SATHEE: current-electricity Question 4

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Question: Q. 3. 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 figure :

(a) The equivalent emf $ε_{e q}$ of the two cells is between $ε_{1}$ and $ε_{2}$ , i.e. $ε_{1} < ε_{e q} < ε_{2}$ .

(b) The equivalent emf $ε_{e q}$ is smaller than $ε_{1}$ .

(d) $ε_{e q}$ is independent of internal resistances $r_{1}$ and $r_{2}$ .

[NCERT Exemplar]

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Solution:

Ans. Correct option : (a)

Explanation: As we know that the equivalent emf in parallel combination of cells is :

$ε_{e q} = \frac{(ε_{1} r_{2} + ε_{2} r_{1})}{(r_{1} + r_{2})}$

so, it is clear that part ’ $c$ ’ and ’ $d$ ’ are incorrect by formula. According to this formula only option (a), is correct.

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