Question

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

• A. $K = \frac { 4 b } { 2 b - d } \& \frac { d } { 3 } < b \leq d$
• B.
• C. $\mathrm { K } = \frac { 2 \mathrm {~b} } { 2 \mathrm {~b} - \mathrm { d } } \& \frac { \mathrm { d } } { 2 } \leq \mathrm { b } \leq 2 \mathrm {~d}$
• D. $\mathrm { K } = \frac { 2 \mathrm {~b} } { 2 \mathrm {~b} - \mathrm { d } } \& \frac { \mathrm { d } } { 4 } \leq \mathrm { b } \leq \mathrm { d }$

Answer 1

Answer: (B)

Answer 2

C_K =

We set b = 0

C_K = $\frac { \varepsilon _ { 0 } \mathrm {~A} } { \mathrm {~d} }$ = C if C_K = 2C

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

K > 0 & b £ d

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

\ $\frac { \mathrm { d } } { 2 } < \mathrm { b } \leq \mathrm { d }$

\ b > $\frac { \mathrm { d } } { 2 }$