1.

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»

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/f23/84.4 or f22 - 1.5f2 - 5625 = 0 or f2 = 75.75Hz.



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