A radio can be tuned into a particular station frequency by adjusting the capaci

Question

A radio can be tuned into a particular station frequency by adjusting the capacitance in an L-C circuit. Suppose that the minimum capacitance of a variable capacitor in a radio is 4.19pF Part(a)What is the inductance L of a coil connected to this capacitor if the oscillation frequency of the L-C circuit is 1.60MHz , corresponding to one end of the AM radio broadcast band, when the capacitor is set to its minimum capacitance? Part(b)The frequency at the other end of the broadcast band is 0.542MHz . What is the maximum capacitance C_max of the capacitor if the oscillation frequency is adjustable over the range of the broadcast band?

Explanation / Answer

PART A: f = 1 / [2•p•v(L•C)] 1.53 ×10^6 = 1 / [2•p•v[L • (4.1×10^-12)] (1.53 ×10^6) • [2•p•v[L • (4.1×10^-12)] = 1 L = 1 / { (4.1×10^-12) • [2•p•(1.53 ×10^6)]² } L = 2.64 mH = 0.00264 Henrys PART B: f = 1 / [2•p•v(L•C)] 0.534 ×10^6 = 1 / [2•p•v[(2.64 ×10^-3) • C] (0.534 ×10^6) • [2•p•v[(2.64 ×10^-3) • C] = 1 C = 1 / { (2.64 ×10^-3) • [2•p•(0.534 ×10^6)]² } C = 33.6 pF = 33.6 ×10^-12 Farads

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