When is displacement current equal to conduction current?

[arvindsharma]

Is displacement current always equals to conduction current?if not then can anyone give me an example for it?if yes,then can anyone prove it?

 

[vanhees71]

The socalled "displacement current" is a misnomer. It's not a current but it's simply part of one of Maxwell's equations, the Ampere-Maxwell Law, which reads in Heaviside-Lorentz units
$$\vec{\nabla} \times \vec{B}-\frac{1}{c} \partial_t \vec{E}=\frac{1}{c} \vec{j}.$$
This is the "microscopic form" of the law, and $\vec{j}$ is the total current density.

The source of the electromagnetic field are charge and current densities.

 

[jtbell]

I think you should tell us some details about the context or background or origin of your question. Do you have a specific example in mind, where the two currents are equal?