Two nonideal batteries are wired in parallel. Evaluate the following statements: (A) The equivalent emf is smaller than either of the individual emfs. (B) The equivalent internal resistance is smaller than either of the individual internal resistances.

Step-by-step solution

For two batteries connected in parallel with emfs E₁ and E₂ and internal resistances r₁ and r₂ , the equivalent emf is given by E_ eq = E₁ r₂ + E₂ r₁ r₁ + r₂ . This expression shows that E_ eq is a weighted average of E₁ and E₂ . Thus, E_ eq always lies between E₁ and E₂ and cannot be smaller than both individual emfs. Hence, statement A is incorrect. The equivalent internal resistance is given by the parallel combination of the individual internal resistances, r_ eq = r₁ r₂ r₁ + r₂ . In a parallel combination of r