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Question
Two non-ideal batteries are connected in parallel. Consider the following statements:-
(A) The equivalent emf is smaller than either of the two emfs.
(B) The equivalent internal resistance is smaller than either of the two internal resistances.
Options
A and B are correct
A is correct but B is wrong
B is correct but A is wrong
A and B are wrong
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Solution
B is correct but A is wrong
The equivalent emf \[\epsilon_0,\] when two non-ideal batteries of emfs \[\epsilon_1\] and \[\epsilon_2\] and internal resistances r1 and r2 respectively are connected in parallel to each other, is given by:-
\[\epsilon_0 = \frac{\epsilon_1 r_1 + \epsilon_2 r_2}{r_1 + r_2}\]
Thus, the equivalent emf is greater than either of the emfs. Thus, statement A is wrong.
For the parallel combination of the batteries of internal resistance r1 and r2, the equivalent internal resistance r is given as
\[r = \frac{r_1 r_2}{r_1 + r_2}\]
Thus, the value of the resultant resistance is even smaller than either resistance.
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