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An RLC circuit is used in a radio to tune into an FM station broadcasting at f = 99.7 MHz. The resistance in the circuit is R = 8.00 ?, and the inductance is L = 2.00 �H. What capacitance should be used?
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The resonance frequency is found from:
f = 1 / (2 * pi * SQRT ( L * C) )
99.7E6 Hz = 1 / (2 * 3.1415 * SQRT ( 2E-6 * C) )
1 / 99.7E6 Hz = 2 * 3.1415 * SQRT ( 2E-6 * C)
10.03E-9 = 6.2830 * SQRT ( 2E-6 * C)
10.03E-9 / 6.2830 = SQRT ( 2E-6 * C)
1.5963E-9 =SQRT ( 2E-6 * C)
(1.5963E-9)^2 = ( 2E-6 * C)
2.5483E-18 = ( 2E-6 * C)
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