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In the following circuit what would be the effect of tying a circuit to the ground from the -2V rail ? I know that no current would flow to the ground since there is no closed loop formed, but assuming the ground is at zero volt level, would the ground pull the -2v rail to zero and change all the node voltages in the circuit accordingly ? And does a setup like this have any usage in real life applications ?

schematic

simulate this circuit – Schematic created using CircuitLab

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    \$\begingroup\$ What is the 2V and -2V relative to, without the earth ground in the circuit? You seem to have a conceptual misunderstanding of what voltage is. \$\endgroup\$
    – Shamtam
    May 16 '16 at 12:10
  • \$\begingroup\$ battery is just providing 4v voltage difference , i picked arbitrary values in reference to earth potential to make a point. What would happen if i ground a floating circuit is my main question . \$\endgroup\$
    – Dogus Ural
    May 16 '16 at 12:54
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In the absence of a ground, how you choose to label the nodes in the circuit is entirely arbitrary. You could use +4V and 0V (which is more conventional), or +2V and -2V, or 0V and -4V. Because you can only measure voltages between two points, it's up to you to choose which point you consider to be 0V and measure relative to that.

By convention, the Earth is at 0V. So if you tie one line to ground, that will now be at 0V. Doing so has no effect on the circuit - you've just chosen which line is now considered to be 0V.

There are no real-life applications of this.

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The effect would be that the rail connected to the battery minus would be forced to earth potential. By convention this potential is zero.

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