My work gave me a mobile internet box to use for work if I don’t have internet and need to use my laptop. I had my laptop and internet box at home and my family connected to it and the usage was a lot. My work incurred a couple thousand dollars extra expenses because of this. Am I obligated to pay for it? 


It depends on the policy of your workplace. If they gave it to you for work purposes only, then you are obligated to pay the difference.