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Question: A capacitor consists of two parallel metal plate of area A separated by a distance d. A dielectric s...

A capacitor consists of two parallel metal plate of area A separated by a distance d. A dielectric slab of area A, thickness b and dielectric constant k is placed inside the capacitor. If CK is the capacitance of capacitor with dielectric, how much K and b be restricted so that CK = 2C, where C is capacitance without dielectric–

A

K =4b2b−d\frac { 4 b } { 2 b - d }&< b £ d

B

K =&< b £ d

C

K = 2b2b−d\frac { 2 b } { 2 b - d } & d2\frac { \mathrm { d } } { 2 } £ b £ 2d

D

K = 2b2b−d\frac { 2 b } { 2 b - d } & d4\frac { d } { 4 } £ b £ d

Answer

K =&< b £ d

Explanation

Solution

CK =

We set b = 0

CK = ε0 A d\frac { \varepsilon _ { 0 } \mathrm {~A} } { \mathrm {~d} } = C if CK = 2C

Then, =̃ K = 2b2b−d\frac { 2 b } { 2 b - d }

\ K > 0 and b £ d

\ K = 2b2b−d\frac { 2 b } { 2 b - d } and 2b – d > 0

\ < b £ d \ b >