Dielectric materials used in the manufacture of capacitors are characterized by conductivities that are small but not zero. Therefore, a cha

Question

Dielectric materials used in the manufacture of capacitors are characterized by conductivities that are small but not zero. Therefore, a charged capacitor slowly loses its charge by “leaking” across the dielectric. If a certain 3.25 µF capacitor leaks charge such that the potential difference decreases to half its initial value in 4 s, what is the equivalent resistance of the dielectric?

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Kim Cúc 4 years 2021-08-05T16:51:56+00:00 1 Answers 35 views 0

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  1. kimchi2
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    2021-08-05T16:53:03+00:00
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    Answer:

    Equivalent resistance of the dielectric= R =1.78 × 10^6 Ω

    Explanation:

    This is just an RC circuit, where

    q = CVoe-t/RC.

    V is proportional to q; so if V has lost half its value, so has q.

    So we need R such that

    e-t/RC = 0.5

    Taking log on both sides, we get

    -t/RC = ln(0.5)

    R = -t/ln(0.5)C

    = (-4 s)/[(3.25×10^-6 F)(-0.693147)]

    = 1.78 × 10^6 Ω

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