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An electric oscillator is made with a 0.10 μF capacitor and a 1.0 mH inductor. The capacitor is initially charged to 5.0 V. What is the maximum current through the inductor as the circuit oscillates?
30. Induction and Inductance
LC Circuits
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What is the resonant frequency of an LC circuit consisting of a inductor paired with a capacitor?
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Verified step by step guidance1
Identify the formula for the resonant frequency of an LC circuit, which is given by \( f = \frac{1}{2\pi\sqrt{LC}} \), where \( L \) is the inductance and \( C \) is the capacitance.
Convert the given values into standard units: the inductance \( L = 2.0 \text{ mH} = 2.0 \times 10^{-3} \text{ H} \) and the capacitance \( C = 300 \text{ nF} = 300 \times 10^{-9} \text{ F} \).
Substitute the values of \( L \) and \( C \) into the resonant frequency formula: \( f = \frac{1}{2\pi\sqrt{(2.0 \times 10^{-3})(300 \times 10^{-9})}} \).
Simplify the expression under the square root: calculate \( L \times C = 2.0 \times 10^{-3} \times 300 \times 10^{-9} \).
Calculate the resonant frequency \( f \) by evaluating the expression \( \frac{1}{2\pi\sqrt{LC}} \) using the simplified value from the previous step.
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