As Larry said, nothing bad should happen when using the 3 Ohm coil.  The resistance of the coil should limit the current through the module to an acceptable level.  What can cause problems is using a low resistance coil on a "standard" ignition wiring system.  That will allow excess current that can damage the ignition components.

Nothing untoward will happen if you use the 3 ohm coil.

Well the car has been all rewired, so colors don't apply.  And there is only 1 wire on each terminal of the coil.  I just tested the old coil and it was 1.5 ohms and my new one is 3 ohm because I thought that was what I read I needed.  What is that going to do?  

I did this in August 2010 - the message bored thread is gone, and my finished installation photograph doesn't have the final wire from the starter solenoid to the coil (+), but you'll get the idea.  I installed a 4-terminal ADU5728 starter solenoid because I felt it simpler than adding diodes. 

Link:  Topic_Adding a Ballast Resistor - YIKES  

This is the coil I used:

Hope this helps -

Like Dan, I don't know the years ballast ignition was used on the Mini.  However, I will offer some observations and advice.

With the Mini, ballast ignitions have (2) wires on coil (+) as Dan said.  One will be white/yellow and the other end of that wire connects to a 4th terminal on the starter solenoid.  The other wire on coil (+) is white/pink and typically looks like it is solid pink.  That wire IS the ballast resistor.  The pink wire is routed through the wiring harness and the other end goes to the ignition switch.

The pink wire has a bad ruputation for overheating and melting adjacent wires in the harness.  If your new coil says that it must have a ballast resistor, the safest thing for you to do is buy an external ballast resistor.  There is nothing particularly special about the resitor.  You simply want one that measures between 1-2 ohms and anything your local parts store has will be suitable.  You would leave the white/yellow wire on coil (+) and connect a new white wire there as well (16 AWG wire will work).  Connect the other end of that white wire to one side of the ballast resistor (either end).  ut a second white wire on the other end of the ballast resistor and run it to a switched terminal on the fuse box.  That will provide a ballast power supply for the coil.  

Any power connections for your Crane ignition should not go to coil (+).  The power wire for the Crane should come from the same switched fuse terminal you connected the ballast wire to so the module gets a full 12V supply.

I don't know anything about your electronic ignition system, but on a Mini, a "ballasted" ignition system was put in "later" cars - I don't know the specific date or year. On a ballasted system, there are two power feeds to the coil - when you are cranking the engine, a terminal on the solenoid connects one of the wires and provides 12V to the coil. Once you stop crtanking and release the key, the solenoid disconnects that wire and connects the other wire which has a specific resistance. The result is that the coil now receives a lower voltage - the normal operating voltage for a ballasted type coil.

In other words, while you're cranking, and the starter motor is drawing huge amounts of current, there would be a voltage drop. This is compensated by providing a direct "full available voltage" connection to the coil.

You won't find a resistor in either of the wires - one of then IS a resistor.

Your battery should provide slightly over 12V to the solenoid. With the ignition in the "run" position, you should read something like 7 to 9 volts at the coil (my manual is in the garage where it should be...so I can't say what the exact voltage should be. On one of the solenoid output terminals you should read 12V. On the other output terminal with only one wire leading directly to the coil (not to the fuse box), the should be zero volts.

As your assistant holds the key to the start position, the second terminal should come alive with 12V and the coil should also receive 12V via that single wire.

Ok, when I bought my car it was already swithed from points to electronic ignition.  It had a Crane Cams XR700 ignition box, the new distributer guts, and new wires but still had an old looking coil.  So I bought a 3 ohm Pertronix coil.  When I went to install it I saw the old coil said on it to only use with an external resistor.  Well the directions on the new one said to use it without a resistor.  I tested the wire on the positive side of the coil to ground with the key on like I read on here to do, and it's like 11 point something, and I traced it all down and dont see any kind of resistor all the way back to the fuse panel.  Now I was looking at some stuff about that XR700 box and it says it needs to be used with a ballast resistor.  So my question is, it has been fine so far, but since this new coil is advertised as 40,000 volts, is it going to draw too much current and burn up that XR700 box?  Is this a big deal to worry about?