JEE Main · 2025 · 22 Jan 2025 · Shift 1 · Current Electricity

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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✓ Correct

Answer: (D)

Solution

For two non-ideal cells (emf

ε_{1}, ε_{2}

; internal resistances

r_{1}, r_{2}

) connected in parallel, the equivalent emf is the current-weighted average

ε_{e q} = \frac{\frac{ε _{1}}{r _{1}} + \frac{ε _{2}}{r _{2}}}{\frac{1}{r _{1}} + \frac{1}{r _{2}}},

which is a weighted mean of

ε_{1}

and

ε_{2}

and so lies between them — it is not always smaller than both emfs. Statement-I is false.

The equivalent internal resistance is

r_{e q} = \frac{r _{1} r _{2}}{r _{1} + r _{2}},

which, for any positive

r_{1}, r_{2}

, is always smaller than the smaller of the two individual resistances — the general property of resistors combined in parallel. Statement-II is true.

Statement-I is false, Statement-II is true.

JEE Main · 2025 · 22 Jan 2025 · Shift 1 · Single correct option

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JEE Main · 2025 · 22 Jan 2025 · Shift 1 · Current Electricity

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