/*! 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 8 A television set draws an rms cu... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 21: Problem 8

A television set draws an rms current of \(2.50 \mathrm{A}\) from a \(60-\mathrm{Hz}\) power line. Find (a) the average current, (b) the average of the square of the current, and (c) the amplitude of the current.

Short Answer

Expert verified
Answer: The average current is 0 A, the average of the square of the current is 6.25 A虏, and the amplitude of the current is 3.54 A.

Step by step solution

01

Calculate the average current

The average current for a sinusoidal waveform is actually zero. This is because there are equal times where the current is positive and negative, which ultimately cancels each other out. So, the average current is 0 A.
02

Calculate the average of the square of the current

To find the average of the square of the current, we square the RMS value: $$(I_{rms})^2 = (2.50 \mathrm{A})^2 = 6.25 \mathrm{A^2}$$ So, the average of the square of the current is \(6.25 \mathrm{A^2}\).
03

Calculate the amplitude of the current

To find the amplitude of the current, we use the formula for RMS value of a sinusoidal waveform, given by: $$I_{rms} = \frac{I_{max}}{\sqrt{2}}$$ Where \(I_{max}\) is the amplitude of the current, and \(I_{rms}\) is the RMS value. We rearrange the equation to solve for \(I_{max}\): $$I_{max} = I_{rms} \cdot \sqrt{2} = 2.50 \mathrm{A} \cdot \sqrt{2} = 3.54 \mathrm{A}$$ So, the amplitude of the current is \(3.54 \mathrm{A}\).

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

A capacitor is connected across the terminals of a 115 \(\mathrm{V}\) rms, \(60.0-\mathrm{Hz}\) generator. For what capacitance is the rms current \(2.3 \mathrm{mA} ?\)
A solenoid with a radius of \(8.0 \times 10^{-3} \mathrm{m}\) and 200 turns/cm is used as an inductor in a circuit. When the solenoid is connected to a source of \(15 \mathrm{V}\) ms at \(22 \mathrm{kHz}\), an \(\mathrm{rms}\) current of \(3.5 \times 10^{-2} \mathrm{A}\) is measured. Assume the resistance of the solenoid is negligible. (a) What is the inductive reactance? (b) What is the length of the solenoid?
A certain circuit has a \(25-\Omega\) resistor and one other component in series with a \(12-\mathrm{V}\) (rms) sinusoidal ac source. The rms current in the circuit is 0.317 A when the frequency is \(150 \mathrm{Hz}\) and increases by \(25.0 \%\) when the frequency increases to \(250 \mathrm{Hz}\). (a) What is the second component in the circuit? (b) What is the current at $250 \mathrm{Hz} ?$ (c) What is the numerical value of the second component?
In the crossover network of Problem \(61,\) the inductance \(L\) is $1.20 \mathrm{mH}$. The capacitor is variable; its capacitance can be adjusted to set the crossover point according to the frequency response of the woofer and tweeter. What should the capacitance be set to for a crossover point of $180 \mathrm{Hz} ?[\text {Hint}:$ At the crossover point, the currents are equal in amplitude. \(]\)
A parallel plate capacitor has two plates, each of area $3.0 \times 10^{-4} \mathrm{m}^{2},\( separated by \)3.5 \times 10^{-4} \mathrm{m} .$ The space between the plates is filled with a dielectric. When the capacitor is connected to a source of \(120 \mathrm{V}\) rms at \(8.0 \mathrm{kHz}\) an mms current of \(1.5 \times 10^{-4} \mathrm{A}\) is measured. (a) What is the capacitive reactance? (b) What is the dielectric constant of the material between the plates of the capacitor?
See all solutions

Recommended explanations on Physics Textbooks

Classical Mechanics

Read Explanation

Work Energy and Power

Read Explanation

Electromagnetism

Read Explanation

Linear Momentum

Read Explanation

Force

Read Explanation

Thermodynamics

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.