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Ch 30: Inductance
Young & Freedman Calc - University Physics 15th Edition
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Not the one you use?Change textbook
All textbooksYoung & Freedman Calc 15th EditionCh 30: InductanceProblem 39a
Chapter 30, Problem 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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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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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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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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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Related Practice
Textbook Question

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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Textbook Question

It has been proposed to use large inductors as energy storage devices. How much electrical energy is converted to light and thermal energy by a 150 W light bulb in one day?

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Textbook Question

A solenoid 25.0 cm long and with a cross-sectional area of 0.500 cm2 contains 400 turns of wire and carries a current of 80.0 A. Calculate: the total energy contained in the coil's magnetic field (assume the field is uniform);

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Textbook Question

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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