Consider only one battery at the circuit. Because the circuit is symmetric about the middle horizontal line, we can say the circuit can be drawn as picture below.Simplify the circuit, then we can get the total resistance at the circuit, it is

Now, we need to find the current flow through "2R" resistors, DA and BC.

For "2R" resistor at DA, we can simply write the equation

And the current flow through "R-R" resistors at DA is the same with above. So, the total current through DA is twice of above.

Now consider there are two batteries connected to the circuit. Assume each of the batteries gives current to the circuit.By using superposition of two batteries, we can get the current flow through "2R" resistor at DA is

Therefore,

That's my solution.

If you have any correction, question, or comment, please leave a comment below.

Thank you.

## 2 comments

I got this question in 8 lines by using symmetry of the circuit.

oh, actually I want to emphasize superposition concept in this problems, but I didn't realize that it can be solved easily using symmetry of circuit.

maybe later I would change the problem to make it a little harder.

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