Making the current measure can be tricky.
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You are using the amp meter the right way, but there is a problem you need to be aware of. Starting in the mid 1990's, most vehicles have at least one computer that needs up to twenty minutes to go to "sleep" mode. During that twenty minutes it can draw up to three amps. Logic would dictate you just have to wait for more than twenty minutes, then start the testing, but there is one more piece to the story. Anything you do to remove power to that computer, even for just a fraction of a second, wakes it up again, and then you have to wait another twenty minutes for it to go to sleep. Once the battery cable is removed, as soon as you connect the final meter lead, the computer will wake up and draw high current.
Most of the common, inexpensive volt/ohm/amp meters have an internal 2-amp fuse for the milliamps and 2-amp range, and they need to have the positive test lead moved to a special jack to use the 10-amp range. That 10-amp jack is rarely fused.
Most people will start the testing with the meter on the 10-amp range, then they can read that 3-amp drain until the computer goes to sleep. Once that happens, we need to switch to a lower range for more accuracy. That means removing the test lead from the 10-amp jack and moving it to the common volts/ohms/milliamps jack. Doing that breaks the circuit, and once reconnected, the computer will draw enough current to blow the meter's internal 2-amp fuse. "Frog fuzz!" Now the frustration begins.
If you are lucky enough to not blow that fuse, you will be on the 2-amp range, and once the computer goes to sleep, you will probably want to switch to a lower range, again, for more accuracy. All voltmeters with a rotary switch use a "break-before-make" switch which means as you slowly rotate the knob, the internal contacts break the connection to one range, then it makes the connection to the next range. That very minute gap is plenty to cause the computer to wake up again. Even if the fuse does not blow, you will get an over-range indication because the computer is drawing much more current than that range can handle.
I am fairly confident this is why you found 2.25 amps of current drain. You may have waited an hour, but you have to wait after making the final meter connection and selecting the range.
There is an easier way though to solve this.
Connect your meter like you did, and start on the 10-amp range. Wait a good twenty minutes or until you see the current drop significantly, then use a small jumper wire to connect the battery cable to the post. You can also jump between the two meter probes. Regardless how you do it, the meter is bypassed, or in effect, shorted out in the circuit. Voltage to the computer has never been lost and you are free to move the meter's probe to the milliamps jack. When you are ready, remove the jumper wire and read the meter.
If you see the current has dropped low enough to warrant switching to a lower range, put the jumper wire back on first, then switch the range. When you remove the jumper wire again, current will have no choice but to go through the meter to get measured.
Unless specified differently by the manufacturer, the industry standard is you're allowed up to 35 ma. (.035A), of current drain to keep all the computer memories alive. Chrysler says at that rate, a good, fully-charged battery will be able to crank an engine fast enough to start after sitting for three weeks. Cadillac is one brand I am aware of that allows up to 50 ma.
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https://www.2carpros.com/questions/parasitic-drain-caused-by-altenater-diodesThis also explains why using a shunt to measure the DC current may be preferable.
