Five cells each of emf E and internal resistance r are connected in series . Due to oversight one cell is connected wrongly . The equivalent internal resistance of the combination is .

Options

A. 3r
B. 2r
C. 5r
D. 4r

Answer

To solve the problem of finding the equivalent internal resistance of five cells connected in series, where one cell is connected incorrectly, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Configuration**:
- We have five cells, each with an electromotive force (emf) \( E \) and internal resistance \( r \).
- Four cells are connected correctly, while one cell is connected in reverse.

2. **Identify the Resistance Contributions**:
- When cells are connected in series, the total internal resistance is the sum of the individual internal resistances.
- For the four cells connected correctly, the total internal resistance will be \( 4r \).
- The cell that is connected in reverse will still contribute its internal resistance \( r \) but will not add to the emf in the same direction.

3. **Calculate the Total Internal Resistance**:
- The total internal resistance of the four correctly connected cells is \( 4r \).
- The incorrectly connected cell also has an internal resistance \( r \) that adds to the total resistance.
- Therefore, the total equivalent internal resistance \( R_{eq} \) can be calculated as:
\[ R_{eq} = 4r + r = 5r \]

4. **Conclusion**:
- The equivalent internal resistance of the combination of the five cells, with one cell connected incorrectly, is \( 5r \).

### Final Answer:
The equivalent internal resistance of the combination is \( 5r \).