The Big Bang Theory Season 3 Episode 4 : The Pirate Solution
Raj must find a new job or be sent back to India. Sheldon has a solution, which is to allow Raj to work "for" him, rather than work "with" him. Raj reluctantly accepts the offer. With Raj working for Sheldon, it makes Howard lonely, so he tries to stay with Leonard and Penny (even making them breakfast) but they would rather be alone. Sheldon and Raj soon disagree on how to solve a work-related problem and Raj walks out. Sheldon actually apologizes at the end of the episode and he accepts that Raj was right but doesn't concede to him being wrong.