Answer
a. $1.3\times10^{-6}H$
b. $9.9\times10^{-11}F$
Work Step by Step
Equation 21-19 gives the resonant frequency of a LC circuit.
$$f_o=\frac{1}{2 \pi}\sqrt{\frac{1}{LC}}$$
We see that the minimum value of the capacitance corresponds to the higher frequency.
a. Find the inductance.
$$L=\frac{1}{4\pi^2(86\times 10^{-12}F)(15.0\times10^6Hz)^2}=1.3\times10^{-6}H$$
b. The maximum value of the capacitance corresponds to the lower frequency.
$$C=\frac{1}{4\pi^2Lf_o^2}$$
$$C=\frac{1}{4\pi^2(1.31\times 10^{-6}H)(14.0\times10^6Hz)^2}=9.9\times10^{-11}F$$
