You have an inductor that you are planning to use in series with a variable capa

Question

You have an inductor that you are planning to use in series with a variable capacitor C in the tuning section of a radio. Neglect the internal resistance of the inductor.

1) If you have a fixed inductance L = 2.9 mH, find the maximum capacitance the variable capacitor must be able to reach in order that the resonant frequencies of the circuit cover the entire AM band: 550 - 1600 kHz. Cmax= ___ F

2) Find the minimum capacitance the variable capacitor must be able to reach in order that the resonant frequencies of the circuit cover the entire AM band: 550 - 1600 kHz. Cmin= ___ F

3) For the parameters of part (1) and (2), if a current is present in the circuit with peak value 2.5 µA, calculate the maximum voltage that appears across the inductor, at the upper end of the AM frequency band. VL max= ___ V

4) For the parameters of part (1) and (2), if a current is present in the circuit with peak value 2.5 µA, calculate the maximum voltage that appears across the capacitor, at the upper end of the AM frequency band. VC max= ___ V

5) Suppose now you wish to build a variable LC circuit whose resonant frequencies cover the full FM band: 88 - 108 MHz. If you choose a fixed inductance L = 33 µH, what is the maximum capacitance the variable capacitor must reach in this case? Cmax= ___ F

6) For the same situation as in part (5), what is the minimum capacitance the variable capacitor must reach in that case? C'min = ___ F

Explanation / Answer

L = 2.9 mH, fL= 550 kHz, fH= 1600 kHz, i = 2.5 A,

fL' = 88 MHz, fH' = 108 MHz, and L' = 33 H

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1. Cmax = 1 /L(2fL)2 = 2.89e-11 F= 28.9e-12 F

2. Cmin = 1 /L(2fH)2= 3.415e-12 F

3. VCmax = VLmax = 2Li fH = 0.072848 V = 7.2848e-2 V

4. VCmax = VLmax = 2Li fH = 0.072848 V = 7.2848e-2 V

5. C'max = 1 / L'(2f'L)2

6. C'min = 1 /L'(2f 'H)2

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