Question

In the series combination of cells each cell having emfs and internal resistance r. It three cells are wrongly connected, then total emf and internal resistance of this combination will be
A. \[n\varepsilon ,\left( {nr - 3r} \right)\]
B. \[\left( {n\varepsilon - 2\varepsilon } \right),nr\]
C. \[\left( {n\varepsilon - 4\varepsilon } \right),nr\]
D. \[\left( {n\varepsilon - 6\varepsilon } \right),nr\]

Answer 1

Hint: Cells can be connected in series, parallel, or a mixture produced by combining both. When cells are connected in series the total voltage of the circuit is equal to the sum of all the individual cell voltages but current remains the same. So this question can be solved by the combination of cells concept.


Formula used:
EMF can be calculated using the formula
\[{\rm{e = IR + Ir}}\]
Where e is electromotive force, ‘I’ is current, R is resistance, r is internal resistance.



Complete answer:

We have been provided in the question that
In the series combination of cells, each cell has emf and internal resistance ‘r’.
Here we are to find the total emf and internal resistance of this combination.
Because there are three cells coupled with opposite polarity in an n-cell combination.
 It signifies that \[\left( {n - 3} \right)\] cells are connected with the right polarity and the remaining \[3\] with the opposing polarity.
We have been knew that the emf’s combination net is,
\[{E_{net}} = (n - 3)E - 3E\]
By solving the equation, it becomes
\[{E_{net}} = (n - 6)E\]
On the other hand, even when batteries are linked with the opposite polarity, the total internal resistance of all the batteries in the circuit is constant.
Consequently, nr will represent the circuit's net internal resistance.
Therefore, the total emf and internal resistance of this combination will be \[\left( {n\varepsilon - 6\varepsilon } \right)nr\]
Hence, the option D is correct.




Note:Parallel and series connections are the most popular methods for connecting electrical components. Students must learn more about how cells behave in both types of connections. The total voltages do not change when cells are connected in parallel configuration, but the current changes.