A coil of inductance `L=5H` and resistance `R=55Omega` is connected in series to the mains alternating voltage of frequency `f=50Hz` in series. What can be the non-zero capacitance of the capacitor (in `muF`) connected in series with the coil, if the power dissipated has to remain unchanged. (take `pi^(2)=10`)

Answer

`1xx10^(-6)`

Explanation

`P_(av)=VI cos phi = V (V/z)=(R/z)=(V^(2)R)/(Z^(2))`
It means `Z` has to be same in both cases
`Z_(1)=Z_(2)impliessqrt(R^(2)+X_(L)^(2))=sqrt(R^(2)+(X_(C)-X_(L))^(2))`
`2X_(L)=X_(C)`
`impliesC=1/(2omega^(2)L)=10^(-6)=1xx10^(-6)`