High School

Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ 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?

Answer :

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]