# Battery Charging Explained — Or… Honey, Who Shrunk The Electrons?

Which charges faster, a Tesla Model S or a Nissan Leaf? Get out your calculators. Ready, set, go.

All batteries are described by their ability to deliver current and voltage. Open circuit voltage is the voltage batteries produce when not connected to a load or to a really small load like a tiny flashlight bulb. All batteries have internal resistance that limits their ability to deliver current. If the current is too high, the voltage drop across the resistance becomes so high that current cannot increase. The resistance makes batteries heat up and become inefficient, and their life is reduced. The internal resistance is determined by battery characteristics and often by the chemistry and type of battery.

Batteries are also described by their amp-hour rating. The amp-hour rating describes how may amps of current they can carry for how long. Multiply by the voltage and you get amp volt hours, also known as watt-hours (Wh). That’s a unit of energy familiar to many of us, as the typical electric utility bill is measured in kilowatt-hours, kWh. A 1 amp hour battery could deliver 1 amp (A) for an hour. But only if its charge rate, C, allowed.

### What’s C?

The guy who invented this charge rate concept and created C was Charles Coulomb. He seemed to like the letter C. Let’s take that 1A-hour (Ahr) battery. If it had a C rate of 1, it could charge at 1A for an hour, the same as its amp-hour rating. If it had a C rating of 2, then it could deliver 2A in a half hour to deliver 1Ahr. But really, it means it could deliver 2A for any time up to a half hour. So, I can combine the information from C and Ahr ratings to determine the maximum current.

### What Does that Mean for Charging?

Let’s look at some cases to try to understand this. Suppose I have a tiny AA battery and it’s rated at 1C. Its amp-hour rating is probably reduced to milliamp-hours or less. But it’s still milliamp-hours. So time is built into the idea. A C rate of 1 for a 1milliamp-hour battery is still 1 hour. So, the current might be a lot lower, but the charge rate for any 1C battery, regardless of capacity, is the same, one hour.

### But How Does this Apply to Different EVs?

If it didn’t depend on charge rate, we could just divide the battery capacity (in kWh) by the charger power (in kW) and wind up with hours. With C rate, we have to look at charger power, battery capacity, and C rate to see which limits charge rate.

Let’s say we have a 10kWh battery pack and a 20kWh battery pack. Both have the same C rate, one hour. As long as my charger can deliver it, they both charge in the same time. But what if my charger is only 10kW? Then the 20kWh battery pack can only be charged at 10kW, so it gets 10kW in the first hour and takes 2 hours to charge to 20kWh. In that case, the charger limits the battery to less than its full C rate, 1 hour. So, charge rate is determined by the charger or the battery, depending on which limits charge rate first.

So, we really can’t tell how fast a pack charges until we know three things; one, the charger rating in kW; two, the battery charge rate; and three, the battery capacity in kWh. But if the charger is always big enough, the charge rate is just limited by the C rate. If two batteries have the same charge rate, and you have a big enough charger, they charge at the same rate. The bigger battery will just charge at a higher current, but take the same amount of time to charge.

But, actually, there’s more. The actual time to charge a battery depends on how much it’s discharged. We just assumed we had a fully discharged battery and we charged it from fully discharged to fully charged. But that’s a horse of a different Coulomb.

Images © Cynthia Shahan

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