Question

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 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

Hint:

For parallel batteries, the total emf is equal to the emf of the strongest battery, and the total internal resistance is lower than the individual resistances.

Answer 1

The Correct Option is D

The determination of why the correct choice is "Statement-I is false but Statement-II is true" necessitates an individual examination of each statement.

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

When two nonideal batteries are connected in parallel, their equivalent emf (E_eq) is determined by a weighted average based on their internal resistances, not simply a value smaller than either individual emf. The formula for the equivalent emf is:

E_eq= (E₁R₂ + E₂R₁)/(R₁+R₂)

In this equation, E₁ and E₂ represent the emfs of the batteries, and R₁ and R₂ are their internal resistances. The resulting E_eq is a weighted average that can be greater than or equal to the smaller emf and less than or equal to the larger emf. Consequently, Statement-I is classified as false.

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."

When internal resistances are combined in parallel, the equivalent resistance (R_eq) is consistently smaller than either of the individual resistances. The governing formula for the equivalent internal resistance is:

1/R_eq = 1/R₁ + 1/R₂

 

This formula demonstrates that R_eq will always be smaller than both R₁ and R₂. Therefore, Statement-II is classified as true.

Accordingly, the correct conclusion is: Statement-I is false but Statement-II is true.