A generator with an adjustable frequency of oscillaton is connected to resistance, `R = 1000 Omega`, inductance, `L_(1) = 1.7 mH` and `L_(2) = 2.3 mH` and capacitance, `C_(1) = 4 mu F, C_(2) = 2.5 mu F` and `C_(3) = 3.5 mu F`. The resonant angular frequency of the circuit is

Options

A. `0.5 "rad"//s`
B. `0.5 xx 10^(4) "rad"//s`
C. `2 "rad"//s`
D. `2 xx 10^(-4) "rad"//s`

Answer

B

Explanation

`C_("eff") = C_(1) + C_(2) + C_(3)`
`= 4 mu F + 2.5 mu F + 3.5 mu F = 10 mu F`
`L_("eff") = L_(1) + L_(2) = 1.7 mH + 2.3 mH = 4 mH`
Resonance frequency,
`omega = (1)/(sqrt(L_("eff") C_("eff"))) = (1)/(sqrt(4 xx 10^(-3) xx 10 xx 10^(-6)))`
`(10^(4))/(2) = 0.5 xx 10^(4) "rad"//s`