Use the diagram to the right for the following two questions. As shown, an AM ra

Question

Use the diagram to the right for the following two questions. As shown, an AM radio tuning circuit consists of an inductor, L = 6.0 times 10^-5 H, in series with a resistance of R = 0.25 Ohm, and a variable capacitor currently tuned to a capacitance of C = 1.5 times 10^-9F. What is the frequency of the station that the radio is tuned to? 5.3 times 10^5 Hz 1.0 times 10^6 Hz 1.6 times 10^6 Hz 3.3 times 10^6Hz 2.1 times 10^7 Hz A station at 1.5 times 10^6 Hz produces a 5 times 10^-3 V RMS signal. What is the RMS current in the radio at this frequency? 8.8 times 10^-6 A 1.0 times 10^-5 A 7.1 times 10^-5 A 1.5 times 10^-2A 2.0 times 10^-2A

Explanation / Answer

We know that in LCr circuit

resonance frequency is W0 = 1/ sqrt(LC)
  

           = 1/ sqrt(6*10^-5*1.5*10^-9) Hz

           = 3333333.3333333335 Hz

           = 3333.3333 kHz
           = 3.3 MHz
           = 3.3*10^6 Hz

          

I rms = Vrms /Z

where Z = sqrt(R^2+(Xl-Xc)^2)

Xl = W*L = 2pi*1.5*10^6*1.6*10^-5 = 150.8 ohm

Xc = 1/Wc = 1/(2pi*1.5*10^6*1.5*10^-9) ohm = 70.74 ohm

so the impedance is Z = sqrt(0.25^2+ (150.8-70.74)^2) ohm = 80.06 ohm

Irms= Vrms/Z = 0.0050/(80.06) A = 6.2453160*10^-5 A

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