In `R-L-C` series circuit, we have same current at angular frequencies `omega_(1)` and `omega_(2)`. The resonant frequency of circuit is

Options

A. `[omega_(1)omega_(2)]^(1//2)`
B. `(omega_(1)+omega_(2))/(2)`
C. `(omega_(1)omega_(2))/(omega_(1)+omega_(2))`
D. None

Answer

A

Explanation

`Z_(1)=Z_(2),sqrt(R^(2)+(X_(C )-X_(L))^(2))` = same
`(X_(C)-X_(L))^(2)` =same
`((1)/(omega_(1)C)-omega_(1)L)=-((1)/(omega,C)-omega_(2)L),(1)/(C )((1)/(omega_(1))+(1)/(omega_(2)))=L(omega_(1)+omega_(2)),(1)/(sqrt(LC))=sqrt(omega_(1)omega_(2))`