Would using a resistor in a circuit make a battery last longer?
Well, just adding resistance to part of a circuit does not guarantee that the current will drop. It depends where the resistance is added and this characteristic of the rest of the circuit. The resistance of the total load must increase.
If you have a purely resistive circuit and add a resistor in series, it will surely increase the total resistance.
Suppose the resistance is the same as the original resistance. Then the total charge resistance doubles and the current are divided by two.
Since the voltage is divided and the current divided by two, the power in the new resistor is 1/4 of that of the original circuit and is wasted as heat.
The power delivered to the original circuit is also 1/4 of that of the original state. Therefore, it will hardly do its job, whether it is a radiator or a light.
Congratulations, you have invented a way to reduce the useful power supplied to a circuit by 1/4 and not to work; you have lost another quarter of the power. But you saved half the power. The battery will last twice as long performing 1/4 of the work.
If you use a small resistance, the current reduction is low, the power lost is low and the reduction in the performance of the load (less heat, less light) will be low. And thus, the increase in the life of the battery will be very low.
It depends a little on the purpose of the circuit. Of course, the greater the resistance in the circuit, the lower the current flowing; therefore, power dissipation will be reduced and the battery will last longer.
But you need to know if the circuit, whatever it is, can do the job you want.
As described above, the resistor reduces the current flow but also dissipates energy and therefore probably generates a waste. Less power does a useful job for you.
Take the case of a 10v battery (theoretical for reasons of easy mathematics) with a capacity of 10Wh. we connect a 5w bulb (rated for 10v, which equals 20 ohm). The bulb will come on for 2 hours.
Now leaves a resistance of 20 ohms in the circuit. Assume that the bulb’s resistance has not changed even though less current is flowing now (the bulbs have no linear resistance but that’s another subject). The total resistance of the circuit has doubled. The current flow is now halved and the battery will last 4 hours.
The bulb lights up twice as long! But in reality, we lost half of the battery’s energy to heat a resistance. And the bulb is very dimly lit, so do not do the work we want.
So, yes, adding resistance to a circuit increases the battery life, but you get less work.
As a parallel exercise, look for the theory of maximum power transfer. In some cases, the goal is to get the source as instant as possible, not just the longest duration.