Question regarding conduction current

[yykcw]

Assume a voltage source connected to a capacitor which filled with a dielectric material having non zero conductivity, then,
displacement current=conduction current of the wire=CdV/dt
while conduction current density of the dielectric=σE=σV/d
But considering dc source,
displacement current=conduction current of the wire=0,
while conduction current density of the dielectric=σV/d and not equals to zero
Why there will be a contradiction?

 

[berkeman]

Assume a voltage source connected to a capacitor which filled with a dielectric material having non zero conductivity, then,
displacement current=conduction current of the wire=CdV/dt
while conduction current density of the dielectric=σE=σV/d
But considering dc source,
displacement current=conduction current of the wire=0,
while conduction current density of the dielectric=σV/d and not equals to zero
Why there will be a contradiction?

Welcome to the PF.

The DC leakage current is continuous through the wire and the dielectric. If there is leakage current in the capacitor, it has to be supplied by the wire.

 

[yykcw]

Welcome to the PF.

The DC leakage current is continuous through the wire and the dielectric. If there is leakage current in the capacitor, it has to be supplied by the wire.

So the equation I=CdV/dt has not considered the dc leakage? the actual conduction current in the wire is=∫σEdS?
How about at other frequency? Is the actual conduction current inside the wire equals to CdV/dt+∫σEdS(σ is the conductivity of the dielectric) but not just CdV/dt?

 

[NascentOxygen]

A practical capacitor can be modeled as an ideal capacitor with two resistances, one in series and the other in parallel.

 

[sardar]

The concept of conduction current and displacement current can be confusing and can lead to contradictions if not properly understood. Conduction current is the flow of electric charge through a conductor, while displacement current is the flow of electric displacement through a region. In the scenario described, the voltage source is connected to a capacitor filled with a dielectric material, which has a non-zero conductivity.

When an alternating current (AC) source is connected to the capacitor, both conduction current and displacement current are present. The displacement current is caused by the changing electric field within the dielectric material, and it is given by the equation CdV/dt. This displacement current is equal to the conduction current in the wire, as both represent the flow of electric charge.

However, when a direct current (DC) source is connected, there is no change in the electric field within the dielectric material. As a result, there is no displacement current, and the equation CdV/dt becomes zero. This does not mean that the conduction current in the wire is also zero. The conduction current will still flow through the wire, as the dielectric material still has a non-zero conductivity. This conduction current is given by the equation σV/d, where σ is the conductivity of the dielectric material and V/d represents the electric field within the material.

In summary, the contradiction arises because the equations for displacement current and conduction current are different, and they represent different physical phenomena. It is important to understand the difference between these two types of current to avoid confusion and contradictions.