A circuit contanining resistance `R_(1)`, Inductance `L_(1)` and capacitance `C_(1)` connected in series resonates at the same frequency`'n'` as a second combination of `R_(2), L_(2)` and `C_(2)` . If the two are connected in series. Then the circuit will resonates at

Options

A. `n`
B. `2 n`
C. `sqrt((L_(2) C_(2))/(L_(1) C_(1)))`
D. `sqrt((L_(1) C_(1))/(L_(2) C_(2)))`

Answer

1

Explanation

`n = (1)/(2*sqrt(L_(1)C_(1))) = (1)/(2*sqrt(L_(2)C_(2)))`
`L_(1)C_(1) = L_(2) C_(2) , L_("net") = L_(1) + L_(2) , C_("net") = (C_(1) C_(2))/(C_(1) + C_(2))`
`L_("net") C_("net") = (L_(1) + L_(2)) ((C_(1) C_(2))/(C_(1) + C_(2))) , L_("net") C_("net") = L_(2) C_(2)`