# How does the current change?

A few days ago a friend of mine proposed this question :

How does the current increase or decrease in a specific circuit ?

and I couldn't help but to post the question here.

Consider, for example, the case of a DC adjustable voltage generator connected to a resistor:

Now when we increase the emf of the generator, the current in the circuit will increase proportionally according to Ohm's law:$$V=RI$$

So the question is, shall the current increase:

1. by an increase of the drift velocity of electrons moving across the circuit, or

2. by an increase of the linear density of electrons forming the current?

• Hmm, I think you need some other assumptions/constraints to go with this. If I assume that # of electrons supplied by my circuit is fixed, then clearly the only thing that charges is the drift velocity, since it is proportional to the electric field and the charge density is assumed fixed. – Ben S Jan 20 '17 at 19:19
• @BenS I think we only need the conductivity of the circuit as a function of the distance traveled from one pole of the battery to the other one. And also the EMF. The other remaining thing is the shape of the conductor. Here, for thin wires, we can assume that the conductor is one dimensional. There are sufficient for solving the boundary value problem, I think. – AHB Jan 20 '17 at 19:23

## 2 Answers

Mainly drift velocity.   Recall that current is the flow of free electrons which already exist in the circuit.   Fot the most part, the voltage source doesn't add them.   However, it could be argued the electrons are slightly compacted with increasing voltage.

• Shall we assume that all free electrons participate in the current for a given voltage ? In fact, we know that current density across a conducting wire is highest at the centre and null at the edges, maybe a higher voltage will enhance more electrons to flow. – Tofi Jan 20 '17 at 19:38
• I think you have that reversed. Current density is highest near the surface. However, all of the free electrons participate. They just move closer to the surface during the flow. – D. Ennis Jan 20 '17 at 20:05
• Current density is highest at the surface only in rapidly alternating currents due to skin effect, not in direct currents. – Tofi Jan 21 '17 at 5:06
• Yes, but I thought it was more pertinent to your line of reasoning to address the reversal of the concept with respect to current distribution. Why do you think "we know" that current density is highest at the center? – D. Ennis Jan 21 '17 at 13:36

This problem has been studied in detail , in the theory of Transmission lines. The Mathematical solution , takes into account Travel-ling Electro Magnetic waves.... Electron density at different points of the Transmission Line ,is considered as a Time-dependent Function. Drift velocity is represented as an equivalent linear resistance of the line.
Drift velocity and Electron Density functions are considered for Electric Current flow through Semiconductors .