Time Constant Induction question

[Wayne]

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

 

[NascentOxygen]

Hi Wayne. Welcome to Physics Forums.

Can you write the full equation that describes the rise of the current vs. time?

 

[Wayne]

i = I (1-e (-t/tc))
i =instantaneous current
I final current I=v/r

 

[NascentOxygen]

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

You know that value of the final current, I_f.

 

[Wayne]

Sorry you lost me! I don't know i as not given and can't calculate I as don't know r to calculate I=v/r

 

[BruceW]

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?

 

[Wayne]

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%

 

[Wayne]

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

 

[BruceW]

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 ...

 

[Wayne]

Opps slight miss calculation
tc=2.88ms?
"-in" means natural logarithm

 

[BruceW]

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

 

[NascentOxygen]

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

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.

Looks like BruceW has put you right now.