# inductive circuit question

Discussion in 'Electronic Basics' started by stephen hallacy, Oct 18, 2003.

1. ### stephen hallacyGuest

Hello,

I decided to review some electronics in my spare time. I came across
an inductor circuit in my electric circuit's text book. The circuit
is given below.

-----------R1 (7.5k)-------------
| |
| |
----L1 (1.25H)--------L3 (6H)----
| |
----L2 (10H)---
|
\\\

The initial currents for L1, L2 and L3 are 2A, 2A and 0A respectively,
and the currents are going from right to left in circuit shown above.
I went through the math and came up with

i1(t) = 2*exp(-1500*t)
i2(t) = 5/4+3/4*exp(-1500*t)
i3(t) = -5/4+5/4*exp(-1500*t)}

where i1(t) is the current in L1, i2(t) is the current in L2 and i3(t)
is the current in L3.

I used the following differential equations to come up with the
solution:

d(i1(t))/dt - d(i2(t))/dt - d(i3(t))/dt = 0
10*d(i2(t))/dt - 6*d(i3(t))/dt = 0
10*d(i2(t))/dt + 1.25*d(i1(t))/dt + 7500*i1(t) = 0

The currents should go to zero, however, the equations show that i2(t)
and i3(t) approach 1.25 Amps. Am I doing something wrong?

By the way, OrCAD Pspice showed the same result.

Regards,
Stephen

2. ### Roy McCammonGuest

Put some small resistance in series with each inductor and try again.
That loop composed entirely of two ideal inductors may be giving
you strange results.

3. ### John LarkinGuest

L2 and L3 can indeed circulate a current forever.

John

4. ### John LarkinGuest

Ever heard of NMR? MRI? They both use big superconductive magnets.
They are shipped warm, and cooled down on-site with liquid nitrogen,
then liquid helium. Once it's cold, a big power supply is connected to
run the current up to a few kiloamps, then a shorting link is closed,
and the power supply is loaded on a truck and taken away. The current
circulates roughly forever, and the magnetic field is stable [1] as
long as the helium level is kept up. Helium is topped off every few
months to correct for boiloff.

John

[1] high-field superconductive magnets are subject to a bit of
pinned-domain slipping, which causes the field to droop very slightly
with time, generally in the 1 PPM per day sort of range. I think this
eventually levels out as things settle.

These things are hell on credit cards and hand tools.

5. ### BaphometGuest

Only if you believe in perpetual motion ;-) By the way, I have this
bridge........

6. ### BaphometGuest

Point well taken John...but as long as energy from an outside source,
however infrequently, must be supplied, it ain't perpetual...pretty darn
close though ;-)

7. ### stephen hallacyGuest

Thanks for the response guys.

I agree John. For this ideal component circuit, the current circulates forever.

Stephen