Choose the correct statement from the following

Options

A. If n identical cells, each of emf E and internal resistance r are connected in series, the emf of combination in nE and the internal resistance of the combination is nr.
B. If n identical cells, each of emf E and internal resistance r are connected in parallel, the emf of the combination is E/n and the internal resistance of the combination is r/n
C. Cells should be connected in series, if the external resistance R is greater than internal resistance r
D. Cells should be connected in parallel if R is smaller than r

Answer

To solve the question, we need to analyze the statements provided and determine which one is correct based on the principles of electricity, particularly focusing on the behavior of cells when connected in series and parallel.

### Step-by-Step Solution:

1. **Analyze Statement 1**:
- If **n identical cells**, each with an **emf (E)** and an **internal resistance (r)**, are connected in **series**:
- The total emf of the combination will be \( nE \) (since the emfs add up).
- The total internal resistance will be \( nr \) (since the internal resistances add up).
- **Conclusion**: This statement is correct.

2. **Analyze Statement 2**:
- If **n identical cells**, each with an **emf (E)** and an **internal resistance (r)**, are connected in **parallel**:
- The total emf of the combination will remain **E** (the emf does not change in parallel).
- The total internal resistance will be \( \frac{r}{n} \) (the internal resistances combine inversely).
- The statement claims the emf is \( \frac{E}{n} \), which is incorrect. Therefore, this statement is incorrect.

3. **Analyze Statement 3**:
- It states that cells should be connected in series if the **external resistance (R)** is greater than the **internal resistance (r)**.
- For optimal performance, cells should be connected in series when the external resistance is **less than** the internal resistance, not greater. Thus, this statement is incorrect.

4. **Analyze Statement 4**:
- It states that cells should be connected in parallel if the **external resistance (R)** is smaller than the **internal resistance (r)**.
- For parallel connections, the external resistance should be **greater than** the internal resistance for effective operation. Thus, this statement is also incorrect.

### Final Conclusion:
After analyzing all four statements, we find that only **Statement 1** is correct.