Question

The plot of the variation of potential difference across a combination of three identical cells in series, versus current is shown below. What is the emf and internal resistance of each cell ?

Answer 1

Let E and r be the EMF and internal resistance of all cells respectively and e and r' be the EMF and internal resistance of each cell respectively.

As we know,

According to the definition of the terminal potential difference,

V = E − Ir 

E is the EMF and r is the total internal resistance of the circuit.

I = 0 ⇒ V = E

From the  graph  we can see

E = 6 V

As there are three cells we can write,

E = 3 × e ⇒ e = 2 V

And, when, V = 0

⇒ E = Ir

`r=E/T=6/1=6Omega`

As per the question the cells are connected in the series, so we can write.

`r'=r/3=2Omega`

Answer 2

Since there are three cells connected in series, Total EMF = E1 + E2 + E3
​We can observe from the graph that,
E1 + E2 + E3 = 6

3E = 6          (E = E1 = E2 = E3, as they are identical cells)
hence, The EMF of each cell is 2Volt.

Now, similarly, the internal resistance is also 2 Ohm for each, because in series combination of cells not only the Emf the internal resistance also gets added up.