An alternating current is flowing through a series LCR circuit. IT is found that the current reaches a value of 1mA at both 200 Hz and 800Hz frequency. What is the resonance frequency of the circuit?

Options

A. 600 Hz
B. 300 Hz
C. 500 Hz
D. 400 Hz

Answer

D

Explanation

For LCR circuit, `I=V_0/sqrt(R^2+(omegaL-1/(omegaC))^2)`
Since currents for frequency 200 Hz and 800HZ are same,
`thereforeV_0/sqrt(R^2(omega_1L-1/(omega_1C))^2)=V_0/sqrt(R^2+(omega_2L-1/(omega_2C))^2)`
or, `(omega_1L-1/(omega_1C))=pm(omega_2L-1/(omega_2C))`...(1)
By intercharging the value of `omega_1` and `omega_2`, the sign of the value of `(omegaL-1/(omega_1C))` may change. So, by considering '+' sign in left side and '-' sign in right hand side of equation (1) , we have
`(omega_1L-1/(omega_1C))=-(omega_2L-1/(omega_2C))`
or, `LC=1/(omega_1omega_2)`or,`omega_1omega_2=1/(LC)`or,`omega_1omega_2=omega_0^2`
or, `f_1f_2=f_0^2[f_0`=resonance frequency]
or, `f_0=400 Hz`