# Current at a node

1. Jun 14, 2015

### erisedk

From the very straightforward kirchoff's current law, based on conservation of charge, currents entering the junction is equal to the currents leaving the junction.

I was wondering how using the equation i = n.e.A.vd, we could justify that the currents change between different paths at a junction.

n is the number of charge carriers per unit volume, that clearly doesn't change
e= electronic charge, doesn't change
A, cross-sectional area of the wire, I believe this changes, but I'm not too sure
vd, drift velocity = eEτ/m, where e is electronic charge, τ is relaxation time, m is mass, and E is electric field across the conductor, i don't think τ changes, but E i'm not sure about again.

Furthermore, does current density stay the same at a junction??

2. Jun 14, 2015

### insightful

I think the problem with this approach is getting E. Normally, E would be calculated from i (via Kirchoff's law) and the physical parameters of the conductors.

The current density would normally not stay the same through the node unless the node were designed specifically to produce that result.