Physics: Principles with Applications
Physics: Principles with Applications
6th Edition
ISBN: 9780130606204
Author: Douglas C. Giancoli
Publisher: Prentice Hall
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Chapter 22, Problem 33P
To determine

The range of values must the inductance have to tune station form 88MHz to 108MHz .

Expert Solution & Answer
Check Mark

Answer to Problem 33P

The answer is 2.59nHL3.89nH .

Explanation of Solution

Given info:

Capacitance of FM radio tuning circuit, C=840pF=840×1012F (fixed)

Primary Frequency of station, f1=88MHz=88000000Hz

Secondary Frequency of station, f2=108MHz=108000000 Hz

Formula used:

Formula for the resonant frequency of an LC circuit

  f=12πLC

Where, f is frequency

  L is inductance and c is capacitance

Calculation:

Rearrange the formula: f=12πLC . So, f=(12π)(1LC)12

Calculation for primary inductance, L1

  f=(12π)(1L1C)12

Substitute the given values:

  88000000Hz=(12π)(1L1(840×1012F))12

  L1=3.89×109H=3.89nH

Calculation for secondary inductance, L2

  f=(12π)(1L1C)12

Substitute the given values:

  108000000 Hz=(12π)(1L2(840×1012F))12

  L2=2.59×109H=2.59nH

Conclusion: The range of values must the inductance have to tune station form 88MHz to 108MHz is 2.59nHL3.89nH .

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