Accessories vs Accessory's

That one.

better: The microphone's switch is broken.

Thanks so much for your reply. Three people are telling me that is incorrect and I need some substantial evidence to prove them wrong. Is that an opinion? If not would you mind elaborating?

It isn't the microphone's switch that is broken. A switch on an accessory that is for the microphone is broken.

If it is ONE accessory switch say:
The microphone accessory switch is not working.

or if it is one of many switches, say:

One of the microphone accessory switches is not working.

IPA for the sentence to make sense you almost have to identify the accessory. Otherwise you might have to say "The microphone's accessory's switch is broken," which sounds hell for silly

A switch on the microphone's accessory, a separate amplifier, is broken

The microphone's accessory, an amplifier, has a broken switch

Though we don't usually refer to a defective switch as "broken"

An accessory to the microphone, its amplifier, has a defective (or even just "bad") power switch

The switch belongs to the microphone accessory.


But you can say either of the following which leads to the confusion:

The microphone switch is broken.
The microphone's switch is broken.


Does the switch control one accessory or does it control accessories?

While it might be correct to say
"The microphones switch is broken" if one switch controls several microphones, it is ambiguous and should be clarified.

Thank you so much for your help. I'm sorry for the lack of context.

We are using a microphone which includes an accessory to add a cut-off switch in line with the main wire.

In the instruction manual it states:
"If the microphone accessories switch is broken, replace immediately."

the manual is wrong. "accessories" is the plural of "accessory"l and you're not talking about more than one accessory, you're talking about a switch that is on the accessory, i.e. that the accessory possesses.
"accessory's" is the possessive of "accessory", i.e it says the switch is on the accessory, which is the case here.
To simplify it considerably, if you have a plural you don't have an apostophe. If you have a possessive (or, in other contets a contraction) you have an apostrophe.

Just eliminate the question of possessive.

If the switch on the microphone accessory(ies) is broken, replace immediately.

The correct way form the possessive of a noun ending in -y, is to add an apostrophe and an s like this:

The factory's owner
The mummy's curse
The accessory's switch

We form the plural of a noun ending in -y using -ies

The factories around Manchester
The mummies in Egypt
The accessories that are available