How to measure the current carrying caoacity of the cable.. Please give me the name of the instument with the help of that I can measure the current carrying capacity..

To measure the actual load use an amp meter.

To measure to capacity use a tool called your eyes.
Look at the listing of the conductor, then go to the code book and, checking all the parameters of the installation, find the ampacity of the conductor in the ampacity tables.

Ammeter