Question

A coil of inductance 9 H and resistance 50 Ω in series with a capacitor is supplied at constant voltage from a variable frequency source. If the maximum current of 1A occurs at 75 Hz, find the frequency when the current is 0.5 A.

Answer 1

Here, N = 10/I = I/0.5 = 2; Q = ω₀L/R = 2π × 75 × 9/50 = 84.8 

Let f₁ and f₂ be the frequencies at which current falls to half its maximum value at resonance frequency. Then, as seen from above

f₀/f₁ - f₁/f₀ = √3/Q or 75/f1 - f1/75 = √3/84.4

or (752 - f²₁)/75f₁  = 0.02 or f²₁ + 1.5f₁ - 5625 = 0 or f₁ = 74.25 Hz

Also f₂/75 - 75/f₂ = √3/84.4 or f²₂ - 1.5f₂ - 5625 = 0 or f₂ = 75.75Hz.