Does the StenLight draw current when it is plugged in but turned off?
Yes, it draws a small amount of current in order to be able to detect when you turn it back on. But this current is extremely small (about 25 microamps, less than the self-discharge rate of any rechargeable battery you’re likely to connect to it). If you are likely to keep the battery on the shelf for 6 months or more, you might as well unplug it, but otherwise it’s not an issue.
