Current at a Junction: Does Current Density Change?

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In summary, using Kirchhoff's current law and the equation i = n.e.A.vd, we can see that the currents change between different paths at a junction due to changes in the cross-sectional area of the wire and the drift velocity, which is affected by the electric field across the conductor. The value of τ may also affect the electric field, but it is not clear. Generally, current density does not stay the same at a junction unless it is intentionally designed that way.
  • #1
erisedk
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From the very straightforward kirchhoffs 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??
 
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  • #2
erisedk said:
From the very straightforward kirchhoffs 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??
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.
 

Related to Current at a Junction: Does Current Density Change?

1. What is current density?

Current density is a measure of the amount of electric current flowing through a unit area of a material. It is represented by the symbol J and is typically measured in amperes per square meter (A/m²).

2. How is current density related to current at a junction?

Current density is directly related to the total current at a junction. At a junction, the total current is equal to the sum of the current densities of all the branches or paths that meet at that junction. This is known as Kirchhoff's Current Law.

3. Does current density change at a junction?

Yes, current density can change at a junction depending on the number of branches or paths that meet at that junction. If there is an increase in the number of branches, the current density will decrease, and vice versa.

4. What factors can affect current density at a junction?

The main factors that can affect current density at a junction are the number of branches or paths, the resistivity of the material, and the cross-sectional area of the material. Additionally, the type of material and the temperature can also have an impact on current density.

5. How is current density calculated?

Current density can be calculated by dividing the total current by the cross-sectional area of the material. It can also be calculated by using Ohm's law, where current density is equal to the electric field strength divided by the material's resistivity.

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