JEE Main 2025 Jan 22 Shift 1, Physics Q17: Introduction And Ohm’s Law

JEE Main2025Jan 22, Shift 1Physics

Given below are two statements :

Statement-I : The equivalent emf of two nonideal batteries connected in parallel is smaller than either of the two emfs.

Statement-II : The equivalent internal resistance of two nonideal batteries connected in parallel is smaller than the internal resistance of either of the two batteries.

In the light of the above statements, choose the correct answer from the options given below.

A
Statement-I is true but Statement-II is false
B
Both Statement-I and Statement-II are false
C
Both Statement-I and Statement-II are true
D
Statement-I is false but Statement-II is true

Solution

For two batteries (emfs $ε_{1}, ε_{2}$ and internal resistances $r_{1}, r_{2}$ ) in parallel:

$ε_{e q} = \frac{ε _{1} / r _{1} + ε _{2} / r _{2}}{1/ r _{1} + 1/ r _{2}}$ , $r_{e q} = \frac{r _{1} r _{2}}{r _{1} + r _{2}}$ .

$ε_{e q}$ is a weighted average of $ε_{1}$ and $ε_{2}$ , so it lies between them, not smaller than both. Statement-I is false.

$r_{e q}$ is the standard parallel-resistor formula, which is always less than either $r_{1}$ or $r_{2}$ . Statement-II is true.

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JEE Main 2025 Jan 22 Shift 1, Physics Q17: Introduction And Ohm’s Law

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