# Internal resistance of a cell

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Here's a question, and my doubt is at the end of the question. I have been struggling with this doubt for quite long and have been receiving mixed opinions.

A cell of emf 12 v supplies a current of 400 mA to an appliance. After some time the current reduces to 320 mA and the appliance stops working. Find the resistance of the appliance, the terminal voltage of the battery when the appliance stops working, and the internal resistance of the cell.

In my book, the answer to this ques is given as follows:

1. Given, emf = 12 volt, I = 0.4 A

Therefore Resistance of the appliance R = emf/ I = 12/0.4 = 30 ohm

2. Given , I' = 0.32 A

Terminal voltage of battery V = I'R = 0.32*30 = 9.6 volt

3. From emf= V - v,

v ( voltage drop) = emf-V= 12-9.6= 2.4 volt

From v= I'r,

r = v/I'= 2.4/0.32= 7.5 ohm ( internal resistance)

My doubt is, in the 1st part, why isn't R= resistance of the appliance + internal resistance? Why is the internal resistance of the cell ignored in part 1?

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3 hours ago, Arnav said:

A cell of emf 12 v supplies a current of 400 mA to an appliance. After some time the current reduces to 320 mA and the appliance stops working. Find the resistance of the appliance, the terminal voltage of the battery when the appliance stops working, and the internal resistance of the cell.

By the way this should be in Physics, not homework help since your book gives working and you are asking for an explanation, not for us to do homework.

I am not suprised you have received conflicting information. Most books are poorly written on this subject, as the example you quote shows.

You are right to seek explanations.

Firstly let us look at the often quoted formula

$I = \frac{E}{{{R_{load}} + {r_{{\mathop{\rm int}} ernal}}}}$

Now if we assume that Rload is constant then for two I hope you can see that for two different currents,

Both E and Rinternal cannot be the same for both currents.

In fact as the cell becomes more and more exhausted the internal resistance rises and the EMF falls.

So the currents of 400mA and 320 mA describe different situations.

Most books will not tell you this.

When I is 400mA the battery is fresh and the internal resistance is taken as zero (or negligable).
So the full 12V EMF is applied to the load determining Rload to be 30 ohm.

As the battery looses charge and the current falls Rinternal  rises from zero and the EMF is shared between the load and the internal resistance.

Since Rload is constant it is still 30 ohms but now passes 320mA so experiences a voltage drop of 9.6V.

Your book must have assumed (again it did not say) that since the battery was still supplying substantial current its EMF has not yet dropped appreciably.
This is often the case that the internal resistance change runs ahead of the EMF fall as that fall it set by the chemical reactions of the battery and it is only in the later stages of exhaustion when the current has dopped  dramatically that other chemical reactions become important.

However it should be noted that these days there are many more types of battery and the relationships between aging, E and Rinternal are more varied. Most books have not caught up with this either.

Does this help ?

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12 hours ago, Arnav said:

A cell of emf 12 v supplies a current of 400 mA to an appliance. After some time the current reduces to 320 mA and the appliance stops working. Find the resistance of the appliance, the terminal voltage of the battery when the appliance stops working, and the internal resistance of the cell.

There is not enough information to answer that question.

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12 hours ago, studiot said:

By the way this should be in Physics, not homework help since your book gives working and you are asking for an explanation, not for us to do homework.

I am not suprised you have received conflicting information. Most books are poorly written on this subject, as the example you quote shows.

You are right to seek explanations.

Firstly let us look at the often quoted formula

Now if we assume that Rload is constant then for two I hope you can see that for two different currents,

Both E and Rinternal cannot be the same for both currents.

In fact as the cell becomes more and more exhausted the internal resistance rises and the EMF falls.

So the currents of 400mA and 320 mA describe different situations.

Most books will not tell you this.

When I is 400mA the battery is fresh and the internal resistance is taken as zero (or negligable).
So the full 12V EMF is applied to the load determining Rload to be 30 ohm.

As the battery looses charge and the current falls Rinternal  rises from zero and the EMF is shared between the load and the internal resistance.

Since Rload is constant it is still 30 ohms but now passes 320mA so experiences a voltage drop of 9.6V.

Your book must have assumed (again it did not say) that since the battery was still supplying substantial current its EMF has not yet dropped appreciably.
This is often the case that the internal resistance change runs ahead of the EMF fall as that fall it set by the chemical reactions of the battery and it is only in the later stages of exhaustion when the current has dopped  dramatically that other chemical reactions become important.

However it should be noted that these days there are many more types of battery and the relationships between aging, E and Rinternal are more varied. Most books have not caught up with this either.

Does this help ?

You see guys, even here I am getting mixed answers, John says the data is insufficient and studiot says the question's fine.

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15 hours ago, studiot said:

By the way this should be in Physics, not homework help since your book gives working and you are asking for an explanation, not for us to do homework.

!

Moderator Note

Moved to Physics.

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5 hours ago, Arnav said:
17 hours ago, studiot said:

You see guys, even here I am getting mixed answers, John says the data is insufficient and studiot says the question's fine.

I see you are here again so I will post half an answer.

Actually John is quite right and I also siad the same thing.

Did you understand that part?

17 hours ago, studiot said:

Now if we assume that Rload is constant then for two I hope you can see that for two different currents,

Both E and Rinternal cannot be the same for both currents.

It would be helpful to say whether you are studying Engineering or Physics, as their view is slightly different.

Here are a few pages from the UK standard intoductory text for at least 50 years.

As you can see it only goes so far in explanation.

I expect it say similar things to your book.

Please compare them and let us know.

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