Obviously the backup can't be completed if it was still in progress when electricity stopped flowing. That doesn't necessarily mean it is corrupt, but it is almost certainly going to be unusable.
In the unlucky (though unlikely) event that you lose power during a full backup, and the database itself was also corrupted as a result (this is not necessarily the case; often databases will recover from a power outage just fine), then you would have to resort to the previous full backup + any diff/log backups taken in the meantime. Similar if you lose power during a log backup, you would have to resort to the last successful log backup. So your recovery plan should account for this possibility (meaning you want your log backups to happen frequently enough that they cover your tolerance for data loss).
Once the database itself is recovered and confirmed to be fine, start the backup chain over by creating a fresh full backup.
BTW this is why people have redundant power supplies and/or UPS devices. This is certainly an avoidable problem at not a very high cost.