# Current electricity

QuestionsCategory: High School PhysicsCurrent electricity
Abhishek Dta II asked 4 years ago

When 6 identical cells of no resistance are connected in series in the secondary circuit,of a potentiometer,the balancing length is l,balance length becomes l/3 when some cells are connected wrongly then the no of cells connected wrongly are?

Big Bang Boffin Moderator replied 4 years ago

I am not really sure but I guess, 2 cells are wrongly connected. Do you have the answer to this question?

Abhishek Dta II replied 4 years ago

Yes but How

Big Bang Boffin Moderator answered 4 years ago

It’s been a long time since I read about potentiometers, or tried any numerical on them, so I might be wrong.
But since the answer that I got is right, let me explain how I arrived at that.

The above picture shows a potentiometer, where E is the emf of the standard cell.
And E1 is the emf of the additional cells that you are going to provide.
Now the important relation between E and E1 is given as:
$\frac{E_1}{E}=\frac{L_1}{L}$
So, you say that when we connect 6 cells, then the balancing length, i.e. $L_1=l$
Which means, $\frac{E_1}{E}=\frac{l}{L} .........(1)$
But, when we change the arrangement of cells, then the balancing length, $L_1'=\frac{l}{3}$
$\implies \frac{E_1'}{E}=\frac{l}{3L}........(2)$

Dividing (1) by (2) we get,

$\frac{E_1}{E_1'}={3}$

So, how can the new arrangement of cells have an EMF which is one third times of that when the cells are in series.
It can happen if 4 cells are connected in series and 2 of them are wrongly connected.
Let’s say each cell has an EMF of 1 volts.
Then $E_1'=4V-2V=2$ Volts(when 2 cells are wrongly connected).
and $E_1=6V$ (cells in series)

Therefore, $\frac{E_1}{E_1'}=3$
Which is what we got earlier using the balance length formula.

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Hope you find it useful!

Abhishek Dta II replied 4 years ago

So, how can the new arrangement of cells have an EMF which is one third times of that when the cells are in series.
It can happen if 4 cells are connected in series and 2 of them are wrongly connected.

Abhishek Dta II replied 4 years ago

I didn’t understand this part

Abhishek Dta II replied 4 years ago

And this is not my homework,I am preparing for olympiads

Big Bang Boffin Moderator replied 4 years ago

E1′ is the emf of the new arrangement where some cells maybe wrongly connected. E1’/E1=1/3(calculated).If each cell has the potential of 1 V, then when they are all in series(the initial arrangement) then E1=6V.
If in the new arrangement we connect 4 in series but 2 in the opp. direction, then E1’=4-2=2V.
So, E1’/ E1=1/3.
Give it some thought. I don’t know any better way to explain it.

Abhishek Dta II replied 4 years ago

Got it

Abhishek Dta II replied 4 years ago