Question

In the series combination of n cells each cell having emf $\epsilon$ and internal resistance r. If three cells are wrongly connected, then total emf and internal resistance of this combination will be.

• A. $n\epsilon ,(nr-3r)$
• B. $(n\epsilon -2\epsilon ),nV$
• C. $(n\epsilon -4\epsilon ),nV$
• D. $(n\epsilon -6\epsilon ),nV$

Answer 1

The correct option is D $(n\epsilon -6\epsilon ),nV$

Since in a combination of $n$ cells, there are $3$ cells connected with opposite polarity. It means that there are $(n-3)$ cells connected with correct polarity and remaining $3$ with opposite polarity.

The net emf of the combination is:

$E_{net}=(n-3)E-3E$

$E_{net}=(n-6)E$

On the other hand, the total internal resistance of all the batteries remains the same for the whole circuit, even for the batteries connected in opposite polarity.

So, the net internal resistance for the circuit will be $nr$.

So, option $\left(D\right)$ is correct.