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,

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

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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

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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

Magnetism

Classical Mechanics

Electrostatics

Torque and Rotational Motion

Solid State Physics

Mechanics and Materials

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?