Question

The ratio of the inductive reactance to the

capacitivereactance is observed to be 5.36 in a series RCL circuit.
Theresonant frequency of the circuit is 225 Hz. What is the
frequency(nonresonant) of the generator that is connected to
thecircuit?

Answer 1

The non resonance frequency of the generator is = 1201.79 Hz

Step-by-step explanation:

At resonance,

f₀ = 1/2π√LC..................... Equation 1

Where f₀ = resonance frequency, L = inductance, C = capacitance

making LC the subject of the equation

LC = 1/4πf₀²..................... Equation 2

Given: f₀ = 225 Hz, and π = 3.143

Substituting these values into equation 2,

LC = 1/(4×3.143²×225²)

LC = 1/2000385.9

LC = 5×10⁻⁷

If the ratio of capacitive reactance to inductive reactance = 5.36

1/2πfC/2πfL = 5.36

1/4π²f²LC = 5.36

Where f = frequency of the non resonant

making f the subject of the equation

f = 5.36/2π√LC ............. Equation 3

Substituting the value of LC = 5×10⁻⁷ into equation 3

f = 5.36/2×3.143√(5×10⁻⁷)

f = 5.36/(6.286×0.00071)

f = 5.36/0.00446

f = 1201.79 Hz

Thus the non resonant frequency of the generator is = 1201.79 Hz