A simple radio-tuning arrangement employs a coil of inductance in series with a…
PHYSICS · Subjective · CBSE · Physics · Alternating Current · Alternating Current
Problem
A simple radio-tuning arrangement employs a coil of inductance 0.20mH in series with a variable air-capacitor whose capacitance can be adjusted from 50pF to 300pF. Neglect the resistance of the coil for the purposes of this question.
(a) Derive an expression for the resonant frequency f0 of this circuit in terms of the variable capacitance C.
(b) Calculate the highest and the lowest resonant frequencies that can be obtained with the given range of C values.
(c) An amplitude-modulated broadcast is transmitted at 1.00MHz. Determine the capacitance setting required to tune the receiver exactly to this station.
(d) With the capacitor set as found in part (c), predict qualitatively how the impedance magnitude and the phase angle of the circuit will change if the capacitance is slowly decreased to one-half of this value, and explain the physical basis of your prediction.