Final answer:
Increasing the resistance in a battery-resistor circuit will decrease the current flowing through the circuit as per Ohm's law. More resistance means greater opposition to charge flow, leading to decreased current and potentially extending the battery life by reducing the current drawn.
Step-by-step explanation:
Increasing the resistance of the resistor in a circuit with a battery will decrease the current flowing through the circuit. According to Ohm's law, current (I) is equal to the voltage (V) divided by the resistance (R), which can be expressed as I = V/R. When you increase the resistance, the current in the circuit will decrease since the amount of voltage pushing the current through remains constant while the resistance against it increases. This is because there is a greater opposition to the flow of charge. Moreover, this would not cause the battery to drain faster; in fact, the battery might last longer because less current is being drawn from it.
Regarding circuits with multiple resistors, when resistors are added in parallel, the total resistance of the circuit decreases, leading to an increase in the overall current. However, if the internal resistance of a battery increases, for instance due to repeated charging in rechargeable batteries, both the terminal voltage decrease and the current decrease could result, potentially causing the battery to overheat.