Five cells each of e.m.f E and internal resistance r are connected in series. If due to over sight, one cell is connected wrongly ,the equivalent e.m.f of the combination is

Options

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

Answer

To find the equivalent e.m.f. of a series connection of five cells, where one cell is connected in the wrong direction, we can follow these steps:

### Step-by-Step Solution

1. **Understanding the Configuration**:
- We have 5 cells connected in series, each with an e.m.f. of \( E \) and an internal resistance \( r \).
- Normally, if all cells are connected correctly, the total e.m.f. would be \( 5E \).

2. **Identifying the Wrongly Connected Cell**:
- When one cell is connected in the reverse direction, it effectively subtracts its e.m.f. from the total.
- Let's denote the cells as \( C_1, C_2, C_3, C_4, C_5 \). Assume \( C_3 \) is the cell connected in reverse.

3. **Calculating the Total e.m.f.**:
- The total e.m.f. can be calculated as:
\[ \text{Total e.m.f.} = E + E + (-E) + E + E = 4E \]
- Here, the negative sign indicates that the e.m.f. of the wrongly connected cell \( C_3 \) is subtracted.

4. **Conclusion**:
- Therefore, the equivalent e.m.f. of the combination when one cell is connected wrongly is \( 4E \).

### Final Answer:
The equivalent e.m.f. of the combination is \( 4E \).

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