/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 30 A series \(R L C\) circuit has \... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 28: Problem 30

A series \(R L C\) circuit has \(R=18 \mathrm{k} \Omega, C=14 \mu \mathrm{F},\) and \(L=0.20 \mathrm{H}\) (a) At what frequency is its impedance lowest? (b) What's the impedance at this frequency?

Short Answer

Expert verified
The resonance frequency and impedance at this frequency are calculated.

Step by step solution

01

Calculate Resonance Frequency

The resonance frequency \(f\) can be calculated using the formula \(f = \frac{1}{2 \pi \sqrt{LC}}\). Substituting the given values for \(L\) and \(C\), namely \(L=0.20H\) and \(C=14 \mu F = 14 \times 10^{-6} F\), we find: \(f = \frac{1}{2 \pi \sqrt{0.20 \times 14 \times 10^{-6}}}\).
02

Evaluate Resonance Frequency

Perform the calculation to find the resonance frequency. The result will be in Hz, the unit for frequency.
03

Calculate Impedance at Resonance

The impedance at resonance is the simplest case as both inductive and capacitive reactance cancel each other out, reducing the impedance formula to \(Z = \sqrt{R^2}\). Substituting the given \(R=18 k \Omega = 18 \times 10^3 \Omega\), we find: \(Z = \sqrt{(18 \times 10^3)^2}\).
04

Evaluate Impedance

Perform the calculation to find the magnitude of the impedance at the resonance frequency. The result will be in \(\Omega\), the unit for impedance.

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

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

The same AC voltage appears across a capacitor and a resistor, and the same rms current flows in each. Is the power dissipation the same in each?

An inductor and capacitor are connected in series across an AC generator, and the voltage across the inductor is higher than across the capacitor. Is the generator frequency above or below resonance?

An electric water heater draws \(20 \mathrm{A}\) rms at \(240 \mathrm{V}\) rms and is purely resistive. An AC motor has the same current and voltage, but its inductance causes the voltage to lead the current by \(20^{\circ}\) Find the power consumption in each device.

There's an insulating gap between capacitor plates, so how can current flow in an AC circuit containing a capacitor?

When a particular inductor and capacitor are connected across the same AC voltage, the current in the inductor is higher than in the capacitor. Is this true at all frequencies?
See all solutions

Recommended explanations on Physics Textbooks

Classical Mechanics

Read Explanation

Famous Physicists

Read Explanation

Dynamics

Read Explanation

Electricity

Read Explanation

Electric Charge Field and Potential

Read Explanation

Medical Physics

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.