Back at the test bench: one resistor, one battery, one ammeter. With a 6.0 V battery, the ammeter reads 0.30 A. Swap in a 12 V battery, with the same resistor, and the ammeter reads 0.60 A.
Only the battery changed, so only the voltage across the resistor changed. The bigger voltage drives more charge around the loop each second: a bigger current.
The pattern does more than give a direction. Double the voltage, and the current doubles. Halve the voltage, and the current halves.
The voltage across a buzzer rises. The buzzer is unchanged. What happens to the current?
A fan motor is moved from a 4.5 V battery to a 3.0 V battery. What happens to the current?
The voltage across a resistor doubles. The resistor is unchanged. What happens to the current?
A camping lantern's 6.0 V battery is replaced with a 9.0 V battery. The lamp is unchanged. What happens to the current through the lamp?
The voltage across a projector lamp is tripled. The lamp is unchanged. What happens to the current?