the 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. (b)A is correct but B is worng
C. (c )B is correct but A is worng
D. (d)each of A and B are worng

Answer

To solve the problem regarding the non-ideal batteries connected in series, we will analyze the statements given:

1. **Understanding Equivalent EMF in Series:**
- When batteries are connected in series, the total or equivalent electromotive force (EMF) is the sum of the individual EMFs of the batteries.
- If we have two batteries with EMFs \( E_1 \) and \( E_2 \), then the equivalent EMF \( E_{eq} \) can be expressed as:
\[ E_{eq} = E_1 + E_2 \]
- Since \( E_{eq} \) is the sum of \( E_1 \) and \( E_2 \), it is clear that:
\[ E_{eq} > E_1 \quad \text{and} \quad E_{eq} > E_2 \]
- Therefore, statement (A) is **true**.

2. **Understanding Equivalent Internal Resistance in Series:**
- The internal resistances of batteries in series add up, similar to how EMFs add up.
- If the internal resistances of the two batteries are \( R_1 \) and \( R_2 \), then the equivalent internal resistance \( R_{eq} \) can be expressed as:
\[ R_{eq} = R_1 + R_2 \]
- Since \( R_{eq} \) is the sum of \( R_1 \) and \( R_2 \), it follows that:
\[ R_{eq} > R_1 \quad \text{and} \quad R_{eq} > R_2 \]
- Therefore, statement (B) is **false**.

3. **Conclusion:**
- From our analysis, we conclude that statement (A) is correct and statement (B) is incorrect.

### Final Answer:
- Statement (A) is true: The equivalent EMF is larger than either of the two EMFs.
- Statement (B) is false: The equivalent internal resistance is not smaller than either of the two internal resistances.