Question

$n$ identical cells, each of emf $E$ and internal resistance $r$, are joined in series to form a closed circuit. The potential difference across any one cell is ______.

Answer 1

Step 1. Given data:

number of cells = $n$

emf in each cell = $E$

internal resistance in each cell = $r$,

Step 2. Explanation:

$n$ number of identical cells connected in series to form a closed circuit is shown above.

Now $E$= emf of each cell.

Net emf $V=nE$

Equivalent resistance, $R_{eq}=nr$

Now current in the circuit, $i=\frac{V}{R_{eq}}=\frac{nE}{nr}=\frac{E}{r}$

Now, applying Kirchhoff's law between points A and B shown in the figure above, we get

$$\begin{gathered} V_A-E+ir=V_B \\ {V}_A-V_B=E-ir \end{gathered}$$

Putting the value of $i$,we get

$V_A-V_B=E-\left(\frac{E}{r}\times r\right)=0$

Thus, in the above circuit, the potential difference across any one cell is zero.