A parallel plate capacitor C with plates of unit area and separation d is filled with a liquid of dielectric constant K = 2 . The level of liquid is 3 d initially. Suppose the liquid level decreases

Question

A parallel plate capacitor C with plates of unit area and separation d is filled with a liquid of dielectric constant K = 2 . The level of liquid is 3 d ​ initially. Suppose the liquid level decreases at a constant speed v , the time constant as a function of time t is

TestHub · Accepted Answer

After time t , thickness of liquid will remain ( 3 d ​ − v t ) . Now, time constant as function of time τ c ​ ​ = CR = ( d − 3 d ​ + v t ) + 2 d /3 − v t ​ ε 0 ​ ( 1 ) ⋅ R ​ Applying C = d − t + k t ​ ε 0 ​ A ​ ) = 5 d + 3 v t 6 ε 0 ​ R ​ ​ ∴ correct option is (a).

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