(a) The resonant frequency of the circuit is
[tex]f=9.00 GHz = 9.00 \cdot 10^9 Hz[/tex]
The relationship between the resonant frequency of a circuit, the inductance L and the capacity C is
[tex]f= \frac{1}{2 \pi \sqrt{LC}}[/tex]
Since the capacitance in the circuit is [tex]C=2.00 pF= 2.00 \cdot 10^{-12} F[/tex], we can use the previous formula to find the inductance L:
[tex]L= \frac{1}{(2 \pi f)^2 C} = \frac{1}{(2 \pi 9.00 \cdot 10^9 Hz)^2(2.00 \cdot 10^{-12} F)}= 1.57 \cdot 10^{-10} H[/tex]
b) The inductive reactance of the circuit is given by:
[tex]X_L = 2 \pi f L[/tex]
where f is the frequency of the circuit. The frequency is still the same of the previous part of the exercise, so the inductive reactance is:
[tex]X_L = 2 \pi (9.00 \cdot 10^9 Hz)(1.57 \cdot 10^{-10}H)=8.87 \Omega[/tex]
