Current Flow in Series Wire with Different Conductivity

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SUMMARY

The discussion centers on the behavior of two wires, A and B, connected in series with differing conductivities under a potential difference (p.d.) V. According to Ohm's law (J = σE), the electric fields in each wire differ, leading to charge accumulation at the junction. This charge accumulation initiates during the transient phase when voltage is first applied, resulting in a longitudinal wave in the electron plasma that carries electric and magnetic fields. The wave reflects at the junction due to differing resistances, causing a temporary discontinuity before a steady current flows uniformly across the junction.

PREREQUISITES
  • Understanding of Ohm's Law and its application (J = σE)
  • Knowledge of electric fields and charge accumulation
  • Familiarity with the concept of longitudinal waves in conductors
  • Basic principles of current flow in electrical circuits
NEXT STEPS
  • Research the effects of varying conductivity on current flow in series circuits
  • Explore the concept of charge accumulation at junctions in electrical conductors
  • Learn about transient responses in electrical circuits and their implications
  • Investigate the behavior of longitudinal waves in electron plasma within conductors
USEFUL FOR

Electrical engineers, physics students, and anyone interested in the dynamics of current flow in series circuits with varying material properties.

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Wire A and B, which have the same cross-sectional area are connected in series. There is a p.d. V across the whole wire.

Suppose the two wires obey Ohm's law J = σE
Also, A and B have different conductivity.

Therefore electric field of A is different from B.
There should be a layer of charge between the junction of A and B.

So, when does the charge accumulation start ?
At the transient time ?

At that moment, current flows in wire A =/= current flows in wire B ?
 
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When the voltage is first applied at the end of the conductor, the electrons of the conductors support a longitudinal wave, which travels along the wire. It may be thought of as being a wave in the electron plasma, and it carries E and B fields along with it. When the wave reaches the junction and encounters different resistance, part of it is reflected back to the source. This explains the discontinuity at the junction. A steady current, caused by very slow electron drift, then continues to flow uniformly across the junction. All steady currents are first set up by a wave traveling along a conductor, and similarly when they are swirtched off.
 

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