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  • In a battery 12 cells each having the same emf are connected in series and are kept in a closed box. Some of the cells are wrongly connected. This battery is connected in series with an ammeter and

In a battery 12 cells each having the same emf are connected in series and are kept in a closed box. Some of the cells are wrongly connected. This battery is connected in series with an ammeter and two cells identical with others.The current is 3A when the cells and battery aid each other and 2A when the cells and battery oppose each other. The number of cells wrongly connected in the battery are

Option: 1

1


Option: 2

2


Option: 3

3


Option: 4

4


Answers (1)

best_answer

As we learnt

Main current / current from each cell -

i=\frac{nE}{R+nr}

- wherein

n- identical cells which connected in series

 

 Let n cells in the battery be wrongly connected.

Then E_B=(12-n)E-nE=(12-2n)E

r_B=12r

\Rightarrow I=\frac{E_{eq}}{R+nr}= \frac{\left ( 12-2n \right )E+2E}{12r+2r}= 3A

\Rightarrow \left ( 14-2n \right )E= 42r.........(1)

2A= \frac{\left ( 12-2n \right )E-2E}{12r+2r}\: \: or\: \: \left ( 10-2n \right )E=28r............(2)

\Rightarrow Eqn(1)/Eqn(2)

\frac{14-2n}{10-2n}= \frac{3}{2}\: \: or\: \: 28-4n=30-6n

or 2n=2 or n=1.

 

 

 

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