How can I find the short circuit current across a and b? In order to find R thevenin, I need to find Isc across a and b since there's a dependent source. Based on my calculations, Vth=500/3V. I've spent countless hours thinking about Isc,please help.

• Please show all of your work so far. -1 for taking a poor photo and not cropping. – Elliot Alderson Jan 2 at 12:50
• indeed,that was poor from my part,I will use circuit lab. – doom Jan 2 at 13:05

First of all, I strongly recommend actually assigning names (like $$\R_1\ldots R_4\$$) to your resistors. It makes talking about schematics much easier.

Anyway, when shorting a-b, your 10 Ω becomes irrelevant.

All the current from the current source goes through that short, so while we have to add that current to the total current through the a-b short in the end, it doesn't interfere with the rest of the calculation. So, you build a "helper" circuit.

Thus, all you have to do is calculate the current through R3 in this circuit: simulate this circuit – Schematic created using CircuitLab

The voltage across R2 (or across R3) is your v_x; I'm sure you can solve this :)