James Wright wrote:
Having the number of ship mounted phasers that it has, how many targets can the refit Enterprise engage in battle?
Also, apply this question to the K't'inga.
I think the Enterprise (refit) could engage potentially 18 targets simultaneously or basically one for each phaser emitter or 9 targets if they fired as pairs. Depending on the bearing of the target(s) it would limit the number of available emitters that can fire.
With that being said, it also depends on how much power they need to put into the phaser attack. In TOS they could put all their power (all four phaser energy banks) into one pair of phasers firing. (Note that they did this while not under attack. So they didn't have to divert some energy for shields.) So they could fire all banks through one pair, or split their power among multiple banks. If all 18 emitters fired, they would be at a much weaker output.
The K'tinga would also have similar issues and that is probably why they fire two disruptors in TOS so the movie versions would likely be similar.
Also, remember that the available power to attack depends on how much power is being used for defense and maneuver. If the Enterprise came under sustained attack from 4 K'tingas it may not have enough power to mount a full power phaser attack since it's shields would be sucking up most of the power. She would have to run and buy time and distance to let her shields rest so power can be diverted back to phasers. If she stayed to fight more than likely she would run out of power for weapons and engines and eventually her shields would go and she would be destroyed, IMHO.