This question involves the concepts of frequency, inductive reactance, and capacitive reactance.
"3.84 x 10⁻⁷ H" inductance should be paired with 7 pf capacitor to build a receiver circuit for this station.
In order to build a receiver circuit, the inductive reactance must be equal to the capacitive reactance.
[tex]X_L=X_C\\\\\omega L=\frac{1}{\omega C}\\\\L=\frac{1}{\omega^2 C}\\\\L=\frac{1}{(2\pi f)^2 C}[/tex]
where,
L = inductance = ?
f = frequency = 97 MHz = 97 x 10⁶ Hz
C = capacitance = 7 pF = 7 x 10⁻¹² F
Therefore,
[tex]L=\frac{1}{(2\pi (97\ x\ 10^{6}\ Hz))^2(7\ x\ 10^{-12}\ F)}[/tex]
L = 3.84 x 10⁻⁷ H = 0.384 μH
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