What happens when you increase the current to a solenoid?

increasing the voltage increases the current. this is because when you increase the voltage you make the pressure that is pushing on the current (which is making it move) greater, therefore increasing it.

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Ohms law states that, the current is directly proportional to the applied (EMF) voltage and inversely proportional to the resistance in a circuit.

The formula you are looking for is I = E/R. You supply some figures for Voltage (E) and Resistance (R).