Question

What would be the resonant frequency for a series RLC circuit with the following components: a 1,000 Ω resistor, a 900 mH inductor, and a 0.014 mF capacitor?

Answer 1

The resonance frequency = 0.978 Hz

Step-by-step explanation:

Resonance: This is a point in an A.c circuit where the capacitive reactance is equal to the inductive reactance. The frequency at resonance is called Resonance Frequency. Mathematically, resonance frequency is expressed as

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

Where f₀ = resonance frequency, L = inductance of the inductor, C = capacitance

Given: L = 900 mH = (900/1000) H = 0.9 H, C = 0.014 mF = (0.014/1000) F = 0.000014 F

Constant: π = 3.143

Substituting these values into equation 1

f₀ = 1/2×3.143√(0.9×0.000014)

f₀ = 1/6.286√(0.0000126)

f₀ = 1/6.286×0.00355

f₀ = 1/0.0223

f₀ = 0.978 Hz.

Therefore the resonance frequency = 0.978 Hz