Why is that large neurons have smaller threshold potentials than small neurons during external stimulation?(adsbygoogle = window.adsbygoogle || []).push({});

My confusion is because the time constant should be larger, right?

tau = (r_m) * (c_m). where r_m is membrane resistance and c_m is membrane capacitance

Capacitance increases proportionally to surface area (proportional to radius squared) and membrane resistance decreases only in proportion to diameter (proportional to radius). The length constant only decreases in proportion to the square root of the radius while the time constant increases in proportion to radius. A higher time constant with only a slightly smaller length constant seems to indicate that larger neurons should be stimulated after smaller neurons. My understanding is definitely flawed somewhere, but I do not know what I am getting wrong. Any help is greatly appreciated.

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# Why do big neurons have lower threshold potentials than small neurons?

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