You can just connect a scope across the fuse. Observe the I/t graph on the scope and when the fuse blows the current on the scope will drop to zero. Just calculte how how it was before the current went to zero.
I have read the defination of a time constant on the internet and yet still don't quite understand it. How do I relate it to the following sentece and what does it mean:
" The transient energy will have a duration much shorter than the thermal time constant of a bridge wire."