# What is the internal resistance r of the battery?

## Homework Statement

The potential difference across the terminals of a battery is 8.20 V when there is a current of 1.54 A in the battery from the negative to the positive terminal. When the current is 3.56 A in the reverse direction, the potential difference becomes 9.40 V. What is the internal resistance r of the battery?

V_ab = E - Ir

## The Attempt at a Solution

So I thought that it would make no difference if the charge was reversed. So I just plugged the values into the equations, so since I have two equations and two variables I could solve for r.

8.56 = E - 1.54r -> E = 8.56 + 1.54r
9.40 = E - 3.56r -> E = 9.40 + 3.56r -
0 = -.84 - 2.02r
r = -.416

Obviously the resistance can't be negative. What am I doing wrong, does it have something to do with the reversing part of the problem?

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dynamicsolo
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## Homework Statement

The potential difference across the terminals of a battery is 8.20 V when there is a current of 1.54 A in the battery from the negative to the positive terminal. When the current is 3.56 A in the reverse direction, the potential difference becomes 9.40 V. What is the internal resistance r of the battery?

## The Attempt at a Solution

8.56 = E - 1.54r -> E = 8.56 + 1.54r
9.40 = E - 3.56r -> E = 9.40 + 3.56r
In your second equation, remember that the direction of the current is reversed. (Just like in a pre-Star Wars science-fiction movie: "Reverse the polarity!")

I don't understand why that makes a difference, because won't the change in potential be the same? So what's negative the potential or the amps??? I'm confused.

dynamicsolo
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I don't understand why that makes a difference, because won't the change in potential be the same? So what's negative the potential or the amps??? I'm confused.
You are asked to reverse the direction of the current through the battery. In the first part, the current flows from the negative to positive terminal within the battery, so you may write

8.20 V = E (in V) - (1.54 A) · r (in ohms) ,

as you did.

But in the second part, we are told that the 3.56 A current is being applied in the opposite direction (positive to negative terminal inside the battery), so the sign of the current must be switched.

Thanks. I guess I need to go back and read up on charges deff. of a Coulomb and such. I knew the potential would be the same.

dynamicsolo
Homework Helper
Thanks. I guess I need to go back and read up on charges deff. of a Coulomb and such. I knew the potential would be the same.
You should get a small value for the battery's internal resistance. (It's typically a fraction of an ohm in such problems.)