In the diagram above, each resistor has a value of 990 ohm. The recursive pattern of branching of the first and third branch continues infinitely.
Calculate the equivalent resistance of this circuit, rounded to the nearest integer.
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Let R = 9 9 0 be the value of an individual resistor, and x the resistance of the entire circuit. The circuit can be analyzed as consisting of two individual resistors, and two copies of itself: Thus we have x = R + ( x ∣ R ∣ x ) where ∣ stands for placing elements in parallel. This translates into the algebraic equation x = R + x 1 + R 1 + x 1 1 ∴ x = R + 2 R + x R x ∴ ( x − R ) ( x + 2 R ) = R x ∴ x 2 − 2 R 2 = 0 ∴ x = 2 R = 1 4 0 0 Ω .