Question

Two ideal batteries of same emf (E₁ = E₂) and same internal resistance (r₁ = r₂) are connected in parallel. Their equivalent emf is E and internal resistance is r. The correct option is

• A. the equivalent emf E is E = E₁ - E₂ and r = r₁ - r₂
• B. the equivalent emf E is E = E₁ + E₂ and r = r₁ + r₂
• C. the equivalent emf E is E = E₁ = E₂ but r<r₁, r'<r₂
• D. the equivalent emf E is E = E₁ but r>r₁, r'>r₂

Hint:

When connecting batteries in parallel, the emf remains the same, but the internal resistance is reduced.

Answer 1

The Correct Option is C

Step 1: Parallel Connection of Batteries.
When two ideal batteries with the same emf and internal resistance are connected in parallel, their combined emf remains the same. The internal resistances, however, combine in parallel, so the resultant internal resistance is less than each individual internal resistance.

Step 2: Analysis of options.
- ( The difference of emf is not correct for parallel batteries.
- ( The sum of emf is incorrect for parallel batteries.
- ( Correct: the combined emf remains the same, but the equivalent internal resistance is less than each individual internal resistance.
- ( Incorrect, the internal resistance will decrease in parallel, not increase.

Step 3: Conclusion.
Thus, the correct answer is ( the equivalent emf E is E₁ = E₂ but r<r₁, r'<r₂.