Question

n identical cells, each of emf $\epsilon$ and internal resistance $r$, are joined in series to form a closed circuit. One 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 =ε

and Internal resistance of each cell =r

One cell is joined in reverse.

∴ Total EMF =n⋅ε−2⋅ε

$i=\frac{(n-2)\epsilon }{nr}$

$V_B-V_A=-ir+\epsilon =\epsilon -\frac{(n-2)\epsilon }{nr}r=\epsilon [1-\frac{n-2}{n}]=\frac{2\epsilon }{n}$