# Electric Circuit Connected to Ground

1. Homework Statement

Given the attached scheme, if $$R_{1}$$=$$R_{2}$$=$$R_{3}$$=10 Ω and $$\epsilon_{1}=20 V$$ , $$\epsilon_{2}=10 V$$ determine the potentials at the points A,B,C,D,E. The sources of emf have no internal resistance.

2. Homework Equations

My question is: Why is it that no current exists along the branch BE? If one made this particular apparatus I am convinced he would observe no current. But in theory, why does this happen? Shouldn't the source of emf $$\epsilon_{2}$$ produce some current?
And even if $$\epsilon_{2}$$ , $$R_{3}$$ did not exist, why would the current ''choose'' to move around the loop instead of going towards the ground?

3. The Attempt at a Solution

Assuming no current exists at the branch BE, we assign zero potential at points D,E. Because of $$\epsilon_{2}$$ we have $$V_{B}=-10 V$$.
Due to our assumption, current exists only within the loop. We easily find its value:
$$I=1 A$$. Using the mathematical expression of Ohm's law we may now easily obtain the wanted potentials:
$$V_{A}=0 V$$ , $$V_{C}=-20 V$$

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