Indeed the psu is inadequate for 1060. It does not have a 6 pin required by 1060.  normally pc would give a loud beep when powered on without 6 pin to video card. basic online psu calculator for your configuration is Load Wattage: 309 WRecommended PSU Wattage: 359 W, assuming 4x2gb ddr3, hdd, dvd. If you switch to sata ssd and disconnect power to dvd, Load Wattage: 270 WRecommended PSU Wattage: 320 W. The 1060 is a good card for your cpu.  I suggest you upgrade the psu to support 1060, rather than downgrade gpu to suit a weak psu. One option: get a Dell OEM 460w psu for XPS 8300-8900 which is inexpensive on eBay used market (sometimes as low as $20) and covers your need. a better option: EVGA 500w psu on sale on Amazon.  29.99. If you prefer to keep using the 275w psu, change gpu to GTX 1650, 1050, 1050Ti or gt1030. however the card would cost much more than upgrading the psu.  
I have a dell optiplex9010 I7-3770 with a geforce gtx 1060 video card.   Shortly after purchasing it, the screen goes black and the video stops.   I have to kill the video in firefox to continue.   Is there a setting that might fix this?   I have installed all upgrades to Bios, Windows 7 64 bit OS and related drivers. If necessary I would buy another video card and would want advice on which to purchase.   The heaviest video work would be Blue Iris with 6-8 POE camera feeds. Thanks for any advice. Lance
optiplex9010 I7-3770 with a geforce gtx 1060 video card Issue