Your Logitech webcam won't work with your Smart TV, as it was designed to be used with personal computers only.

NOTE: The Logitech TV Cam for Skype will work with some Panasonic Smart TVs (see answer 360023253574 for the list of supported TVs). The Logitech TV Cam HD will work with any TV that has an available HDMI input (see answer 40690 for more information).