How would In Amber Clad's reactor destroy High Charity and Delta Halo?

Cortana's plan to detonate the reactors just like Pillar of Autumn makes less sense the more I think about it.

First off, High Charity is only in proximity to the ring, not parked on it like the PoA. Secondly, the PoA had 3 reactors including an experimental prototype and is overall a much larger ship with larger power demands thus the reactors must be much more powerful.

In Amber Clad by comparison is a dinky little Stalwart-class frigate. One of the smallest capital ships in the UNSC. Make it make sense.