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Chapter 30: Q55P (page 899)

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

Short Answer

Expert verified

t=6.90蟿L

Step by step solution

01

Given

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

02

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=VR1-e-t蟿L

03

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

We know 蟿L=LR,and 0.100% less means 0.999% , so we can write

i=0.999VR

Using this intheequation of current, we get

0.999VR=VR1-e-t蟿L0.999=1-e-t蟿Le-t蟿L=1-0.999e-t蟿L=1-0.0010

Taking log on both sides,

-t蟿L=-6.90t=6.90蟿L

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