As shared earlier, I found some online references where users were able to successfully use GTX 650 with 350W power supply. However, if you run demanding or graphics intensive applications which require heavier processing capabilities from system, it will lead to a load on power supply. In such a case, the system might overheat and even shutdown abruptly due to lack of power. The results are uncertain and might cause damage to any of the components including motherboard, processor or hard drive.
The power supply requirement can not be computed alone from video card. It also depends upon processor, no. of memory, hard drives, optical drives connected, internal expansion cards or external peripherals attached to system. While researching, I found that various power supply manufacturers have a power supply calculator tool on their websites that you may use to compute the PSU requirements for your system. One such example is Here.
Note : The above link is for reference purpose only. Dell has neither tested nor endorses these tools.
The power calculated by tool is approximate power needed by your system. In my personal experience, I have observed that power supplies may not work at 100% efficiency. If we take PSU efficiency to be at around 70-75% and if the tool calculates your system power requirement to be around 300W, then you would need a power supply of atleast 300*100/75 = 400W. For more information, you may refer to link Here.
Hope this helps.