In the same time, the greater the current in the appliance, the more work the current does? Is that right? Why not

In the same time, the greater the current in the appliance, the more work the current does? Is that right? Why not

No. let's make the current bigger and u smaller. As long as u decreases and R decreases, the current will be bigger, but the function remains unchanged

The work done by an electric current in a unit time is called electric power

P=UI
P=W/t

Is electrical power the work done by current?
For example, is the work done by an electric current passing through a small light bulb electric power?

Power cannot be compared with work
Two different concepts

What is the work done by current in unit time? What is the definition of work? What is the difference between work and electric power?

The work done by the current to the object in one second is 1J, the work is in J, w = uit, the electric power is in W, P = UI!