Tune Radio to 5.30 MHz with 1.04 µH Inductance

[nemzy]

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 can't find it anywhere in my book

 

[da_willem]

For a capacitor and inductance the relation between current and voltage are:

I=C\frac{dV}{dt}
V=L\frac{dI}{dt}

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

Z_C=\frac{1}{j \omega C}
Z_L=j\omega L

 

[Curious3141]

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 can't find it anywhere in my book

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 \omega for which the impedance is a minimum ? What is the value of that minimum impedance ? What frequency does this occur at (\omega = 2\pi f) ? 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.

 

[poolwin2001]

w=1/(LC)^1/2
TOO lazy to use latex

 

[Curious3141]

w=1/(LC)^1/2
TOO lazy to use latex

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.