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Answer :
The capacitance needed in an RLC circuit to tune into an FM station broadcasting at 99.7 MHz, with a resistance of 11.8Ω, and an inductance of 1.50 μH, is 2.54 pF.
The resonance frequency f in an RLC circuit is given by the formula f = 1/ (2π √LC), where f is frequency, L is inductance, and C is capacitance. We can rearrange this formula to solve for C: C = 1 / (4π²f²L). Substituting the given values, the capacitance [tex]C = 1 / (4π²(99.7 x 10^6 Hz)²(1.50 x 10^-6 H)) = 2.54 x 10^-12[/tex] Farads or 2.54 pF.
Therefore, a capacitance of 2.54 pF should be used in the RLC circuit to tune into the FM station broadcasting at 99.7 MHz.
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