If R = 6 4 Ω , find the equivalent resistance between A and B in ohms.
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There are two parallel systems which are just the same, so we can find the total resistance of one of them ( R t o t 1 ) and the answer will be its half ( R t o t = 2 R t o t 1 ). So we have, at one of the systems: R t o t 1 = 2 R + 2 R ⇒ R t o t = R + 4 R = 6 4 + 1 6 = 8 0
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In the second step, I have used a shortcut, i.e I used the symmetry of the current in the upper and the lower branch to simplify it to a circuit with fewer equipotential points. I just merged the equipotential points to make the situation easier.