A parallel plate capacitor is to be designed using a dielectric of dielectric constant 5, so as to have a dielectric strength of `10^(9) Vm^(-1)`. If the voltage rating of the capacitor is 12 kV, the minimum area of each plate required to have a capacitance of 80 pF is .........

Options

A. `10.5xx10^(-6) m^(2)`
B. `21.7xx10^(-6) m^(2)`
C. `25.0xx10^(-5) m^(2)`
D. `12.5xx10^(-5) m^(2)`

Answer

A, B

Explanation

V =Ed
`:. D=(V)/(E)`
`C= (K in_(0)A)/(d)`
`:. A = (Cd)/(K in_(0))`
`= (CV)/(KE in_(0))`
`=(80xx10^(-12)xx12xx10^(3))/(5xx10^(9)xx8.85xx10^(-12))`
`=21.69xx10^(-6)`
`= 21.7xx10^(-6) m^(2)`
Second Method :
Q = CV
`sigma A = CV`
`:. sigma = (CV)/(A)`
`E = (E_(0))/(K) ` but `E_(0)= (sigma)/(in_(0))`
`:. E= (sigma)/(K in_(0))`
From (1)
`E = (CV)/(AK in_(0))`
`:. A =(CV)/(EK in_(0))`
`=(80xx10^(-12)xx12xx10^(3))/(5xx10^(9)xx8.85xx10^(-12))`
`:. A = 21.69xx10^(-6)`
`:. A = 21.7xx10^(-6) m^(2)`