In a series L - R - C circuit connected to an alternating current generator whos

Question

In a series L-R-C circuit connected to an alternating current generator whose maximum voltage is 205 V , the resistance is 57.0 and the capacitance is 6.42 F . The inductance L can be varied from 2.0 mH to 40.0 mH by adjusting an iron core in the solenoid of the inductor. The angular frequency of the generator is 3550 rad/s . If the capacitor voltage is not to exceed 145 V , find the maximum and minimum inductance, Lmax and Lmin, that define the range of inductance that is safe to use.

What are the maximum and minimum inductance, Lmax and Lmin, that define the range of inductance that is safe to use if the capacitor voltage is not to exceed 145 V ?

Explanation / Answer

V_ac = 205 V
R = 57 ohm
C = 6.42microF
omega = 3550 rad/s
I_max = 3,01 A

L = 1/(omega^2*C) + sqrt((V_ac/I_max)^2- R^2)/omega
L_max = 1/(3550^2*(6.42*10^-6)) + sqrt((205/3.01)^2 - 57^2)/3550
L_min = 1/(3550^2*(6.42*10^-6)) - sqrt((205/3.01)^2 - 57^2)/3550

So I thought:
L_max = 0,0285 H
L_min = 0,00185 H

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