The current does change though, current is proportional to voltage (Ohms law).

Double the voltage, double the current.

Power is the product of the voltage and current (Watt's law).

But you double one, you double the other. So double the voltage = double the current and as both are doubled, the power increases by the square of the voltage.

• 2V @ 300Ω = 13.3 mW
• 4V @ 300Ω = 53.3 mW

And this is actually the typical power you get out of 2V single ended / 4V balanced stuff.

Look for example here at actual measurements of the Moondrop MoonRiver 2 which does max 2V SE, 4V balanced.

At 300Ω, it is able to reach the full 2/4V without clipping and does ~13mW single ended, ~53mW balanced. At 68Ω, it's still hitting the full 2/4V and the power is ~59/235mW. The balanced power in both these cases is 4x exactly. So any headphone over 68Ω, you will get 4x the power on the balanced.

At low impedances, there can be a limit to current, so the amplifier will clip and you won't get 4x. You can see this here with 32Ω, where it gets 125mW single ended but only ~250mW balanced- and it then clips and distorts, rather than running out of voltage as in the other cases.

But you typically will get the full 4x at double voltage, into higher impedances.

Exactly how much at a given impedance depends on the design of the amp. But 4x is the theoretical increase in power, if current is not a limiting factor. And it typically won't be, into higher impedances. Check the spec sheets for some other amps with both, like the Topping A90D, you can see that 250mW SE but 1,000mW balanced into 300Ω. If you go all the way down to 16Ω, it's less, it's 3,300mW vs 9,800mW, i.e. 3x. Because there's a current limit. It's still over 2x though even at 16Ω.