Consider the FM antenna circuit shown in the figure, with , , and . The radio signal induces an alternating emf in the antenna with . We have to find (a) the frequency of the incoming waves for which the antenna is in “tune”; (b) the rms current in the antenna, and (c) the rms potential difference across the capacitor.

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The inductance of the antenna

,

and the capacitance of the antenna

.

Therefore, the frequency of the incoming waves for which the antenna is in “tune” will be

The radio signal induces an alternating emf in the antenna with . As the antenna is tuned to the frequency of the FM signal, the impedance will be resistive and as the resistance of the antenna , the rms current in the antenna will be

The capacitive reactance of the antenna will be

The rms potential difference across the capacitor will be