An inductor, a capacitor, and a resistor are in series with an AC source. If the capacitor is $470\text{nF}$, the inductor is $24\text{mH}$, and the resistor is $800\Omega$. what is the circuit's resonant frequency?

• A. $190\mathrm{ Hz}$
• B. $510\mathrm{ Hz}$
• C. $720\mathrm{ Hz}$
• D. $1100\mathrm{ Hz}$
• E. $1900\mathrm{ Hz}$
• F. $1500\mathrm{ Hz}$

Answer: (F)

Verified step by step guidance

1. Identify that the problem involves a series RLC circuit, which consists of a resistor (R), an inductor (L), and a capacitor (C) connected in series with an AC source.
2. Recall that the resonant frequency \( f_0 \) of a series RLC circuit is given by the formula: \( f_0 = \frac{1}{2\pi\sqrt{LC}} \), where \( L \) is the inductance and \( C \) is the capacitance.
3. Substitute the given values into the formula: \( L = 24 \text{ mH} = 24 \times 10^{-3} \text{ H} \) and \( C = 470 \text{ nF} = 470 \times 10^{-9} \text{ F} \).
4. Calculate the expression under the square root: \( \sqrt{LC} = \sqrt{(24 \times 10^{-3})(470 \times 10^{-9})} \).
5. Finally, compute the resonant frequency using the formula: \( f_0 = \frac{1}{2\pi\sqrt{LC}} \) to find the frequency in hertz (Hz).