For a test I have an Ibanez active bass at my disposal. This bass guitar is powered by a PP3 (9 Volt, 6F22) battery.
I wanted to measure the current draw under different conditions, so I connected an ammeter between the guitar and the battery.
When the audio jack is plugged into the guitar, the current is about 1.3 mA in standby mode. Hmmm, I expected a lower value. Turning any knob doesn't change that. During playing the current increases to 1.4-1.5 mA.
There is no explicit power switch. The only way to reduce the current to zero is to unplug the audio jack from the bass. I have heard this before and it is true, there is an internal power switch in the guitar jack socket. When the audio jack is unplugged, the current is 0.
Conclusions:
1. There is not much difference in power consumption between playing and standby.
2. Turning down the volume doesn't help reduce standby power.
3. Unplug the audio jack from the bass to conserve battery power.
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