Suppose you have DC power supply and a consumer connected to it (i.e. computer PSU and a hard drive).

Suppose PSU which was supplied with the consumer has output 5V 1A. So I assume that the consumer should not consume more than 1A.

Suppose the original PSU is broken now and I want to replace it with the one I have which is 5V 10A.

My guess is that current is something which depends on the consumer. So if the consumer consumes normally 1A then it will not consume more than that even if it is connected to 10A PSU.

In other word - am I right assuming that the consumer will not burn out being connected to a power supply with higher current output?

P.S. my understanding is that voltage is something independent from the consumer. If you give it higher voltage it will burn (voltage is from PSU to the consumer). However current must be in opposite - consumer sucks as much current as it need not as much as PSU can provide (of course given that max PSU current is greater than the consumer needs)