"In "Mudd's Women", after the 3rd circuit blew out, they had to use battery power for the transport of the 3 women. During that time, they still had to maintain maneuvering and shields to protect Mudd's ship which in mind, lead to the cracking of the 4th crystal."
Or the shields were equally powered by this enigmatic "battery power":
FARRELL: We're clearing the asteroid belt now, Captain.
KIRK: Deflector screen down, Mister Farrell. Save the power.
We do know from "Mudd's Women" that the Enterprise
only had 4 dilithium circuits onboard, we have seen 4 dilithium circuits in "The Alternative Factor" and do not know the exact energy output of "battery power".