As per your request, I am giving you list of the some core Electronics and Instrumentation companies for internship.

Government Companies

National Thermal Power Corporation(NTPC)
Bharat Heavy Electricals limited(BHEL)
Jindal Steel and Power Limited
Steel Authority of India Limited(SAIL)
Bharat Electronics Ltd.(BEL)
TERI
BBNL
BSNL
BARC ( BHABHA ATOMIC RESEARCH CENTER )
NALCO
HPCL
GAIL ( GAS AUTHORITY OF INDIA LTD. )
BPCL
IOCL

Private companies

Addison & Co Ltd
Ashok Leyland Ltd, Ennore
Axles India Ltd
Chennai Petroleum Corp Ltd
Ennore Foundries Ltd
Esab India Ltd
Flakt (India) Ltd
Ford India Ltd
Integral Coach Factory, Perambur
Heavy Vehicles Factory, Avadi
Hindustan Motors Ltd
Hyundai Motors India Ltd
Nokia India Ltd
Royal Enfield Ltd
Saint-Gobain Glass India Ltd
Samsung India Electronics
Sundaram-Clayton Ltd
Tractor and Farm Equipment (TAFE)
Tube Investments of India Ltd
Westas Wind Technology India Pvt Ltdi