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Very simple problem

  1. Feb 1, 2005 #1
    A fixed inductance of 1.04 µH is used in series with a variable capacitor in the tuning section of a radio. What capacitance tunes the circuit to the signal from a station broadcasting at 5.30 MHz?

    Hmm, i have no idea how i can relate capacitance with frequency and with indunctance? is there a formula that i am overlooking? I cant find it anywhere in my book
     
  2. jcsd
  3. Feb 1, 2005 #2
    For a capacitor and inductance the relation between current and voltage are:

    [tex]I=C\frac{dV}{dt}[/tex]
    [tex]V=L\frac{dI}{dt}[/tex]

    Now if you a apply an ac signal the impedance will depend on frequency. E.g with a sinosoidal signal with frequency [tex]\omega[/tex]: [itex]I=I_0 e^{j \omega t}[/itex] (do you know this complex notation?) differenting and integrating yield for the impedances:

    [tex]Z_C=\frac{1}{j \omega C}[/tex]
    [tex]Z_L=j\omega L[/tex]
     
  4. Feb 1, 2005 #3

    Curious3141

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    Da Willem gave you two vital formulas for the reactances of the (pure) capacitance and (pure) inductance. Use those, in complex form to find an expression for the total impedance of a series combination of them.

    Now, using that expression for the total impedance, can you find the value of [itex]\omega[/itex] for which the impedance is a minimum ? What is the value of that minimum impedance ? What frequency does this occur at ([itex]\omega = 2\pi f[/itex]) ? What state is said to exist at this frequency (hint : r_s_n___e) ?

    EDIT : Sorry, upon closer reading of the question, the required r_s_n__t frequency is given, they want you to find the value of C that causes that state at that given frequency. Still, work through the algebra above as I prescribed, it'll greatly aid understanding and it'll be satisfying to get it from first principles.
     
    Last edited: Feb 1, 2005
  5. Feb 1, 2005 #4
    w=1/(LC)^1/2
    TOO lazy to use latex
     
  6. Feb 1, 2005 #5

    Curious3141

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    We try not to give away the answers until the poster has demonstrated serious effort in trying it out himself. I could've easily typed that out and been done with it. :uhh:
     
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