Single terminal of battery alone connected to earth.
I have attached the photo of the battery that i used.
I am sure that LED's were working properly and battery had enough capacity to provide current.

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The difference in electrical potential exists between the positive and negative terminals of your battery. There is no inherent relationship between the (-) terminal of a power supply and "ground." Don't confuse the two. Connecting to (or labeling) the negative as such is merely the most common usage of ground.
Ground is simply a reference. It's perfectly acceptable to connect the positive battery terminal to ground. Connected in such a way, positive is the ground reference and the negative terminal of your battery is now -12 volts when compared to ground. But there is no difference in the potential between the two battery terminals.
Bipolar power supplies have the ground reference in the middle, between a positive and a negative supply (like +/-12V).
At one point early in the transistor revolution it was quite common that circuits built around PNP transistors had a positive ground. Most computer power supplies are bipolar, or include a negative voltage component.
^will probably be taken off youtube soon for copyright infringment; but its the electricity episode.
From about 2 minutes onward you see why a circuit is important.
Thanks for posting it :-)
If that is so then what about this case? I will connect positive terminal of 12 v battery to ground (negative terminal will not be connected) and then positive terminal of 6 volt battery to the ground and in this case also i wont connect negative terminal of the battery. While there is potential difference of 6 v between both positive terminals of battery, will it be like there is no potential difference between one terminal of each battery and earth?
It is like saying a=b=a, but a is not equal to c.
Please help me
Batteries in a very rudimentary form act as an electron pump, it needs an input and an output -- otherwise it does no work.
if you had
{not connected)---A---battery++++ ground ++++battery---B----(not connected) between
assuming ground is conductive in this case
testing between A and B you would have a circuit (through the tester) and since the batteries are parallel (positive to positive) would be battery1 minus battery2 voltage (which they generally don't like).