Q: is ELCapitan ok to install on a 2010 MAC 3.2core i3 4GB 1333 dddr3

I'm not sure that you have identified you iMac properly. 27" Mid 2010 iMacs shipped with either i5s or i7s, not i3s.

Click on the Apple menu's, "About This Mac," then System Report, look for your iMac's Model Identifier number and report back.

Lanny

It appears as if your information is incorrect.

http://www.everymac.com/systems/apple/imac/specs/imac-core-i3-3.2-27-inch-alumin um-mid-2010-specs.html

This machine, identified as an iMac 3.2GHz, does contain an i3 and is from Mid-2010.

It should run El Capitan just fine.

Upgrade to OS X El Capitan - Apple Support

Oops, I stand corrected.

Sure, no problem.  I've made my stare ...

You might, at some point, want to consider upgrading your RAM from 4 Gigs though. Your model can handle a maximum of 32 Gigs.

4 Gigs is enough, but 8 might be a better solution.

Glad that helped.

At some point, you might want to consider Lanny's suggestion to upgrade your RAM, or possibly consider replacing your six year old Mac.  But yes, your current Mac can run El Capitan.

Along with Lanny and sberman I strongly second the motion on the ram upgrade to 8 Gib or more. El Capitan runs OK with 4 but will perform considerably better with more. Virtually all versions of OS X - or any other "modern" OS, especially after transitioning from 32 to 64 bits - will multitask better with more ram than it had initially. What they are initially equipped with is determined by selling price enormously more than by performance.

OS's are geared toward holding processes in memory whenever possible, to yield faster task switching. Apps are loaded at login for the same reason - see your login items in your account settings for examples.

Trauts

I would recommend OWC. They specialize in Macs, and they backup their products. http://eshop.macsales.com/shop/memory/iMac/2010/DDR3_21.5_27