Buckmaster
Senior Member
It has to do with electron speed, and the conductivity of the battery cable material -
If v t h {\displaystyle v_{th}} v_{{th}} is defined as the most probable speed, then
v t h = 2 k B T m {\displaystyle v_{th}={\sqrt {\frac {2k_{B}T}{m}}}} v_{{th}}={\sqrt {{\frac {2k_{B}T}{m}}}}.
If v t h {\displaystyle v_{th}} v_{{th}} is defined as the root mean square of the total velocity (in three dimensions), then
v t h = 3 k B T m {\displaystyle v_{th}={\sqrt {\frac {3k_{B}T}{m}}}} v_{{th}}={\sqrt {{\frac {3k_{B}T}{m}}}}.
If v t h {\displaystyle v_{th}} v_{{th}} is defined as the mean of the magnitude of the velocity of the atoms or molecules, then
v t h = 8 k B T m π {\displaystyle v_{th}={\sqrt {\frac {8k_{B}T}{m\pi }}}} v_{{th}}={\sqrt {{\frac {8k_{B}T}{m\pi }}}}.
Thanks for the explanation Dan. It makes sense now.