Electronics Engineering (ELEX) Board Practice Exam

What is the calculated frequency of oscillations for an LC tuned circuit with L₁ = 58.6 µH and C₁ = 300 pF?

1. 600 kHz

2. 1199 kHz

3. 1500 kHz

4. 2000 kHz

The correct answer is: 1199 kHz

To find the frequency of oscillations for an LC tuned circuit, the formula used is: \[ f = \frac{1}{2\pi\sqrt{LC}} \] where \( f \) is the frequency in hertz, \( L \) is the inductance in henries, and \( C \) is the capacitance in farads. First, we need to ensure that both \( L \) and \( C \) are in the correct units. In this case: - \( L = 58.6 \, \mu H = 58.6 \times 10^{-6} \, H \) - \( C = 300 \, pF = 300 \times 10^{-12} \, F \) Now substituting the values into the formula: \[ f = \frac{1}{2\pi\sqrt{(58.6 \times 10^{-6})(300 \times 10^{-12})}} \] Calculating the product of \( L \) and \( C \): \[ L \times C = 58.6 \times 10^{-6} \times 300 \times 10^{-12} = 1.758