/*! 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 11 A net charge of 20 C passes a lo... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 17: Problem 11

A net charge of 20 C passes a location in a wire in 1.25 min. How long does it take for a net 30 - C charge to pass that location if the current in the wire is doubled?

Short Answer

Expert verified
56.25 seconds.

Step by step solution

01

Understand the Problem

We need to determine how long it takes for a net charge of 30 C to pass through a location if the current is doubled. Initially, a 20 C charge takes 1.25 minutes.
02

Calculate Initial Current

The current ( I ) is defined as charge ( Q ) divided by time ( t ). Here, the initial current can be calculated as:\[ I = \frac{20 \, \text{C}}{1.25 \, \text{min}} \]We need to convert minutes to seconds:\[ 1.25 \, \text{min} = 75 \, \text{s} \]Thus, the initial current is:\[ I = \frac{20}{75} = \frac{4}{15} \, \text{A} \]
03

Determine New Current

Since the current is doubled, the new current is:\[ I_{new} = 2 \times \frac{4}{15} = \frac{8}{15} \, \text{A} \]
04

Calculate Time for 30 C Charge with New Current

To find the time ( t ) it takes for a 30 C charge to pass, use the formula:\[ I = \frac{Q}{t} \]Rearrange it to solve for t :\[ t = \frac{Q}{I} \]Plug in the new current and charge values:\[ t = \frac{30 \, \text{C}}{\frac{8}{15} \, \text{A}} \]This gives:\[ t = \frac{30 \times 15}{8} \, \text{s} = 56.25 \, \text{s} \]
05

Conclusion

Thus, it takes 56.25 seconds for a 30 C charge to pass with the doubled current.

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.

Understanding Electric Charge
Electric charge is a fundamental property of matter carried by subatomic particles, primarily through electrons and protons. It's measured in Coulombs (C), where one Coulomb is equivalent to the charge of approximately 6.242 x 10^18 electrons. Charges can be positive or negative, with opposite charges attracting each other and same charges repelling.
When a charge moves within a conductor, we refer to it as electric current. In our exercise, a total net charge of 20 C passing through a location in 1.25 minutes highlights how charge movement is measured in terms of time. Understanding this movement is crucial for calculating the current and the effects of altering it.
Current Calculation Essentials
Current, measured in amperes (A), represents the rate of charge flow through a conductor. To calculate the current, we use the formula \( I = \frac{Q}{t} \), where \( I \) is the current, \( Q \) is the charge in Coulombs, and \( t \) is the time in seconds. By understanding this formula, you can see how much charge passes a point in one second.
In our example, the initial current was calculated with 20 C in 75 seconds. This calculation led to a current of \( \frac{4}{15} \) A. Converting time from minutes to seconds ensures consistency in calculations, as the SI unit for time is seconds, which impacts current computation significantly.
Calculating Time from Current
To determine how long it takes for a specific charge to pass, use the rearranged current formula: \( t = \frac{Q}{I} \). Here, \( t \) is the time, \( Q \) is the charge, and \( I \) is the current.
This formula allows us to find the time required for a new charge of 30 C to pass after the current has been doubled. After finding the new current \( \frac{8}{15} \) A through doubling, substituting these values gives a time of 56.25 seconds for the 30 C charge. These calculations are pivotal for planning and understanding electric circuit behavior.
Impact of Doubling Current
Doubling the current in a circuit directly affects how quickly charge can move through it. The relationship between current and time is inversely proportional, meaning that if the current increases, the time it takes for the same charge to pass decreases.
In practical terms, when the current doubled in our exercise, the time for a 30 C charge to pass reduced significantly compared to the initial condition. This outcome highlights how amplifying the current makes circuits more efficient in transmitting charge over shorter time spans. Understanding this effect is essential for designing systems that require rapid charge transport.

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

An ohmic resistor in a circuit is designed to operate at \(120 \mathrm{~V}\). (a) If you connect the resistor to a \(60-\mathrm{V}\) power source, will the resistor dissipate heat at (1) 2, (2) \(4,(3) \frac{1}{2},\) or (4)\(\frac{1}{4}\) times the designed power? Why? (b) If the designed power is \(90 \mathrm{~W}\) at \(120 \mathrm{~V},\) but the resistor is connected to a \(30-\mathrm{V}\) power supply, what is the power delivered to the resistor?

A computer CD-ROM drive that operates on \(120 \mathrm{~V}\) is rated at \(40 \mathrm{~W}\) when it is operating. (a) How much current does the drive draw? (b) What is the drive's resistance? (c) How much energy (in \(\mathrm{kWh}\) ) does this drive use per month assuming it operates 15 min per day? (d) Estimate the electric energy bill per month, assuming 15 cents per \(\mathrm{kWh}\).

The current in a refrigerator with a resistance of \(12 \Omega\) is \(13 \mathrm{~A}\) (when the refrigerator is on). What is the power delivered to the refrigerator?

A wire \(5.0 \mathrm{~m}\) long and \(3.0 \mathrm{~mm}\) in diameter has a resistance of \(100 \Omega\). A 15-V potential difference is applied across the wire. Find (a) the current in the wire, (b) the resistivity of its material, and (c) the rate at which heat is being produced in the wire.

During a research experiment on the conduction of current in the human body, a medical technician attaches one electrode to the wrist and a second to the shoulder of a patient. If \(100 \mathrm{mV}\) is applied across the two electrodes and the resulting current is \(12.5 \mathrm{~mA},\) what is the overall resistance of the patient's arm?
See all solutions

Recommended explanations on Physics Textbooks

Particle Model of Matter

Read Explanation

Mechanics and Materials

Read Explanation

Thermodynamics

Read Explanation

Medical Physics

Read Explanation

Space Physics

Read Explanation

Electrostatics

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.