/*! 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 14 What is the net number of electr... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 14

What is the net number of electrons per second that pass through the cross- section of a wire carrying \(5 \mathrm{~A}\) of dc current? The current flow is due to electrons, and the magnitude of the charge of each electron is \(1.60 \times 10^{-19} \mathrm{C}\).

Short Answer

Expert verified
3.125 x 10^{19} electrons per second pass through the wire.

Step by step solution

01

Understanding the Given Values

We know that a current of 5 A (Amperes) is flowing in a wire. The charge of an electron is given as \(1.60 \times 10^{-19} \text{ C}\). We are asked to find the net number of electrons passing a cross-section of the wire per second.
02

Using the Formula for Current Flow

Current (\(I\)) can be expressed as \(I = \frac{Q}{t}\), where \(Q\) is the total charge passing through the cross-section in time \(t\). Since current is 5 A, \(Q = 5 \text{ C/s}\).
03

Calculating the Number of Electrons

To find the number of electrons \(n\), use \(Q = n \times e\), where \(e = 1.60 \times 10^{-19} \text{ C}\) is the charge of one electron. Hence, \(n = \frac{Q}{e} = \frac{5}{1.60 \times 10^{-19}}\).
04

Perform Calculation

Substitute the values to find \(n\):\[n = \frac{5}{1.60 \times 10^{-19}} = 3.125 \times 10^{19}\]Therefore, \(3.125 \times 10^{19}\) electrons pass through each second.

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!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

DC Current
Direct Current (DC) is the type of electrical current that flows in one constant direction. This is different from alternating current (AC), where the flow periodically reverses direction.
In DC circuits, the current remains steady and stable, making it easier to work with in calculations. Batteries are the most common sources of DC power. When connected in a circuit, they push current consistently in one direction. This consistent flow is what makes devices like flashlights run without flickering.
For this exercise, our circuit is experiencing a DC current of 5 amperes (A), which means that 5 coulombs of charge pass a given point in the circuit every second.
Charge of Electron
Electrons, which are negatively charged particles, are fundamental to the flow of electricity. Each electron carries a specific charge amount known as the elementary charge.
This charge is quantified as \(1.60 \times 10^{-19} \text{ C}\), where C stands for coulombs.
Understanding this value is essential, as it serves as a standard for calculating how many electrons contribute to a specific amount of charge. In our problem, the charge of the electron helps us bridge the gap between the macroscopic measurement of current (in amperes) and the microscopic level (individual electron movement)."
  • Fundamental charge unit: \(1.60 \times 10^{-19} \text{ C}\)
  • Allows for electron counting in electrical studies
Current Flow
Current flow refers to the movement of electric charge through a conductor. In electrical engineering, current is often symbolized by the letter \(I\) and is measured in amperes (A).
The basic formula to understand current flow is \(I = \frac{Q}{t}\), where \(Q\) represents charge, and \(t\) represents time. In this formula, the connection between current, charge, and time is made explicit.
In the case of a DC current of 5 A, this means every second, 5 coulombs of charge are flowing through the wire. This flow occurs because a large number of electrons, each with a tiny charge, are in motion, creating an observable current through the conductor.
Number of Electrons
Determining the number of electrons explains the micro-level process of electricity. In the case of our exercise, we need to understand how many electrons correspond to a charge flow of 5 coulombs per second.
The formula to find the number of electrons \(n\) is \(n = \frac{Q}{e}\), where \(Q\) is the charge (in coulombs) and \(e\) is the charge of one electron.
By substituting the known values: \[n = \frac{5}{1.60 \times 10^{-19}}\] we find the number of electrons to be \(3.125 \times 10^{19}\). This means that each second, approximately \(3.125 \times 10^{19}\) electrons pass through the cross-section of the wire.
  • Helps quantify electron flow in practical terms
  • Links the microscopic and macroscopic views of electricity

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 fully charged deep-cycle lead-acid storage battery is rated for \(12.6 \mathrm{~V}\) and 100 ampere hours. (The ampere-hour rating of the battery is the operating time to discharge the battery multiplied by the current.) This battery is used aboard a sailboat to power the electronics which consume 30 W. Assume that the battery voltage is constant during the discharge. For how many hours can the electronics be operated from the battery without recharging? How much energy in kilowatt hours is initially stored in the battery? If the battery costs \(\$ 95\) and has a life of 250 chargedischarge cycles, what is the cost of the energy in dollars per kilowatt hour? Neglect the cost of recharging the battery.

A certain battery has terminals labeled \(a\) and b. The battery voltage is \(v_{a b}=12 \mathrm{~V}\). To increase the chemical energy stored in the battery by \(600 \mathrm{~J}\), how much charge must move through the battery? Should electrons move from \(a\) to \(b\) or from \(b\) to \(a\) ?

A power of \(100 \mathrm{~W}\) is delivered to a certain resistor when the applied voltage is \(100 \mathrm{~V}\). Find the resistance. Suppose that the voltage is reduced by 10 percent (to \(90 \mathrm{~V}\) ). By what percentage is the power reduced? Assume that the resistance remains constant.

In the fluid-flow analogy for an electrical circuit, the analog of electrical current is volumetric flow rate with units of \(\mathrm{cm}^{3} / \mathrm{s}\). For a proper analogy to electrical circuits, must the fluid be compressible or incompressible? Must the walls of the pipes be elastic or inelastic? Explain your answers.

State Kirchhoff's current law in your own words. Why is it true?
See all solutions

Recommended explanations on Physics Textbooks

Energy Physics

Read Explanation

Scientific Method Physics

Read Explanation

Physical Quantities And Units

Read Explanation

Work Energy and Power

Read Explanation

Magnetism and Electromagnetic Induction

Read Explanation

Electricity and Magnetism

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.