the right hand side (according to ohms law) my units are current. This process of dropping units and just filling matrices seems to be prevalent throughout chapter three. Can someone please help me understand his logic? Should I find a new textbook or is there something fundamental I am missing? Thank you for your time and patience.

• $$5i$$ is value of dependent voltage and its unit is in volt ,for simplicity you can think of this dependent voltage as a product of$$(i amp * 5ohm)$$and hence we get volt as a unit Commented Feb 10, 2021 at 23:41

This is a classic circuit theory example. The book you are working out of is probably a good one. This chapter is going to be rather math heavy with many systems of equations. Circuit theory as a whole is very math heavy, so be prepared for that.

In your description you call that a dependent current source, but have drawn a dependent voltage source. Based on your explanation it seems like that stems from your voltage/current confusion.

In this particular case the dependent voltage source is dependent on a current somewhere else in the circuit. This doesn't mean that current = voltage. It means that in this case the voltage changes based on the current through a different part of the circuit. Its just an exercise in practicing whatever circuit analysis concept they are trying to teach.

((Changing the problem)) They could have just as easily said that the dependent voltage source = 5V2. Now its a voltage source dependent on a voltage. All they are doing is getting you to practice with all the different elements in circuits.

Later on in your studies you will come across bjt's and other active circuit components that are modeled with dependent sources.

http://fourier.eng.hmc.edu/e84/lectures/ch4/node8.html

• Thank you very much for your clear and concise answer ! Commented Feb 10, 2021 at 23:57