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Ch 30: Inductance
Young & Freedman Calc - University Physics 15th Edition
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Non è quello che usi tu?Cambia libro di testo
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Capitolo 30, Problema 39a

An L-R-C series circuit has L = 0.450 H, C = 2.50 × 10-5 F, and resistance R. What is the angular frequency of the circuit when R = 0?

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Start by understanding the concept of an L-R-C series circuit, which consists of an inductor (L), a capacitor (C), and a resistor (R) connected in series. The angular frequency of such a circuit is determined by the inductance and capacitance when the resistance is zero.
Recall the formula for the angular frequency \( \omega \) of an L-R-C circuit when the resistance \( R = 0 \). The formula is given by \( \omega = \frac{1}{\sqrt{LC}} \). This formula is derived from the resonance condition of the circuit.
Substitute the given values into the formula. Here, \( L = 0.450 \) H and \( C = 2.50 \times 10^{-5} \) F. The substitution will look like \( \omega = \frac{1}{\sqrt{0.450 \times 2.50 \times 10^{-5}}} \).
Simplify the expression inside the square root. Calculate \( 0.450 \times 2.50 \times 10^{-5} \) to find the product of the inductance and capacitance.
Finally, take the square root of the product calculated in the previous step and then find the reciprocal to determine the angular frequency \( \omega \). This will give you the angular frequency of the circuit when \( R = 0 \).

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Angular Frequency in L-R-C Circuits

Angular frequency in an L-R-C circuit is a measure of how rapidly the circuit oscillates. When resistance R is zero, the circuit is purely oscillatory, and the angular frequency is determined by the inductance (L) and capacitance (C) using the formula ω = 1/√(LC). This frequency is crucial for understanding the natural oscillations of the circuit.
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LRC Circuits

Inductance

Inductance (L) is a property of a coil or inductor that quantifies its ability to store energy in a magnetic field when electrical current flows through it. In an L-R-C circuit, inductance affects the rate of change of current and plays a key role in determining the circuit's angular frequency, especially when resistance is negligible.
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Mutual Induction

Capacitance

Capacitance (C) is the ability of a capacitor to store electrical energy in an electric field. It is a measure of how much charge a capacitor can hold per unit voltage. In an L-R-C circuit, capacitance influences the oscillation frequency, as it determines how quickly the circuit can charge and discharge, affecting the angular frequency when resistance is zero.
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Capacitors & Capacitance (Intro)
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Domanda del libro di testo

An L-R-C series circuit has L = 0.450 H, C = 2.50 × 10-5 F, and resistance R. What value must R have to give a 5.0% decrease in angular frequency compared to the value calculated in part (a)?

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It has been proposed to use large inductors as energy storage devices. If the amount of energy calculated in part is stored in an inductor in which the current is 80.0 A, what is the inductance?

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