Question

An ac generator with E_m -229 V and opersting at 391 Hz causes oscilliations in a series RLC circuit having R= 220, L=147 mH, and C=25.0 uF. Find a) The capacitive reactance Xc, b) The impedance Z, and c) the current amplitude I. A second capacitor of the same capacitance is then connected in series with the other components. Determine whether the values of d) Xc

e) Z and f) I increase , decrease, or remain the same

Answer 1

Em=229 volts

f=391 Hz

R=220 ohms

L=0.147 H

C=25 uH

part a:

capacitive reactance=Xc=1/(2*pi*f*C)

=16.282 ohms

part b:

inductive reactance=Xl=2*pi*f*L

=361.14 ohms

so net impedance=R+i*(Xl-Xc)

=220+i*(361.14-16.282)

=220 + i*344.86 ohms

impedance=Z=sqrt(220^2+344.86^2)

=409.06 ohms

part c:

current amplitude=Em/impedance ampltiude

=229/409.06

=0.56 A

part d:

as for capacitors in series, net capacitance decreases.

as Xc=1/(2*pi*f*capacitance)

Xc will increase as capacitance decreases.

Z =R+i*(Xl-Xc)

as Xc increases, Z will decrease.

part f:

as Z decreases, I=E_m/Z will increase.