A tuning circuit consists of a 10.0 ohm resistor, a 1.00 pF capacitor and a 14.1

Question

A tuning circuit consists of a 10.0 ohm resistor, a 1.00 pF capacitor and a 14.1 mH inductor. What is the resonant frequency (in Hz) of the radio station to which this circuit is tuned? If the rms voltage of the station s signal is 50.0 mV. what is the rms current in the circuit? What is the rms voltage just across the inductor? Assume a 100 W light bulb radiates isotropically. If your eye can detect an intensity as little as 2.0 mu W/m^2, from how far from the bike be seen? What is the rms value of the magnetic field at this intensity?

Explanation / Answer

a) fo = 1/2*pi(14.1*10^-3*1*10^-12)^0.5 = 1340326.411 Hz

b) Impedence Z = (R^2 + (Xl - Xc)^2)0.5

At resonance Xl = Xc

Hence Z = R

So Irms = Vrms/Z = 50*10^-3/10 = 5 mA

c) Since they are in series so same current flows throughout

So

Vrms across inductor = Irms *Xl

Xl = 2*pi*fo*L = 118743.42 ohms

Hence Vrms = 5*10^-3*118743.42 = 593.72 V

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