yes i expect a working as you said.. when powering with adapter get supply through normally open (connected to adapter) and when adapter off get supply through normally closed point(connected to battery).. but my problem is that, when i switch on adapter relay switches to NO and when i power off the adapter the relay do not switch back to NC.. and on that i get a 2.7v across the coil( i dont know from where it coming) and when i check the continuity i gey COM,NC,No are short for some moments.... but if i disconnect the battery then relay switch perfectly to NO and NC ....
Yeah, that's not going to work. There is something wrong with your "adaptor" setup that you are not telling us. What do you mean by "switch off my adaptor " ?
You understand that if you had a real switch in series with the adaptor voltage to the relay coil and you opened that switch it would be impossible for there to be ANY voltage on the relay coil so this means there is something about your adaptor wiring or setup that you are not telling us. Post a link for the adaptor and a photo of the adaptor showing the writing on the label and also a photo of the actual wiring of the adaptor.
Try unplugging the "adaptor" from the wall.
Post a vendor link for the adaptor.
Try putting a 1 k ohm resistor across the relay coil.