For what value of the resistor X will the equivalent resistance of the two circuits shown be the same ?

Engineering

Physics

Ohm Law and Current Basics

Question

$\frac{\sqrt{5} - 1}{2} R$

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$\frac{(R + x) 6 R}{R + x + 6 R} = x$
6R² + 6Rx = 7Rx + x²
x²+ Rx – 6R² = 0
$x = \frac{- R + \sqrt{R^{2} + 24 R^{2}}}{2} = 2 R$