Connect external hard drive to imac

Just for clarification:

• USB 1.x, 2.x, 3.x, etc. are USB standards.
• USB A, B, C, etc. are USB connection "physical" types.

What you are showing us in the image is a USB-A type connector. The fact that it is blue, and has an SS "SuperSpeed" label, would indicate that is can support up to the USB 3.2 Gen 1x1 standard ... with a max. throughput of 5 Gbps.

If your new iMac is the 2013 M3, it came with two model types: 2-port or 4-port.

• The 2-port model has 2 Thunderbolt/USB 4 ports (40 Gbps). These are both USB-C types.
• The 4-port model comes with 2 Thunderbolt/USB 4 ports (40 Gbps), and 2 USB 3 ports (10 Gbps)

Based on what you provided in your post, I'm assuming that you have the 4-port model. As such, you should be able to connect your external drive, using a USB-A to USB-C adapter (rkaufmann87 has already provided you with an excellent recommendation).

Since this external drive is limited to USB 3.2 Gen 1.1, you should connect it to one of the Mac's USB 3 ports. However, even though those ports support up to 10 Gbps, your external drive cannot exceed 5 Gbps at best.

It looks like a USB cable, if that is correct you simply need a USB to USB C adapter. You can find them cheaply at Amazon for example:

https://www.amazon.com/Syntech-Adapter-Thunderbolt-Compatible-MacBook/dp/B07CVX3516/ref=sr_1_2_sspa?crid=3SPE1EMZ91LIF&dib=eyJ2IjoiMSJ9.-bjTLQnyDjtK2zgc9rHz3Fejbr5A_nwHSUwnCwAcpvO6DH1r5F2-IgMlHhwrQHGgmU0buWHdscGeOciR9rf6DaIfXPW30d7XOQJ4G37c0CdjWEyKsiT3niW5_OGl5L1OeBBewVDrE2gUIEFl4y9EYVxOR7LNxMmNFh-nO-XxIDQmunWgjYXYMsYGSxym-gM1iNfyhrzNstMEtVN5NvGzhZjOsAoE-diYtM_h-UGwwKE.-WHDtlhIrqtXKPAQRzhYFmHrNukemp5N6tf7KmeCbaI&dib_tag=se&keywords=usb%2Bto%2Busb%2Bc%2Badapter&qid=1717613164&sprefix=usb%2Bto%2**%2Caps%2C196&sr=8-2-spons&sp_csd=d2lkZ2V0TmFtZT1zcF9hdGY&th=1

It may helped positively identify your cable by showing us the end that plugs into the computer.

At least four types of connectors can lay claim to the name "USB 3":

• USB 3.0 Type A – The one on the end of your cable.
• USB 3.0 Type C – The one on your 24" iMac.
• USB 3.0 Type B – The one on the back of my external optical drive.
• USB 3.0 Micro B - The one on the back of many portable bus-powered USB 3.0 drives.

When going from USB 2 to USB 3, the standards group had to add more pins to carry extra signals. For Type A, they fit the extra connections into connectors with the same overall shape. You can plug a USB 2.0 Type A cable into a USB 3.0 Type A port, or vice versa, and everything gets sorted out.

With Type B and Micro B, the USB 3.0 connectors are bigger than the USB 2.0 ones, and will not fit into USB 2.0 sockets. There were USB Mini connectors that supported USB 2.0 speeds, but I think the market for those Mini connectors must have dried up enough that nobody wanted to bother making USB 3.0 versions!

https://www.cablestogo.com/learning/connector-guides/usb

https://www.anker.com/blogs/cables/how-to-identify-different-types-of-usb-cables-a-brief-guide