Question

$n$ identical cells, each of emf $E$ and internal resistance $r$, are joined in series to form a closed circuit. One of the cell $A$ is joined with reversed polarity. The potential difference across each cell except $A$, is

• A. $\frac{2\epsilon }{n}$
• B. $\frac{n-1}{n}\epsilon$
• C. $\frac{n-2}{n}\epsilon$
• D. $\frac{2n}{n-2}\epsilon$

Answer 1

The correct option is A $\frac{2\epsilon }{n}$

Given,

Number of cells $=n$

EMF of each cell $=\epsilon$

and Internal resistance of each cell $=r$

One cell is joined in reverse.

$\therefore$ Total EMF $=n\cdot \epsilon -2\cdot \epsilon$

Current in the circuit, $I=\frac{n\cdot \epsilon -2\cdot \epsilon }{n\cdot r}=\frac{\epsilon \cdot (n-2)}{n\cdot r}$

Potential difference, $V=\epsilon -I\cdot r$

$=\epsilon -\left(\frac{\epsilon \cdot (n-2)}{n\cdot r}\right)\cdot r=\epsilon -\left(\frac{\epsilon \cdot (n-2)}{n}\right)$

$=\frac{n\cdot \epsilon -n\cdot \epsilon +2\cdot \epsilon }{n}=\frac{2\cdot \epsilon }{n}$