Question

- A series RLC circuit has R=15 ?, L=1.5 H, and C=15 ?F. (a) For what angular frequency of applied emf will the current be a maximum? (b) At what angular frequencies will the current be half maximum?

please help me as fast as possible thank you

Answer 1

current= voltage/impedance

so current will be maximum when impedance is minimum

as impedance will be minimum when capactive impedance is equal and opposite of inductive reactance

so if angualr frequency is w,

then 1/(w*C)=w*L

then w=210.82 rad/sec

frequency=w/(2*pi)=33.553 Hz

part 2:

for current to be half of the maximum, the impedance has to be twice the minimum

hence sqrt(R^2+(Xl-Xc)^2)=2*R=30

where Xl=w*1.5

Xc=1/(w*15*10^(-6))

then 15^2+(Xl-Xc)^2=30^2

Xl-Xc=675

1.5*w-(6.67*10^4/w)=675

1.5*w^2-6.67*10^4=675*w

solving for w , we get

w=533.33 rad/sec

in Hz, it will be w/(2*pi)=84.882 Hz