Last weekend AC stop working

I checked the pressures and all seems to be fine ... After some tests it seems to be the Low pressure switch ..

Replaced BUT now the Compressor Rapidly Cycling On and Off (Off @ 35 ... On @ 80 on and on ) while car is stop and RPM are about 1200 (not sure if thats how it worked before)

Everything seems to work good while idle .. Low pressure steady at 45 .. High about 200
But once RPM goes over 1000 the Low pressure gets to 35 PSi and the compressor start the cycling

Is this normal ? .. Low pressure switch should open at 35 psi ?
Could be due the 90 degrees outside temp , high rev and car stopped?

BTw I jumped the switch and cycling stopped . but a jump switch isnt a good fixed idea

Could be a brand new defective switch ?

Any other issue in the system

Please give me some ideas .. Thanlk you

 

Could the clutch on the compressor be going bad? AC is tough to figure out. It's the only time I've had to take a car to someone to get fixed. Even though I have repaired the AC before, this one instance I was out of my league and had to relent. Keep us posted.

 

Clutch looks to be fine . the Ac is working at idle . also when bypass the pressure switch it works perfect