Chapter 30: Q55P (page 899)

A battery is connected to a series RL circuit at time t = 0 . At what multiple of $τ_{L}$ will the current be 0.100% less than its equilibrium value?

Short Answer

Expert verified

$t = 6.90 τ_{L}$

Step by step solution

Given

A battery is connected to a series RL circuit at time t = 0

Understanding the concept

We use the concept of current through RL circuit. Using the equation, we can find the time at the given value of current.

Formulae:

$i = \frac{V}{R} (1 - e^{- \frac{t}{τ_{L}}})$

Calculate at what multiple of τL will the current be 0.100% less than its equilibrium value

We know $τ_{L} = \frac{L}{R}$ ,and 0.100% less means 0.999% , so we can write

$i = 0.999 (\frac{V}{R})$

Using this intheequation of current, we get

$0.999 (\frac{V}{R}) = \frac{V}{R} (1 - e^{- \frac{t}{τ_{L}}}) 0.999 = 1 - e^{- \frac{t}{τ_{L}}} e^{- \frac{t}{τ_{L}}} = 1 - 0.999 e^{- \frac{t}{τ_{L}}} = 1 - 0.0010$

Taking log on both sides,

$- \frac{t}{τ_{L}} = - 6.90 t = 6.90 τ_{L}$

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

A battery is connected to a series RL circuit at time t = 0 . At what multiple of $τ_{L}$ will the current be 0.100% less than its equilibrium value?

Short Answer

Step by step solution

Given

Understanding the concept

Calculate at what multiple of τL will the current be 0.100% less than its equilibrium value

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Famous Physicists

Nuclear Physics

Conservation of Energy and Momentum

Magnetism and Electromagnetic Induction

Work Energy and Power

Radiation

Study anywhere. Anytime. Across all devices.

A battery is connected to a series RL circuit at time t = 0 . At what multiple ofτLwill the current be 0.100% less than its equilibrium value?

Short Answer

Step by step solution

Given

Understanding the concept

Calculate at what multiple of τL will the current be 0.100% less than its equilibrium value

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Famous Physicists

Nuclear Physics

Conservation of Energy and Momentum

Magnetism and Electromagnetic Induction

Work Energy and Power

Radiation

Study anywhere. Anytime. Across all devices.

A battery is connected to a series RL circuit at time t = 0 . At what multiple of $τ_{L}$ will the current be 0.100% less than its equilibrium value?