Question

I have a slab of some insulator with an unknown permittivity . To determine experimentally I go to the lab and insert the slab in between the plates of a capacitor whose plate spacing exactly matches the width of the slab. I observe that the time constant of exponential decay of the capacitor voltage in an RC circuit that I construct increases by 50% when the slab is inserted to replace the air spacing. Determine in terms of o. Explain your reasoning carefully.

Answer 1

The answer is ε = 1.5*εo

Step-by-step explanation:

we have to:

I = R*C

also:

C´ = (A*ε)/α

C = (A*εo)/α

So:

I´ = ε*I

Given by the exercise:

I´/I = 1.5 (50% of increase)

Thus:

ε/εo = 1.5

Clearing ε:

ε = 1.5*εo