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.

Question

Physics

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20 January, 13:40

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.

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Answers (1)

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Jimmy Montgomery · Answer 1

The answer is ε = 1.5*εo

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