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

Question

In a series L-R-C circuit connected to an alternating current generator whose maximum voltage is 205V , the resistance is 71.0? and the capacitance is 4.86?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 3550rad/s . If the capacitor voltage is not to exceed 145V , 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 145V ?

Explanation / Answer

inductive reactance

XL=WL =3550*L

Capacitive reactance

Xc=1/WC =1/3550*4.86*10^-6

Xc=57.96 ohms

Impedance

Z=sqrt[R^2+(XL-Xc)^2]

Z=sqrt[71^2+(3550*L-57.96)^2]

Total current in the circuit

I=V/Z =205/sqrt[5041+(3550*L-57.96)^2]

it was given ,capacitor voltage not to exceed 145 V

Vc=145 V

V=I/Xc

I=V*Xc

205/sqrt[5041+(3550*L-57.96)^2] =205*57.96

57.96=sqrt[5041+(3550*L-57.96)^2]

3359.36=[5041+(3550*L-57.96)^2]

12602500*L^2 -411516*L+1681.64 =0

so

L1=0.02786 H

L2=4.7887*10^-3 H

so

Lmin =4.79 mH

Lmax=27.86 mH

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