Multiple Choice
An inductor, a capacitor, and a resistor are in series with a AC source. If the capacitor is , the inductor is , and the resistor is , what is the impedance?
31. Alternating Current
Series LRC Circuits
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An inductor, a capacitor, and a resistor are in series with an AC source. If the capacitor is , the inductor is , and the resistor is . what is the circuit's resonant frequency?
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Verified step by step guidance1
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.
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.
Substitute the given values into the formula: \( L = 24 \text{ mH} = 24 \times 10^{-3} \text{ H} \) and \( C = 470 \text{ nF} = 470 \times 10^{-9} \text{ F} \).
Calculate the expression under the square root: \( \sqrt{LC} = \sqrt{(24 \times 10^{-3})(470 \times 10^{-9})} \).
Finally, compute the resonant frequency using the formula: \( f_0 = \frac{1}{2\pi\sqrt{LC}} \) to find the frequency in hertz (Hz).
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