Question

Obtain an expression for impedance and current in series LCR circuit. Deduce an expression for the resonating frequency of an LCR series resonating circuit

Answer 1

Answer:

inductive reactance=X

L

=2πfL=ωL

Capacitive reactanceX

C

=

2πfC

1

=

ωC

1

total circuit reactance=X

T

=X

L

−X

C

or X

C

−X

L

total circuit impendance =Z=

R

2

+X

T

2

for minimum impendance X

T

should be equals to 0

⇒X

T

=X

C

−X

L

=

ωC

1

−ωL=0

⇒ω=

LC

=2πf

⇒f=

2π

LC

Hertz