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 4.16 pF

A.

What is the inductance L of a coil connected to this capacitor if the oscillation frequency of the L-C circuit is 1.66 MHz , corresponding to one end of the AM radio broadcast band, when the capacitor is set to its minimum capacitance?

Express your answer in henrys to three significant figures.

B.

The frequency at the other end of the broadcast band is 0.543 MHz . What is the maximum capacitance Cmax of the capacitor if the oscillation frequency is adjustable over the range of the broadcast band?

Express your answer in farads to three significant figures.

Explanation / Answer

  PART A:

f = 1 [2••(L•C)]

1.66 ×10^6 = 1 [2••[L • (4.16×10^-12)]

(1.66 ×10^6) • [2••[L • (4.16×10^-12)] = 1

L = 1 { (4.16×10^-12) • [2••(1.66 ×10^6)]² }

L = 2.209 mH = 0.00209 Henrys

PART B:

f = 1 [2••(L•C)]

0.534 ×10^6 = 1 [2••[(2.20 ×10^-3) • C]

(0.534 ×10^6) • [2••[(2.20 ×10^-3) • C] = 1

C = 1 { (2.20 ×10^-3) • [2••(0.534 ×10^6)]² }

C = 33.6 pF = 40.37 ×10^-12Farads

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