Question 6A103

The resonant frequency ($f_r$) of a tuned LC circuit is determined by the inductance (L) and capacitance (C) values, and is calculated using the formula: $f_r = \frac{1}{2\pi\sqrt{LC}}$ In this question, the "150 microfarad tuning coil" is a likely typo; coils are inductors measured in Henries, not Farads. Assuming it should be 150 microhenries ($\mu$H) for the coil's inductance: L = 150 $\mu$H = $150 \times 10^{-6}$ H C = 500 pF = $500 \times 10^{-12}$ F Substituting these values: $f_r = \frac{1}{2\pi\sqrt{(150 \times 10^{-6})(500 \times 10^{-12})}}$ $f_r = \frac{1}{2\pi\sqrt{7.5 \times 10^{-14}}}$ $f_r \approx \frac{1}{2\pi \times 2.7386 \times 10^{-7}}$ $f_r \approx 581120 \text{ Hz}$, which is approximately 581 kHz. The 10 ohms resistance affects the Q-factor and bandwidth of the circuit but does not change the calculated resonant frequency. Options B, C, and D are incorrect as they do not result from the correct application of the resonant frequency formula with the given component values (assuming the $\mu$F to $\mu$H correction).