A battery consists of a variable number 'n' of identical cells (having internal resistance 'r' each) which are connected in series. The terminals of the battery are short-circuited and the current I is measured. Which of the graphs shows the correct relationship between I and n ?

CONCEPT:

The equivalent Emf of the given circuit with the 'n' number of the identical cell is written as;

\(\varepsilon= n\varepsilon\)

here \(\varepsilon\) is the emf of the circuit.

and The equivalent resistance of the given circuit with the 'n' number of the identical cell is written as;

R = nr

here, R is the equivalent resistance, and r is the resistance of the circuit.

CALCULATIONS:

As we know, equivalent emf and equivalent resistance are written as;

\(\varepsilon= n\varepsilon\)

and R = nr

Therefore, the current is equal to;

\(I = \frac{{n\varepsilon }}{{nr}} = \frac{\varepsilon }{r}\)

So here we can see ' I 'is independent of ' n ' and ' I ' is constant. 

Therefore, the relationship between n and 'I' with the help of a graph is shown below;

Hence, option 1) is the correct answer.