# DIFFERENCE BETWEEN DISPLACEMENT CURRENT AND CONDUCTION CURRENT

CONCEPT OF DISPLACEMENT CURRENT (DIFFERENCE BETWEEN DISPLACEMENT CURRENT AND CONDUCTION CURRENT)

Let there be a parallel R-C network with a voltage V as shown in fig .Let the current through resistor R is Ic and by Ohm’s law it is given by

Ic=V/R

And current through capacitor C is Id and is given by

Id=dQ/dt

Id=Cdv/dt                                ( dQ=Cdv)(1)

In practice ,the current does not flow through the capacitor . But ,the current that flows out of one electrode of capacitor equals the current that flows in to the other electrode. The net effect is as if there is a current flowing through the path containing the capacitor. But current, Icactually flows through the resistor.

Hence ,from the above result ,current flowing through the resistor is known as conduction current and it obeys Ohm’s law,while the current flowing through the capacitor is commonly known as Displacement current.

Mathematical Proof.As the electric field inside each element equals the voltage V across the element divided by its length d

That is                           E=V/d or V=ED                                                  (2)

Now the current density in resistor is given by

Jc=Ic/A=σE                                                  (3)

Where  A= cross-sectional area

σ=conductivity of resistance element

Also capacitance of a parallel plate capacitor is given by

C=ε0A/d                                                                   (4)

Now rewrite equation(1)

Id=C dV/dt

By substituting the values of V and C from equations (2 and 4) in above equation,we get

Id= ε 0A/d( E/t)

Id= ε0A E/t                                             (5)

Therefore current density Jd inside capacitor is

Jd=Id/A

Substititing value of Id from equation (5) in above equation,we get

Jd= ε 0/A E/t

Or Jd= ε0 E/t                                      (6a)

Or                                             Jd= D/t                                                  (6b)

Where                      D= ε 0E=Electric displacement vector

And                           Jd=Displacement current density

Equation (6a) proves that displacement current density arises whenever there will be change in electric field E that is (E/t≠0)