Ch 30: Inductance

Young & Freedman Calc - University Physics 14th Edition

Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook

Young & Freedman Calc 14th Edition

Ch 30: Inductance

Problem 38a

Chapter 30, Problem 38a

An L-R-C series circuit has L = 0.600 H and C = 3.00 mF. Calculate the angular frequency of oscillation for the circuit when R = 0.

Verified step by step guidance

First, understand that the angular frequency of oscillation in an L-R-C circuit is given by the formula \( \omega = \frac{1}{\sqrt{LC}} \), where \( L \) is the inductance and \( C \) is the capacitance.

Identify the given values: \( L = 0.600 \) H (henries) and \( C = 3.00 \) mF (millifarads). Note that 1 millifarad is equal to \( 1 \times 10^{-3} \) farads.

Convert the capacitance from millifarads to farads: \( C = 3.00 \times 10^{-3} \) F.

Substitute the values of \( L \) and \( C \) into the formula for angular frequency: \( \omega = \frac{1}{\sqrt{0.600 \times 3.00 \times 10^{-3}}} \).

Simplify the expression under the square root and calculate \( \omega \) using the formula. This will give you the angular frequency of oscillation for the circuit.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

Key Concepts

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

Angular Frequency

Angular frequency, denoted by ω, is a measure of how quickly an oscillating system cycles through its motion. In the context of an L-R-C circuit, it represents the rate of oscillation of the circuit's current and voltage. It is related to the frequency by the formula ω = 2πf, where f is the frequency in hertz.

Resonance in L-R-C Circuits

Resonance occurs in an L-R-C circuit when the inductive reactance and capacitive reactance are equal, leading to maximum energy transfer and oscillation. At resonance, the circuit oscillates at its natural frequency, which is determined by the inductance (L) and capacitance (C) of the circuit, and is independent of resistance (R) when R = 0.

Formula for Angular Frequency in L-R-C Circuits

The angular frequency of oscillation for an L-R-C circuit with no resistance (R = 0) is given by the formula ω = 1/√(LC). This formula arises from the balance between the inductive and capacitive reactances at resonance, allowing the circuit to oscillate freely at its natural frequency. It highlights the inverse relationship between angular frequency and the square root of the product of inductance and capacitance.

Recommended video:

Guided course

04:26

Oscillations in an LC Circuit

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 is the angular frequency of the circuit when R = 0?

views

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)?

views

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?

views

Textbook Question

An L-R-C series circuit has L = 0.600 H and C = 3.00 mF. What value of R gives critical damping?

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);

views

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?

views