How a Geiger counter counts
Geiger counters monitor voltage rather than current
The counter really checks the voltage across a capacitor rather than current.
The power supply removes some of the electrons in the central wire so it has a net positive charge. When the cascade of electrons falls on the wire the net positive charge is reduced and the potential drops.
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The power supply tries to drag these extra electrons off and get the potential back to 400 V again. However a very large resistance means this happens slowly enough for the voltage drop across the capacitor to be detected.
Once the voltage drops below some threshold, a count is registered.
Geiger counters can't keep up with very high count rates
It takes perhaps 200 microseconds for the voltage to reset. So it can’t detect the next particle before the end of this ‘dead time’. This puts an upper limit on most Geiger counters of about 5000 counts per second.









