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Chapter 30: Q50P (page 899)

The current in an RL circuit builds up to one-third of its steady-state value in 5.00 s . Find the inductive time constant.

Short Answer

Expert verified

τL=12.3s

Step by step solution

01

Given

02

Understanding the concept

im-currentatsteadyvalueIf a constant emf εis introduced into a single-loop circuit containing a resistance Rand an inductance L, the current rises to an equilibrium value ofε/Ras

i=εR(1-e-tτL)

Formulae:

i=εR(1-e-tτL)

Here,ε-emf;R-resistance;t-time;τL-inductivetimeconstantofcircuit

Given:

At t=5.0s,i=im/3

03

Calculate the inductive time constant

We have current in the inductive circuit as\

i=εR(1-e-tτL)

We know that steady state current of RL circuit is

im=ε/R

Now plug in this value in equation:

im3=εR1-e-tτLε3R=εR1-e-tτLe-tτL=1-13=2/3

Hence,

-tτL=In23--0.5τL=-0.4054

Therefore,

τL=12.3s

The inductive time constant is 12.3s

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Most popular questions from this chapter

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