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25 October, 09:11

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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  1. 25 October, 09:12
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    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
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