What if batteries stored less energy?

Phones, lamps and toys can run on batteries. A battery holds energy inside.

What if a battery held only a little energy? Would the lamp still shine all evening?

A battery is a store of energy. When you switch a device on, it draws energy out of the battery, bit by bit, until the store is empty and the device stops.

So what would happen if a battery could only hold a quarter as much energy? Would a lamp shine a little less brightly, or for a shorter time, or not at all? In this lab you can shrink the battery and time the lamp.

Batteries are rated by the energy they store, in watt hours (Wh); devices are rated by the power they draw, in watts (W). Power is a rate of energy use, so the two are linked by time.

This lab asks how runtime depends on capacity when the device stays the same, and why the answer is a simple proportion in the model but a more complicated one for real batteries.

In the model, Olly's battery is full of energy. A lamp sips the energy slowly.

The lamp shines for 6 hours. Then the battery is empty.

Two numbers matter. The watt is a unit of power: it tells you how fast a device uses energy at each moment. The watt hour is a unit of energy: one watt used for one hour. For example, a 40-watt bulb left on for five hours uses 200 watt hours.

In the model, the battery starts with 60 watt hours, the model's laptop-sized setting. A 10-watt LED lamp uses 10 watt hours every hour, so the battery lasts 60 ÷ 10 = 6 hours.

The U.S. Energy Information Administration defines one watthour as one watt used for one hour; a 40 W bulb running five hours uses 200 Wh, or 0.2 kWh. Runtime follows from t = E ÷ P.

The model starts with a 60 Wh battery (its laptop-sized preset) and a steady 10 W load, so t = 60 Wh ÷ 10 W = 6 h. The charge falls in a straight line, because the load never changes, and it assumes all 60 Wh can be used and reach the lamp.

Now Olly makes the battery much smaller. It holds only a quarter of the energy.

The lamp shines just as brightly. But it runs out much sooner: after only an hour and a half.

Set the battery to 15 watt hours, a quarter of the start. The lamp still uses 10 watts, so it shines just as brightly, but the energy runs out after 15 ÷ 10 = 1.5 hours instead of 6.

Try other devices too. A phone that uses about 3 watts would run for 5 hours on the small battery. A 2,000-watt heater would empty it in about 27 seconds. A smaller battery never changes how much power a device needs; it changes how long the device can have it.

With capacity at 15 Wh the model gives t = 15 ÷ 10 = 1.5 h: a quarter of the energy, a quarter of the time. Runtime is proportional to capacity and inversely proportional to load, so a 3 W phone gets 5 h and a 2,000 W heater gets 0.0075 h, about 27 s.

The advanced controls apply losses. At 90 percent conversion efficiency, the 15 Wh battery delivers 13.5 Wh and the lamp runs 1.35 h (1 h 21 min). Set the usable share to 70 percent and only 10.5 Wh is available: 1.05 h.

Think of a water bottle. A big bottle lasts a long time. A small bottle runs out fast, even if you sip the same way.

A battery is like that, but full of energy.

Energy in a battery works like water in a bottle. The device sips it at its own steady speed, its power. A big bottle lasts a long time; a small bottle sipped at the same speed is empty sooner.

That is why the lamp shines just as brightly from the small battery. Its sips are the same size. There are simply fewer of them before the bottle is dry.

Energy is power multiplied by time, E = P·t, so for a fixed load P the runtime t = E/P scales linearly with stored energy. Halving capacity halves runtime; doubling the load halves it too.

The model's limits, from its own documentation: the load is constant, the battery delivers its full usable capacity whatever the power, temperature or age, and it tracks only energy, not the voltage that real cells lose as they empty. Real phones and laptops change their power from moment to moment.

Real batteries can hold less when they get old. They also work less well on very cold days.

Scientists keep working to make batteries last longer.

Real batteries really can end up storing less. Electric car batteries slowly lose capacity as they age; studies show one can still have at least 70 percent of its first capacity at the end of its life in a car, and then keep working in another job.

Cold weather matters too. In tests, electric cars driven at 20 °F with the heater on went about 41 percent less far on a charge than in mild weather, partly because heating the cabin uses energy. Without the heater the drop was about 12 percent. Lithium-ion batteries are used in phones and laptops because they pack a lot of energy into a small, light package.

The Alternative Fuels Data Center reports that an EV battery could retain at least 70 percent of its initial capacity at end of vehicle life and serve another 10 years or more in stationary storage. FuelEconomy.gov, citing a 2019 AAA study, reports EV range about 41 percent lower at 20 °F with cabin heating (about two thirds of the extra energy heats the cabin) and about 12 percent lower without it.

In the model, a 70 percent usable share gives 70 percent of the runtime. That is a simplification: real capacity loss also depends on temperature, charging habits and power level, and charging itself is often 84 to 93 percent efficient.