Question

the total voltage change around a circuit is always positive.

this is a false statement. why?

Answer 1

The total voltage change around a circuit always changes..

There ALWAYS be a potential drop (negative potential) whenever you go across a resistor.

Yes, because if there wasn't, you wouldn't call it a resistor.

With no drop and no change at all, the component would simply be called a conductor.

The whole point in resistors is to control current by limiting and reducing it in fitting amounts. It does this by reducing the voltage, which is the driving force that causes current.

It doesn't really make much sense to talk about "direction of voltage". Voltage is not a flow like current. Two points can have different potentials, and the voltage is just found by subtracting one from the other. Voltage is just difference in potential.

A difference is always end-situation minus start-situation. Naturally, since current runs from high to low potential, the end-situation is at a lower value of potential than the start-situation, and so the difference - the voltage - will be negative.

Across other components, like e.g. a battery or other voltage source, the end-situation (the positive terminal where current leaves from) will be at a higherpotential than the start-situation (the negative terminal where current arrives at). The voltage would here be positive. But the point is not these signs - the only important thing is what the signs are compared between components (battery voltage will be opposite in sign to resistors, always).