A televizions station broadcasts at a frequency of 86 MHz. The circui cotains an inductor with an inducace?

Question

L = 1.2 * 10^-6 H and a variable-capacitance C. Determine the value of C that allows this television station to be tuned in.

Answer 1

To tune in the signal, the capacitance has to be adjusted such that the resonance frequency of the LC-circuit is identical to signal frequency.

Resonance frequency of the circuit is given by:

f = 1/(2∙π∙√(L∙C))

Therefore

C = 1/((2∙π∙f)²∙L)

= 1/( (2∙π ∙ 86∙10⁶s⁻¹)² ∙1.2∙10⁻⁶H)

= 2.854∙10⁻¹²F

= 2.854pF