1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Time Constant Induction question

  1. Jul 17, 2014 #1
    Hi all, I need your help with a Time constant question? I am studying for an exam via distance learning and don't feel they have covered this question, question taken from past paper.

    2. A coil of inductance 2 H and unknown resistance is connected to a D.C. supply of
    100 volts. After 4 ms the current has risen to 75% of its final steady state value.
    Calculate EACH of the following:
    (a) the resistance by the coil;
    (b) the energy stored in the coil when the current has reached its steady state value;
    (c) the time taken for the current to fall to 50% of its steady state value when the supply
    is switched off.

    The question I am stuck on is a, If I can find out what 75% is I can then find out full current and time constant to to transpose, tc=L/R?

    I understand 1 tc is 63.2% and 5 tc is 100%

    Thank you in advanced.

    Wayne
     
  2. jcsd
  3. Jul 17, 2014 #2

    NascentOxygen

    User Avatar

    Staff: Mentor

    Hi Wayne. Welcome to Physics Forums. :wink:

    Can you write the full equation that describes the rise of the current vs. time?
     
  4. Jul 17, 2014 #3
    i = I (1-e (-t/tc))
    i =instantaneous current
    I final current I=v/r
     
  5. Jul 17, 2014 #4

    NascentOxygen

    User Avatar

    Staff: Mentor

    So at t=4ms equate this to 75% of If.

    You know that value of the final current, If.
     
  6. Jul 17, 2014 #5
    Sorry you lost me! I don't know i as not given and cant calculate I as don't know r to calculate I=v/r
     
  7. Jul 17, 2014 #6

    BruceW

    User Avatar
    Homework Helper

    but they do tell you that 'i' is 75% of 'I'. So looking at your equation i = I (1-e (-t/tc)) Can you rearrange, so that you don't actually need to find 'i' and 'I' separately?
     
  8. Jul 17, 2014 #7
    Sorry I totally not getting this been looking at this for a week before I decided to put it on here.

    I understand i is 75% of I and took 4 ms, and guessing I have to us e as the curve is expo-dental 1 tc=63.5% &
    5 tc is 100%
     
  9. Jul 17, 2014 #8
    Ok has the penny just dropped?

    if formula i = I (1-e (-i/I))

    Is transposed to

    if tc = t / ( -in ((1- (i/I)))

    i= 0.75 & I =1

    Then tc = t / (-in ((1- (0.75/1))) tc= 1.68 ms
     
    Last edited: Jul 17, 2014
  10. Jul 17, 2014 #9

    BruceW

    User Avatar
    Homework Helper

    I think you are almost on the right track now. But your equations are a little hard to read. I think you might have made a couple of typing mistakes... I'm guessing for the first formula you meant i = I (1-exp(-t/tc)) and I'm guessing that 'in' means natural logarithm. Then I would say your final equation tc = t / (-in ((1- (0.75/1))) is correct. But I don't get 1.68ms when I solve for tc ...
     
  11. Jul 17, 2014 #10
    Opps slight miss calculation
    tc=2.88ms?
    "-in" means natural logarithm
     
  12. Jul 17, 2014 #11

    BruceW

    User Avatar
    Homework Helper

    yeah :) I got tc=2.88ms too. nice. p.s. I think there should also be a negative sign in the calculation somewhere. But 2.88ms is the right answer, so I guess you did remember to use the negative sign in there when you did the calculation.

    edit: or actually, I got 2.89ms, you might want to check the rounding of the number
     
    Last edited: Jul 17, 2014
  13. Jul 17, 2014 #12

    NascentOxygen

    User Avatar

    Staff: Mentor

    This should be i=0.75I, so the exponent becomes 0.75I/I. Then the I/I cancels.

    I'm not sure why you are using "in" for "ln" but the latter is definitely recommended. :wink:

    Looks like BruceW has put you right now.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Time Constant Induction question
  1. Time Constant (Replies: 3)

  2. Inductance Question (Replies: 2)

  3. Decay time constant (Replies: 9)

Loading...