# Battery (amp hours, total charge, total current)

• tony873004
In summary, a 12-V car battery with a rating of 120 Ah can supply power at 29 W for approximately 20 minutes. The amount of charge that flows through the battery during this time is 432000 C. The initial energy stored in the battery is 36000 Joules. However, when taking into account the internal resistance, the actual timing for supplying power at 29 W would be approximately 50 hours.
tony873004
Gold Member
A 12-V car battery is rated at 120 Ah. Assuming that the terminal voltage remains 12 V, for how long can this battery supply power at 29 W? How much charge flows through this battery in this time? How much energy is initially stored in the battery?

I know that an Amp Hour is 3600 C
I know that a Watt is a Joule / s
I know that 1 J= 1C/V

3600 C * 120

So the initial energy stored in the battery is (3600*120) / 12V=36000 Joules

29 Watts=29 J/s

So this battery is delivering 36000 Joules at a rate of 29 J/s
36000/29 = 1241 seconds.

This is only about 20 minutes. This seems very short. I use 7Amp hour batteries at work. I've used them to power a light for a few hours.
So my intuition tells me this answer can't be right.

How much charge flows through the battery during this time? : I=Q/t = 432000 C / 1241 s = 348 Amps. But this assumes I got the seconds correct.

Did I do this right?

tony873004 said:
A 12-V car battery is rated at 120 Ah. Assuming that the terminal voltage remains 12 V, for how long can this battery supply power at 29 W? How much charge flows through this battery in this time? How much energy is initially stored in the battery?

I know that an Amp Hour is 3600 C
I know that a Watt is a Joule / s
I know that 1 J= 1C/V

3600 C * 120

So the initial energy stored in the battery is (3600*120) / 12V=36000 Joules

?

What's wrong with that part? It wants energy, so my answer should have units of Joules, right?

A joule is a Coulomb / Volt, and the battery has 3600*120=432000 coulombs
43200 / 12 is 36000 Joules. At least my units work. What did I do wrong? Is energy in a battery not expressed in Joules.

1 watt hour is 3600 joules. Should I have expressed it as 10 watt hours?

tony873004 said:
A joule is a Coulomb / Volt...

A joule is a Coulomb*Volt.

oops. Thanks for that.

Now I get 2 days. I guess that's about right. A fresh car battery can burn a single light (I'm guessing about 22W) for about 2 days.

So I imagine I answered the Charge part wrong too. ( I computed current). The charge should be 120Ah * 3600 C/Ah = 432000 C.

tony873004 said:
A 12-V car battery is rated at 120 Ah. Assuming that the terminal voltage remains 12 V, for how long can this battery supply power at 29 W? How much charge flows through this battery in this time? How much energy is initially stored in the battery?

I know that an Amp Hour is 3600 C
I know that a Watt is a Joule / s
I know that 1 J= 1C/V

3600 C * 120

So the initial energy stored in the battery is (3600*120) / 12V=36000 Joules

29 Watts=29 J/s

So this battery is delivering 36000 Joules at a rate of 29 J/s
36000/29 = 1241 seconds.

This is only about 20 minutes. This seems very short. I use 7Amp hour batteries at work. I've used them to power a light for a few hours.
So my intuition tells me this answer can't be right.

How much charge flows through the battery during this time? : I=Q/t = 432000 C / 1241 s = 348 Amps. But this assumes I got the seconds correct.

Did I do this right?

Following up Mr.Ohm for DC circuits:

Power[watt] = Voltage[Volt] * Current[Amp],
so Current[Amp] = Power[watt] / Voltage[Volt],
so Current[Amp] = 29 / 12 = 2.42 [Amp]
and
Time[h] = Capacity[Ah] / Current[Amp]
Time[h] = 120 / 2.42 =~ 50[h]

EURECA! The answer is 50 hours.

Note: This calculation assumes the battery is an ideal source of current (which is not, since it has some internal resistance). Actual timing may be a few percent less than 50 hours.

Last edited:

## What is the definition of "amp hours" for a battery?

Amp hours (Ah) is a unit of measurement for the amount of charge a battery can hold. It represents the amount of current that can be delivered by the battery over a period of time. For example, a 10Ah battery can deliver 1 amp of current for 10 hours, or 10 amps of current for 1 hour.

## How is the total charge of a battery calculated?

The total charge of a battery is calculated by multiplying the amp hours (Ah) by the battery's voltage. For example, a 12V battery with 10Ah of capacity would have a total charge of 120 watt-hours (Wh).

## What is the difference between "total charge" and "total current" for a battery?

Total charge refers to the total amount of energy that a battery can store, while total current refers to the rate at which the battery can deliver that energy. Think of it like a water tank - the total charge is the size of the tank, while the total current is the flow rate at which water can be pumped out.

## How does the amp hour rating affect the performance of a battery?

The amp hour rating of a battery is a measure of its capacity, meaning the amount of energy it can store. A higher amp hour rating indicates a larger capacity, which means the battery can power devices for longer periods of time before needing to be recharged.

## Is it better to have a higher or lower amp hour rating for a battery?

The optimal amp hour rating for a battery depends on the intended use. For devices that require a lot of power, a higher amp hour rating would be more beneficial as it would provide longer run time. However, for devices that require less power, a lower amp hour rating may be more cost-effective and practical.

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