Answer: the increase in the external resistor will affect and decrease the current in the circuit.
Explanation: A battery has it own internal resistance, r, and given an external resistor of resistance, R, the equation of typical of Ohm's law giving the flow of current is
E = IR + Ir = I(R + r)........(1)
Where IR is the potential difference flowing in the external circuit and Or is the lost voltage due to internal resistance of battery. From (1)
I = E/(R + r)
As R increases, and E, r remain constant, the value (R + r) increases, hence the value of current, I, in the external circuit decreases.