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 = 18.0 \, \Omega[/tex], and the inductance is [tex]L = 2.00 \, \mu \text{H}[/tex]. What capacitance (in pF) is required for the circuit?

To tune into an FM station broadcasting at 99.7MHz with an RLC circuit containing an inductance of 2.00 mu H, you can calculate the required capacitance using the resonant frequency formula for an RLC circuit, and then convert the result to picofarads.

To find the required capacitance for an RLC circuit to tune into an FM station broadcasting at 99.7MHz, we use the resonant frequency formula for an RLC circuit:

f = 1 / (2 * pi * sqrt(L * C))

Solving for C gives us:

[tex]C = 1 / (4 * pi^2 * f^2 * L)[/tex]

After plugging in the given values:

[tex]f = 99.7MHz = 99.7 x 10^6 Hz[/tex]

[tex]L = 2.00 mu H = 2.00 x 10^-6 H[/tex]

We get:

[tex]C = 1 / (4 * pi^2 * (99.7 x 10^6)^2 * 2.00 x 10^-6)[/tex]

After calculating the value, we can convert the capacitance into picofarads (pF):

C = capacitance in farads (F)

[tex]C x 10^12 = capacitance in picofarads (pF)[/tex]