Question

At a certain frequency `omega_(1)`, the reactance of a certain capacitor equals that of a certain inductor. If the frequency is changed to`omega_(2) = 2omega_(1)`, the raito of reactance of the inductor to that of the capacitor is :

Answer 1

Correct Answer - 4
As `X_(L_(1)) = X_(C_(1))` so `omega_(1) L = (1)/(omega_(1) C)`
Thus `X_(L_(2)) = omega_(2) L = 2 omega_(1) L = 2 ((1)/(omega C)) = 2 ((2)/(omega_(2) C))`
`= 4 X_(C_(2))`
i.e., `(X_(L_(2)))/(X_(C_(2)))` = 4`