An inductance of 1 mH, a condenser of 10 `mu`F and a resistance of 50 `Omega` are connected in series. The reactances of inductors and condensers are same. What will be the reactance of either of them ?

Options

A. `5 Omega`
B. `3 Omega`
C. `7Omega`
D. `10 Omega`

Answer

D

Explanation

Here L=1mH = `1xx10^(-3)` H
`C=10 muF =10xx10^(-6)`F
`R=50 Omega " " therefore=10^4` rad/s
`X_L=X_C` and `X_L=omegaL`
`=10^4 xx 1xx10^(-3)`
`omegaL=1/(omegaC)`
`therefore X_L=10Omega`
`therefore omega^2=1/(LC) " " X_C=1/(OmegaC)`
`=1/(1xx10^(-3)xx10xx10^(-6)) " " 1/(10^4xx10xx10^(-6))`
`=10^8`
`therefore X_C=10 Omega`