Before you connect the resistor across the battery, no current flows. When you connect the resistor across the battery, a specific amount current will flow.
How much current will flow? Well, it depends. On two things:
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The battery voltage, which is given in Volts. All else being equal, the higher the battery voltage, the higher the current.
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The value of resistance, which is given in Ohms. All else being equal, the lower the resistor’s resistance value, the higher the current.
This can be tidied up with Ohm’s law:
I = V / R
where V is in Volts, R is in Ohms, and I is in Amps.
In other words, if you keep the resistance constant and vary the voltage, the current will be proportional to the voltage. And if you keep the voltage constant and vary the resistance, the current will be a hyperbolic function of the resistance.
Of course, if the voltage is fixed, and the resistance is fixed, the current is fixed.
To sum up, a specific voltage value and a specific resistance value will give you a specific current value. The actual value of current (in Amps) depends on the actual voltage (in Volts) and resistance (in Ohms).
And as someone else has pointed out,
- the current entering the resistor, and
- the current exiting the resistor, and
- the current entering the battery, and
- the current exiting the battery
are all the same. The current is the same everywhere in the circuit, and (of course) is calculating using Ohm’s Law.
Hope this helps.
P.S.: This is really a first-order / ideal explanation. While Ohm’s law is always true, in reality there are many other variables involved, e.g. temperature and RH dependence on resistance, voltage coefficient of resistance (VCR), lead resistance, source impedance of battery, tolerances, leakage currents, etc. etc. etc.