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1. Homework Statement
Given the attached scheme, if [tex]R_{1}[/tex]=[tex]R_{2}[/tex]=[tex]R_{3}[/tex]=10 Ω and [tex]\epsilon_{1}=20 V[/tex] , [tex]\epsilon_{2}=10 V[/tex] 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 [tex]\epsilon_{2}[/tex] produce some current?
And even if [tex]\epsilon_{2}[/tex] , [tex]R_{3}[/tex] 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 [tex]\epsilon_{2}[/tex] we have [tex]V_{B}=10 V[/tex].
Due to our assumption, current exists only within the loop. We easily find its value:
[tex]I=1 A[/tex]. Using the mathematical expression of Ohm's law we may now easily obtain the wanted potentials:
[tex]V_{A}=0 V[/tex] , [tex]V_{C}=20 V[/tex]
Given the attached scheme, if [tex]R_{1}[/tex]=[tex]R_{2}[/tex]=[tex]R_{3}[/tex]=10 Ω and [tex]\epsilon_{1}=20 V[/tex] , [tex]\epsilon_{2}=10 V[/tex] 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 [tex]\epsilon_{2}[/tex] produce some current?
And even if [tex]\epsilon_{2}[/tex] , [tex]R_{3}[/tex] 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 [tex]\epsilon_{2}[/tex] we have [tex]V_{B}=10 V[/tex].
Due to our assumption, current exists only within the loop. We easily find its value:
[tex]I=1 A[/tex]. Using the mathematical expression of Ohm's law we may now easily obtain the wanted potentials:
[tex]V_{A}=0 V[/tex] , [tex]V_{C}=20 V[/tex]
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