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Counter-Strike: Source (2004)

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A parallel plate capacitor \( \mathrm{C} \) with plates of unit area and separation \( \mathrm{d} \) is filled with a liquid of dielectric constant \( \mathrm{K}=2 \). The level of liquid is \( \frac{\mathrm{d}}{3} \) initially. Suppose the liquid level decreases at a constant speed V, the time constant as a function of time \( t \) is
\( P \)
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(A) \( \frac{6 \varepsilon_{0} \mathrm{R}}{5 \mathrm{~d}+3 \mathrm{Vt}} \)
(B) \( \frac{(15 d+9 V t) \varepsilon_{0} R}{2 d^{2}-3 d V t-9 V^{2} t^{2}} \) (C) \( \frac{6 \varepsilon_{0} R}{5 d-3 V t} \)
(D) \( \frac{(15 \mathrm{~d}-9 \mathrm{Vt}) \varepsilon_{0} \mathrm{R}}{2 \mathrm{~d}^{2}+3 \mathrm{dVt}-9 \mathrm{~V}^{2} \mathrm{t}^{2}} \)
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