High School

An RLC circuit is used in a radio to tune into an FM station broadcasting at [tex]f = 99.7 \text{ MHz}[/tex]. The resistance in the circuit is [tex]R = 11.8 \, \Omega[/tex], and the inductance is [tex]L = 1.50 \, \mu\text{H}[/tex]. What capacitance should be used?

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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