Electronics Engineering (ELEX) Board Practice Exam

The frequency of an LC oscillator can be calculated using the formula for the resonant frequency of an LC circuit, given by:

\[ f = \frac{1}{2\pi \sqrt{LC}} \]

where \( f \) is the frequency in hertz, \( L \) is the inductance in henries, and \( C \) is the capacitance in farads. To find the required capacitance for a given frequency and inductance, we can rearrange the formula to solve for \( C \):

\[ C = \frac{1}{(2\pi f)^2 L} \]

Plugging in the values:

- Frequency \( f = 1 \, \text{GHz} = 1 \times 10^9 \, \text{Hz} \)

- Inductance \( L = 1 \, \text{mH} = 1 \times 10^{-3} \, \text{H} \)

Now substituting these values into the capacitance formula:

\[ C = \frac{1}{(2\pi (1 \times 10^9))^2 (1 \times 10^{-3})} \]

Calculating \( (