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

Options

A. (a)Both A and B are correct
B. (b)A is correct but B is worng
C. (c )B is correct but A is worng
D. (d)Both A and B are worng

Answer

To solve the question regarding the two non-ideal batteries connected in parallel and evaluate the statements about their equivalent EMF and internal resistance, we will follow these steps:

### Step-by-Step Solution:

1. **Understanding the Configuration**:
- We have two non-ideal batteries connected in parallel. Let’s denote their EMFs as \( E_1 \) and \( E_2 \), and their internal resistances as \( r_1 \) and \( r_2 \).

2. **Calculating the Equivalent EMF**:
- For batteries in parallel, the formula for the equivalent EMF (\( E_{eq} \)) is given by:
\[ E_{eq} = \frac{E_1 r_1 + E_2 r_2}{r_1 + r_2} \]
- This equation shows that the equivalent EMF is a weighted average of the individual EMFs, influenced by their internal resistances.

3. **Analyzing Statement A**:
- We need to determine if \( E_{eq} < E_1 \) and \( E_{eq} < E_2 \).
- From the formula, since both \( E_1 \) and \( E_2 \) are in the numerator and \( r_1 \) and \( r_2 \) are positive values, it can be concluded that:
\[ E_{eq} > E_1 \quad \text{and} \quad E_{eq} > E_2 \]
- Therefore, **Statement A** is **incorrect**.

4. **Calculating the Equivalent Internal Resistance**:
- For internal resistances in parallel, the equivalent internal resistance (\( r_{eq} \)) is calculated using:
\[ \frac{1}{r_{eq}} = \frac{1}{r_1} + \frac{1}{r_2} \]
- This implies:
\[ r_{eq} < r_1 \quad \text{and} \quad r_{eq} < r_2 \]
- Hence, **Statement B** is **correct**.

5. **Conclusion**:
- Based on the analysis:
- Statement A is incorrect.
- Statement B is correct.
- Therefore, the correct answer is that **A is incorrect, B is correct**.

### Final Answer:
The answer to the question is: **A is incorrect, B is correct**.