Page 402 - Basic Electrical Engineering

This is the resonance frequency of a parallel L and C circuit.

If we consider the value of R as negligible, then the resonance frequency is

This value is the same as calculated for a series resonance circuit. The line
current I is equal to I cos ϕL which is the minimum current occurring at
L
resonance. If the value of R is reduced, the cosine component of I will get
L
reduced. When R is made equal to zero, I ϕ will be zero and the whole of I L
L
L
will be reactive or wattless component and will be equal and opposite to I .
C
I = I cos ϕ is in phase with V when resonance occurs. The circuit
L
L
impedance, Z is calculated as
0

From the condition of resonance

or,

Thus,

or,