According to Ohm's Law, current increases, when voltage increases - I=V/R. But current decreases, when voltage increases according to P=VI.
I'm confused, what is going on?
E is the electromotive force, one of three variables in ohms law, E = IR.
be careful as to which on you hold steady and which ones you let vary!
P is power such as watts or horsepower, (746 watts / horsepower)
Power is not to be confused with E, I, or R, Power "P" depends on E, I, and R.
P= EI , P=I squared R, and P= Vsquared / R are all power formulas. The one you use is dependent on which two you know or can compute.
E = I times R is a variation of ohms law as is I = E/R and R = I/E
First, line up the equations in question so that you may see in your minds eye the movement of values.
e = i r if you hold r, e & i move directly proportional, either up or down
p = i times e if you hold e, p & i move directly proportional, either up or down
p = i times i r therefore, you have four components to contend with and you pick three at a time, so depending on which or what three you select will determine which two will move proportionately together in the same direction as you hold the third.
Now, using simple integers, assign values to the variables such as r = 3 ohms; i = 2 amps; e = 6 volts and p = 12 watts, insert the values.
6 = 2 x 3 if you hold 3, then double or halve 6 & 2
12 = 2 x 6 if you hold 6, then double or halve 12 & 2
12 = 2 x 2 x 3 Notice that i or 2 are mutually inclusive, they are like simese twins attached at the hip.
So far we have seen what happens when you hold a component on the right side of the equation, the remainder components both move in the same direction. If you decide to hold the component on the left side of the equation, in these cases p, then the right side two components move indirectly proportional to each other; for example, a teeter totter balanced on a center fulcrum which does not move, as one side goes up the other side goes down and vice versa.
You will not get the full comprehension from a simple definition. You have to apply your experience in the world with other knowledge learned through good competent teachers to be able to visualize in abstract form in your mind in order to get the feel for what is going on. The feel is mucvh more important than the understanding, else it is rote memorization.
For example, change the voltage pressure to gravity/height, the current capacity to water in a bucket and the resistance to the size of hole at the bottom of the bucket and finally the power to pressure force of the water coming out and hitting your eye. Remember this is just a thought experiment. Another one is if you live in cold climate, think about the forces and variables as you write your name on snow, just don't apply this experiment to your eye, or if you are facing the wind.
Lastly, in your intitial question "According to Ohm's Law, current increases, when voltage increases - I=V/R. But current decreases, when voltage increases according to P=VI." In the first part I=V/R you are holding R and in the second part P=VI you are holding I. Notice that R & I are not the same; furthermore, it is best to analyze a series circuit with R and a parallel circuit with G, which is the reciporcal of resistance called conductance. Ouch! yet another component, but yet makes for an easier analysis for the calculation of series-parallel circuits.
The laws of physics and nature are not just really good ideas.