# Homework Help: How long will a battery last?

1. Feb 9, 2012

### sweetreason

This isn't actually a homework/schoolwork question, but all the stickies on the other boards say that anything that is a school-work *type* question should go here. Not sure if this qualifies, but I figured I'd err on the side of caution. I took physics II last year and now I'm trying to do a little electronics project -- and to my consternation it appears I didn't learn how to compute something pretty simple!

Suppose I know the total resistance of components in a circuit. In my case it's R = 2292 Ohms. And suppose I've got a battery with an EMF of 14.8 V. How would I find out the time it would take for my battery to run down? Do I need more information? It seems my most relevant equation is that for power delivered to a resistor: $$P = V_{ab} = I^2R = (V_{ab})^2 /R$$

However, I don't want the power, which is the work/time, I just want the time. I don't know how I would find out the work that's done. the circuit elements are four motors which are labeled "90W", but I don't know if that means they require 90W every second, or what. How do I find a "t" variable in this equation that I can solve for?

Thanks!
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Feb 9, 2012

### Staff: Mentor

Batteries have ratings for both voltage and available energy. The energy is typically given in Amp hours (Ah) for large batteries or milliamp hours (mAh) for smaller ones. Essentially it tells you how much current x time the battery can usefully produce before its voltage begins to degrade and the battery heads towards unusable (discharged).

Look up the characteristics of your particular battery.

3. Feb 9, 2012

### Staff: Mentor

Determining the life expectation of a battery is an imprecise endeavour. First, you need to find the ampere-hour rating of the battery, when new. Then, knowing the current drain, you can arrive at a figure for the time the battery will last while delivering that current. There are many associated provisos, but that's a start.

4. Feb 9, 2012

### sweetreason

Sorry, I should have included that information. The capacity of the battery is 1800mah. But how do I use this information? Wouldn't I first need to figure out how much current my circuit elements are drawing? How do I find that? I know the resistance (573 Ohms x 4 elements) and there is a power rating on the circuit elements (90w) but I think that is the maximum power that these circuit elements can tolerate.

5. Feb 9, 2012

### Staff: Mentor

Determine the average current that your whole circuit will draw from the battery either by measurement or calculation. You can use that with the ampere-hour rating to estimate the working life.

6. Feb 9, 2012

### sweetreason

gneill, how do I do that? can I use V=IR with V as the battery voltage and R the total resistance in the circuit?

7. Feb 9, 2012

### sweetreason

I don't actually have the all the components in front of me, I'm trying to determine how the components will drain the battery before I buy the components. So I can't test the circuit, I've got to calculate it.

8. Feb 9, 2012

### Staff: Mentor

Yes, that'll do it. The total resistance, otherwise known as the equivalent resistance, is the resistance that the circuit presents to the battery where it connects.

9. Feb 10, 2012

### Staff: Mentor

You have a 14.8v battery, of capacity 1.8 Ahr. You say you have 4 motors, and seem to imply you can represent each as a 573Ω resistor. They must be very tiny motors if that is the case. How did you determine that resistance? Are you planning to power the 4 motors in series or parallel? What is their voltage rating?

10. Feb 10, 2012

### sweetreason

Nascent,
I got the resistance figure from the parts store I'm looking at. The specs of the part are here. The same page says the max voltage is 15 V.

I'd guess the motors are giong to be in parallel, but I'm not really sure -- they're going to be hooked up to pins on a microcontroller like this one, I don't know enough about microcontrollers to say with certainty what kinds of connections those are. Would it make a difference to how fast the battery drains?

11. Feb 10, 2012

### Staff: Mentor

There are many motors there. Which one?
They are 15v motors, so with a 14.8v battery they will be in parallel.

If you have 4 motors, running under conditions where each draws, say, 5A, then your battery will last about 2 or 3 mins. If it's rechargeable, then it will have a shortened life, because a 1.8Ahr capacity is far from optimal for a load of more than an amp.