The current through a circuit is directly proportional to the battery voltage. An increase in voltage leads to a higher current, while a decrease results in a reduced current, provided the circuit's resistance remains constant.
When the battery voltage value changes, the current through the circuit changes according to Ohm's law, which states that the current (I) is equal to the voltage (V) divided by the resistance (R), or I = V/R. If the voltage increases and the resistance remains constant, the current increases proportionally. Conversely, if the voltage decreases, the current through the circuit will decrease, assuming the resistance remains unchanged.
This relationship is highlighted when considering that the terminal voltage of a battery is Vt = ε - Ir, where ε is the electromotive force or nominal voltage of the battery, I is the current in the circuit, and r is the internal resistance of the battery. Therefore, any changes in the voltage or internal resistance will affect the current flowing through the circuit. For example, an increased internal resistance due to a low battery can decrease the terminal voltage and thus the current.
In conclusion, the current through a circuit is directly affected by changes in the battery's voltage, and the internal resistance also plays a role in determining the final current value.