Ncert Exercises & Solutions

Two batteries of emf $ε_{1} and ε_{2} (ε_{2} > ε_{1})$ and internal resistances $r_{1} and r_{2}$ respectively are connected in parallel as shown in the figure.

1.	The equivalent emf $ε_{eq}$ of the two cells is between $ε_{1} and ε_{2} . i.e, ε_{1} < ε_{e q} < ε_{2}$
2.	The equivalent emf $ε_{eq}$ is smaller than $ε_{1}$
3.	The $ε_{eq}$ is given by $ε_{e q} = ε_{1} + ε_{2}$ always
4.	$ε_{eq}$ is independent of internal resistances $r_{1} and r_{2}$

(a) Hint: Use the concept of the parallel combination of cells.

Step 1:

The equivalent emf of this combination is given by:

$ε_{eq} = \frac{ε_{2} r_{1} + ε_{2} r_{2}}{r_{1} + r_{2}}$

Step 2:

This suggests that the equivalent emf $ε_{eq}$ of the two cells is:

$ε_{1} < ε_{eq} < ε_{2}$

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