A capacitor has a resistance of `1200 M Omega` and capacitance of `22 mu F`. When connected to an a.c. supply of frequency 80 hertz, then the alternating voltage supply requried to drive a current of 10 virtual ampere is

Options

A. `904 sqrt(2) V`
B. `904 V`
C. `904 sqrt(2) V`
D. `452 V`

Answer

2

Explanation

`f = 80 Hz, I_(V) = 10 A`
Current through `R, I_(R ) = (E_(V))/(R ) = (E_(V))/(12 xx 10^(8))`
current through `C I_(C) = (E_(V))/(X_(C)) = 2 pi fC xx E_(V)`
`2 pi xx 80 xx 22 10^(-6) xx E_(V)`
`= 352 pi xx 10^(-5) xx E_(V)` `I_(V)^(2) = I_(R )^(2) + I_(C )^(2)`
`(10)^(2) (E_(V)^(2))/((12 xx 10^(8))^(2)) + (352 xx 10^(-5) xx E_(V))^(2)`
`= E_(V)^(2) ((1)/(144 xx 10^(16)) + 1.2 xx 10^(-4))`
`E_(V)^(2) = (100 xx 10^(4))/(1.2) E_(V) ~~ 904` volt