A circuit consists of an ideal battery of electromotive force \(\mathcal{E}\), three identical fixed resistors labeled \(R_1\), \(R_2\), and \(R_3\) (each of resistance \(R\)), and a variable resistor with adjustable resistance \(R_x\).

Resistor \(R_1\) is connected in series with the battery, and this combination is connected to a two-branch parallel network.

Branch 1 contains resistor \(R_2\), while Branch 2 contains resistor \(R_3\) connected in series with the variable resistor \(R_x\).

If the variable resistor is adjusted from \(R_x = 0\) to its maximum value of \(R_x = 2R\), what is the ratio of the new total power delivered by the battery to the initial total power delivered by the battery?