Answer :

Time constant for capacitor:



Where R is the resistance through which the capacitor is being charged/discharged and C is the capacitance.


Capacitance of a Capacitor in presence of a dielectric:
The capacitance of the capacitor is initially C0 and then a dielectric medium of dielectric constant K is inserted between the plates. The new capacitance is



Also for parallel plate capacitors,



Where ϵ0 is the permittivity of free space, A is the area of plate and l is the distance between the plates.


Resistance and Resistivity:


For a material of length l and uniform cross-section A and reistivity ρ, the resistance is given by:



Note the area of cross section of the material is the same as the area of the capacitor plates and the length of the material is the same as the distance of separation between the plates.


Now,






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