Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 28: Problem 25

An LC circuit with \(C=18\) mF undergoes oscillations with period \(2.4 \mathrm{s}\). Find the inductance.

Short Answer

Expert verified
The inductance of the LC circuit is 0.091 Henrys (H).

Step by step solution

01

Identify given quantities

The capacitance C is \(18 × 10^{-3}\) F (since mF means milliFarads which is \(10^{-3}\) Farads) and the oscillation period T is 2.4s.
02

Calculate the frequency

The frequency f of the oscillations can be found by taking the reciprocal of the period T. Hence, \(f = 1/T = 1/2.4 s = 0.4167 Hz\).
03

Calculate the inductance

The frequency of the LC circuit can be represented by the equation \(f = 1/(2π√(LC))\). We can rearrange this equation to solve for L by squaring both sides, then dividing by \(4π^2f^2\) to get \(L = 1/(4π^2f^2C)\). Substituting the given values of C and calculated f gives \(L = 1/(4π^2(0.4167 Hz)^2 × 18 × 10^{-3} F) = 0.091 H\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Your professor tells you about the days before digital computers when engineers used electric circuits to model mechanical systems. Suppose a \(5.0-\mathrm{kg}\) mass is connected to a spring with \(k=1.44 \mathrm{kN} / \mathrm{m} .\) This is then modeled by an \(L C\) circuit with \(L=2.5 \mathrm{H} .\) What should \(C\) be in order for the \(L C\) circuit to have the same resonant frequency as the mass-spring system?

A series \(R L C\) circuit with \(R=47 \Omega, L=250 \mathrm{mH},\) and \(C=\) \(4.0 \mu \mathrm{F}\) is connected across a sine-wave generator whose peak output voltage is independent of frequency. Find the frequency range over which the peak current will exceed half its value at resonance.

An RLC circuit includes a 1.5 -H inductor and a \(250-\mu \mathrm{F}\) capacitor rated at 400 V. The circuit is connected across a sine-wave generator with \(V_{\mathrm{p}}=32 \mathrm{V} .\) What minimum resistance will ensure that the capacitor voltage does not exceed its rated value when the circuit is at resonance?

A series \(R L C\) circuit with \(R=1.3 \Omega, L=27 \mathrm{mH},\) and \(C=\) \(0.33 \mu \mathrm{F}\) is connected across a sine-wave generator. If the capacitor's peak voltage rating is \(600 \mathrm{V},\) what's the maximum safe value for the generator's peak output voltage when it's tuned to resonance?

A 15 - \(\mu\) F capacitor carries \(1.4 \mathrm{A}\) rms. What's its minimum safe voltage rating if the frequency is (a) \(60 \mathrm{Hz}\) and (b) \(1.0 \mathrm{kHz} ?\)
See all solutions

Recommended explanations on Physics Textbooks

Atoms and Radioactivity

Read Explanation

Waves Physics

Read Explanation

Turning Points in Physics

Read Explanation

Mechanics and Materials

Read Explanation

Solid State Physics

Read Explanation

Wave Optics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free