/*! 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 54 The current in a series \(R L\) ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 27: Problem 54

The current in a series \(R L\) circuit rises to half its final value in \(7.6 \mathrm{s}\) What's the time constant?

Short Answer

Expert verified
The time constant of the RL circuit is \(10.9s\).

Step by step solution

01

Understanding the concept of Time constant

As we know, in an RL series circuit which consists of a resistor (R) and an inductor (L), the time constant is the time it takes for the current in the inductor to rise to \(1 - 1/e\) (about 63.2%) of its maximum value. This time constant is represented by \(蟿 = L / R\), where L is the inductance and R is the resistance of the circuit.
02

Appropriating given information to the circuit's exponential growth

We are given that the current reaches half of its maximum value in 7.6 seconds. The time for the current to reach any fraction \(x\) of its maximum value in such a circuit is given by the formula \(t = -蟿 * \ln{(1-x)}\), where \(\ln\) is the natural logarithm function.
03

Calculation of the Time constant

We can transform that equation and solve for the time constant \(蟿\). The formula will then be: \(蟿 = -t / \ln{(1-x)}\). We sub in \(t = 7.6s\) and \(x = 0.5\) (since the current reaches half of its final value) into our formula: \(蟿 = -(7.6s) / \ln{(1-0.5)}\)
04

Complete the calculation

Perform the calculations which gives the result of \(蟿 = 10.9s\).

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

Find the magnetic flux through a 5.0 -cm-diameter circular loop oriented with the loop normal at \(36^{\circ}\) to a uniform \(75-\mathrm{mT}\) magnetic field.

You and your roommate are headed to Canc煤n for spring break. Your roommate, who has had only high school physics, has read that an emf can be induced in the wings of an airplane and wonders whether this would give enough voltage to power a portable music player. What's your answer? (Assume that the wingspan of your 747 is \(60 \mathrm{m},\) the plane is flying at 600 mph, and Earth's magnetic field is \(0.3 \mathrm{G} .\) )

A car battery has a \(12-\mathrm{V}\) emf, yet energy from the battery provides the 30,000 -V spark that ignites the gasoline. How is this possible?

A circular wire loop \(45 \mathrm{cm}\) in diameter has resistance \(120 \Omega\) and lies in a horizontal plane. A uniform magnetic field points vertically downward, and in 25 ms it increases linearly from \(5.0 \mathrm{mT}\) to \(55 \mathrm{mT.}\) Find the magnetic flux through the loop at (a) the beginning and (b) the end of the 25 -ms period. (c) What's the loop current during this time? (d) Which way does this current flow?

A conducting loop with area \(0.15 \mathrm{m}^{2}\) and resistance \(6.0 \Omega\) lies in the \(x-y\) plane. A spatially uniform magnetic field points in the z-direction. The field varies with time according to \(B_{z}=a t^{2}-b\) where \(a=2.0 \mathrm{T} / \mathrm{s}^{2}\) and \(b=8.0 \mathrm{T} .\) Find the loop current (a) at \(t=3.0 \mathrm{s}\) and \((\mathrm{b})\) when \(B_{z}=0.\)
See all solutions

Recommended explanations on Physics Textbooks

Physical Quantities And Units

Read Explanation

Mechanics and Materials

Read Explanation

Quantum Physics

Read Explanation

Particle Model of Matter

Read Explanation

Medical Physics

Read Explanation

Circular Motion and Gravitation

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.