the two nonideal batteries are connected in series. Consider the following statements :
(A)The equivalent emf is larger than either of the two emfs.
(B) the equivalent internal resistances is smaller than either of the two internal resistances.

Options

A. Each of A and B is correct
B. A is correct but B is wrong
C. B is correct but A is wrong
D. Each of A and B is wrong

Answer

To solve the question regarding the two non-ideal batteries connected in series, we will analyze the statements provided step by step.

### Step 1: Understand the Concept of EMF in Series
When two batteries are connected in series, the total or equivalent EMF (E_net) of the system is the sum of the individual EMFs of the batteries.

**Mathematical Representation:**
\[ E_{\text{net}} = E_1 + E_2 \]

### Step 2: Analyze Statement A
Statement A claims that the equivalent EMF is larger than either of the two EMFs. Since both E1 and E2 are positive values, the equivalent EMF will indeed be greater than either of the individual EMFs.

**Conclusion for Statement A:**
\[ E_{\text{net}} > E_1 \quad \text{and} \quad E_{\text{net}} > E_2 \]
Thus, Statement A is **correct**.

### Step 3: Understand the Concept of Internal Resistance in Series
When batteries are connected in series, the total internal resistance (R_net) of the system is the sum of the individual internal resistances of the batteries.

**Mathematical Representation:**
\[ R_{\text{net}} = R_1 + R_2 \]

### Step 4: Analyze Statement B
Statement B claims that the equivalent internal resistance is smaller than either of the two internal resistances. Since R_net is the sum of R1 and R2, it is clear that R_net will be greater than either R1 or R2.

**Conclusion for Statement B:**
\[ R_{\text{net}} > R_1 \quad \text{and} \quad R_{\text{net}} > R_2 \]
Thus, Statement B is **incorrect**.

### Final Conclusion
Based on the analysis:
- Statement A is correct.
- Statement B is incorrect.

Therefore, the correct option is that A is correct but B is wrong.