At what frequency a coil of 1 mH will have a reactance of `3142Omega` What is the capacity of capacitor, which has the same reactance of the same frequency ?

Explanation

Frequency = v = ?
`L = 1 mH = 10^(-3) H`
Reactance `X_L = 3142 Omega`
`X_L = 2pi vL`
`v = (X_L)/(2piL)`
`v = (3142)/(2xx3.142 xx10^(-3))`
`= (3142 xx10^3)/(2xx3142xx10^(-3))`
`=1/2 xx10^6`
`= 0.5 xx10^6`
`v = 5 xx 10^5 Hz`
Now `X_C = 3142 Omega` (Given)
`1/(2pivC) = 3142`
`C =1/(2pivxx3142)`
`=1/(2 xx3.14 xx5 xx10^5 xx3142)`
`1/(3.14 xx3142)xx10^(-6)`
`= 0.000101xx10^(-6)`
` = 1.01 xx10^(-10)F`