how is dielectric constant of material and conductivity is related ....intuitively and mathematically .
I would be grateful for any answers

Hi Shantanu,
The dielectric constant of a material is it's electrical permittivity.
A dielectric is an insulator that (in an electric circuit) is a material put between 2 metal plates to make a capacitor. If you have a [metal plate/dielectric material/metal plate] you have a capacitor. If you put this in series it will block direct current but, depending on the capacitance (I'll explain later), it will pass an alternating current (AC or RF). If you put a capacitor in parallel, you can short any AC to ground, but not short you Direct Current.
Backing up a bit, a capacitor is defined by the area of the metal plates, the thickness of the dielectric (or distance between plates), and the electrical permittivity of the dielectric. The formula for capacitance is : {E(permittivity of the dielectric) x area}/d(thickness of the dielectric)or (E x A/D).
I've got to run, but I'll come back to you after dinner.
Peace,
Ron

Hi again, S,
To address your question "how is dielectric constant of material and conductivity is related?" A dielectric material is an insulator and does not conduct DC electricity. That said, when put together as a capacitor, depending on the dielectric (and Area and Distance), when a DC potential is placed across a capacitor, the charged components of the dielectric will move to either side of the capacitor and hold a voltage equal to that of the potential placed across it. This voltage can be charged or discharged according to a time constant : RC (a resistor in series with the capacitor). Time to charge a capacitor to it's highest potential is 5 x RC. (You can look up capacitive time constant to see the time curve.) Since the charges within the dielectric are mobile, AC can pass through a capacitor just like a conductor (depending on the frequency and the capacitance. So, the short answer is : capacitive reactance (Xc) is an AC resistance. so conductivity for an AC signal is related to the reactance (or AC resistance) where Xc=[1/(2 x pi x f x c)] where Xc is capacitive reactance, pi is 3.14, f is frequency and c is capacitance.
Let me know if I can clarify further.
Peace,
Ron

I=U/R,
P=U*I=(U^2)/R,
where U is voltage in volts, R is dialectric resitance in oms, I is Electric current in ampers, P is Power in wats.

David,
That is just Ohm's law. A dielectric is not a resistor.
Ron

In a dielectric, charge carriers (let's say electrons) stop moving very soon, usually before they moved one atomic radius. So there is no DC current in a dielectric. With an AC voltage of high enough frequency, the small displacement does give some AC current, called a displacement current.

In a conductor, some charge carriers can move between atoms, enabling a conduction current even in DC.