Yes. Most insurance companies cover electronic devices. All you have to do is to provide the receipts of the device to prove that the device belongs to you. However, there might be exclusions for expensive or luxury electronic devices. You should check your renters insurance delcartion page to review the exclusion terms.
The information in this answer is general in nature and is not legal or insurance advice for your specific situation. Policy language varies carrier by carrier; your declarations page is the final word. If you're unsure, call your agent before you need to file.