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Question

Half of the space between the plates of parallel plate capacitor is filled with a medium of dielectric constant K parallel to the plates. If initially the capacitance is C, then the new capacitance will be

A
2KCK+1
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B
(K+1)C2
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C
KCK+1
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D
KC
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Solution

The correct option is A 2KCK+1

If the area of the plates is A and the initial separation between them is d then the capacitance will beC=ε0Ad....(1)As we know that capacitance of partially filled dielectric slab of thickness t and dielectric constant K is given byC=ε0Adt+tK....(2)Since, here half of the space is filled with dielectric so, t=d2. From equation (2),

C=ε0Add2+d2K

C=ε0Ad2+d2K

C=2ε0AdKK+1

From equation (1),

C=2CKK+1

Hence, option (a) is the correct answer.
Key Concept:

The capacitance of partially filled dielectric slab of thickness t and dielectric constant K is given byC=ε0Adt+tK

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