A parallel-plate capacitor C of unit plate area and separation d is filled to height d/3 by a liquid dielectric K=2. The liquid level decreases at constant speed v while the capacitor discharges through R. Which expression gives the time constant as a function of t?
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Question

A parallel-plate capacitor C of unit plate area and separation d is filled to height d/3 by a liquid dielectric K=2. The liquid level decreases at constant speed v while the capacitor discharges through R. Which expression gives the time constant as a function of t?

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G1 Physics · Accepted Answer

The partially filled capacitor is a parallel combination of air and dielectric area portions. With liquid height h=d/3−vt, C(t)=ε₀[1+(K−1)h/d]/d = 6ε₀/(5d+3vt) for K=2 in the source geometry. Therefore τ=R C(t)=6ε₀R/(5d+3vt). Correct answer: A.