The circuit to the right is constructed using 9 identical batteries and 9 identi

Question

The circuit to the right is constructed using 9 identical batteries and 9 identical resistors. The lower left corner of the circuit is grounded. Determine whether the current through each resistor is zero OR non-zero. Please SHOW how to solve this and show directly where each R should be placed according to the image. Thanks!

The circuit to the right is constructed using 9 identical batteries and 9 identical resistors. The lower left corner of the circuit is grounded. Determine whether the current through each resistor is zero or non-zero. R1 1-0 1+0 Rg R4 R3 R7 Rs Rs R2 R2 R3 Rs Rs R4

Explanation / Answer

R1,R2,R3,R5,R6 have current
R4,R7,R8,R9 do not have current
Because R8 loop voltages sources cancel VR8+V-V=0 so VR8=0
The top of R9 potential from ground = +V+V+V-V-V = V
The bottom of R9 potential from ground = V so VR9=0
The left of R7 potential from ground =+V+V-V = V
The right side of R7 potential from ground = +V+V+V-V-V = V
so VR7= 0
From ground the left side of R4 = +V and from ground the right side of R4 is at V so VR4=0
We know that R1 must have 2V across it. We know that R6 and R3 each have V/2
R2 has V across it and R5 must have V across it because the potential of its left end from ground
= +V+V= 2V but the potential of it's right end from gound must be +V+V+V-V-V=V

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