Hello,
You can use the query below, execute it every 30 seconds or so .. and whatch the number of connections as well !
SELECT
SUM(current_workers_count)current_visible_workers,
SUM(active_workers_count)active_visible_workers,
(SELECT COUNT(*) FROM sys.dm_exec_connections) connections
FROM sys.dm_os_schedulers
-- Those schedulers that have IDs greater than or equal to 255 are used internally by SQL Server
-- check BOL !
WHERE scheduler_id < 255
Cheers,
R