Consider Ohm's law:
$$ E = IR $$
Here, we have three variables: voltage, current, resistance. For any resistive load, the three will always be related by this equation.
If that's hard to understand, consider a more observable, familiar three variable equation, Newton's second law:
$$ F = ma $$
Force is the product of mass and acceleration. In a frictionless environment, something that is not accelerating must have no force applied. Accounting for friction, something that is not accelerating must have forces applied that exactly cancel friction, such that there is zero net force. When there is force, a mass will accelerate; and it will accelerate less if it is more massive.
Say you wanted to tow a trailer at a constant speed. Your trailer is going to have some friction from air and the tires, and the towing machine will have to balance that force to maintain your desired speed. If the trailer isn't already moving, the towing machine will have to apply more force to accelerate the trailer. If you are towing uphill, yet more force will be required to overcome gravity. Going downhill you might need to apply a backwards force.
It doesn't matter if you use a bicycle or a locomotive as your towing machine, as long as you can apply enough force to maintain your desired speed. In either case the force is the same, though the range of forces that can be supplied by a bicycle and a locomotive are obviously much different.
You could also have a towing machine which instead of being programmed to travel at a constant speed, is programmed to apply a constant force. In this case, assuming the mass of the trailer is constant, acceleration will be whatever it needs to be to satisfy \$F=ma\$. If we assume a flat highway, probably you will accelerate the trailer to some speed until friction prevents further acceleration, and then your speed will be constant.
Most electrical power supplies are designed to maintain a constant voltage. For most loads, if you want more current to move through them, you must apply a higher voltage to overcome the opposing forces created by the resistance of the load. \$E\$ is set by the power supply, and \$R\$ by the load, thus, there will be only one \$I\$ which will satisfy \$E = IR\$. Not all power supplies will be capable of supplying enough current (and less commonly, a power supply may have a minimum current), but provided the circuit is operating within the supply's specifications, voltage will remain constant, and current will change according to the load.