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Physics · Current Electricity

JEE Main 2025 — 22 January, Morning Shift — Question 58

Given below are two statements : one is labelled as Statement I and the other is labelled as Statement II :

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.

  1. Option A:

    Statement-I is true but Statement-II is false

  2. Option B:

    Both Statement-I and Statement-II are false

  3. Option C:

    Both Statement-I and Statement-II are true

  4. Option D:

    Statement-I is false but Statement-II is true

    Correct

Answer: D

Step-by-step solution

Let the common open-circuit voltage be VV. With no external load,

E1−Vr1+E2−Vr2=0\frac{E_1 - V}{r_1} + \frac{E_2 - V}{r_2} = 0 ⇒Eeq=V=E1/r1+E2/r21/r1+1/r2=E1r2+E2r1r1+r2.\Rightarrow\quad E_{\mathrm{eq}} = V = \frac{E_1/r_1 + E_2/r_2}{1/r_1 + 1/r_2} = \frac{E_1 r_2 + E_2 r_1}{r_1 + r_2}.

The equivalent internal resistance is

req=r1r2r1+r2.r_{\mathrm{eq}} = \frac{r_1 r_2}{r_1 + r_2}.
  1. EeqE_{\mathrm{eq}} lies between E1E_1 and E2E_2 → Statement I false.
  2. req=r1r2r1+r2<min⁡(r1,r2)r_{\mathrm{eq}} = \dfrac{r_1 r_2}{r_1 + r_2} < \min(r_1, r_2) → Statement II true.

Statement I false, Statement II true → Correct choice D

Answer key and solution verified before publishing.

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Exam
JEE Main 2025
Paper
22 January, Morning Shift
Subject
Physics
Chapter
Current Electricity
Topic
Combination of Resistors and cells, Wheatstone Bridge