Two non ideal batteries are connected in parallel with positive terminals. 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 problem regarding the two non-ideal batteries connected in parallel, we will analyze the given statements step by step.

### Step 1: Understand the Configuration
We have two batteries connected in parallel, which means their positive terminals are connected together, and their negative terminals are also connected together. Let’s denote the following:
- \( \epsilon_1 \) = emf of battery 1
- \( \epsilon_2 \) = emf of battery 2
- \( r_1 \) = internal resistance of battery 1
- \( r_2 \) = internal resistance of battery 2

### Step 2: Equivalent EMF Calculation
For batteries in parallel, the equivalent emf (\( \epsilon_{eq} \)) can be calculated using the formula:
\[ \epsilon_{eq} = \frac{\epsilon_1/r_1 + \epsilon_2/r_2}{1/r_1 + 1/r_2} \]
This formula takes into account the internal resistances of the batteries.

### Step 3: Equivalent Internal Resistance Calculation
The equivalent internal resistance (\( r_{eq} \)) of two resistors in parallel is given by:
\[ r_{eq} = \frac{r_1 \cdot r_2}{r_1 + r_2} \]

### Step 4: Analyze Statement (A)
The first statement claims that the equivalent emf is smaller than either of the two emfs.
- Since the formula for \( \epsilon_{eq} \) involves a weighted average of the emfs divided by their respective internal resistances, it is possible for \( \epsilon_{eq} \) to be less than both \( \epsilon_1 \) and \( \epsilon_2 \), especially if one battery has a significantly higher internal resistance compared to the other. However, in general, the equivalent emf can also be greater than one of the individual emfs depending on the values of \( \epsilon_1 \), \( \epsilon_2 \), \( r_1 \), and \( r_2 \).

### Step 5: Analyze Statement (B)
The second statement claims that the equivalent internal resistance is smaller than either of the two internal resistances.
- From the formula for \( r_{eq} \), we see that when resistors are in parallel, the equivalent resistance is always less than the smallest individual resistance. Therefore, this statement is true.

### Conclusion
- Statement (A) is not necessarily true as the equivalent emf can be greater than one of the individual emfs.
- Statement (B) is true as the equivalent internal resistance is indeed smaller than either of the two internal resistances.

### Final Answer
- **Statement A**: False
- **Statement B**: True