Question

The tuner knob on an FM radio moves the plates of an adjustable capacitor that is in series with a 0.900-uH inductor and a net resistance of 1000 22. The peak current induced in the circuit by a radio wave of a specific carrier frequency becomes large when the natural frequency of the circuit matches the carrier frequency. What is the frequency f of the FM station that is tuned in when the capacitor in the radio is adjusted to 5.10 pF?

Answer 1

The frequency of the FM station is found using the resonant frequency formula for an LC circuit. With the provided inductance and capacitance values, the frequency can be calculated.

Step-by-step explanation:

The frequency f of the FM station that the radio is tuned into when the capacitor in the radio is adjusted to 5.10 pF can be determined using the formula for the resonant frequency f of a LC circuit, which is f = 1 / (2π∙sqrt(LC)), where L is the inductance and C is the capacitance. Given that the inductance L is 0.900 µH (or 0.900 x 10-6 H) and the capacitance C is 5.10 pF (or 5.10 x 10-12 F), we can calculate the resonant frequency. Plugging the values into the formula, we get:

f = 1 / (2π∙sqrt(0.900 x 10-6 H × 5.10 x 10-12 F))

After calculating the square root and then the division, we find the frequency f that the radio is tuned into.