Six cell each of emf `E` and internal resistance `r` are connected in series. If due to over sight, two cells are connected wrongly, then the equivalent emf and internal resistance of the combination is

Options

A. `6 E,6 r`
B. `4 E,6 r`
C. `2 E,6 r`
D. `2 E,4 r`

Explanation

To solve the problem of finding the equivalent EMF and internal resistance of six cells connected in series, where two cells are connected incorrectly, we can follow these steps:

### Step 1: Understand the Configuration
We have 6 cells, each with an EMF of \( E \) and an internal resistance of \( r \). When connected in series, the total EMF and total internal resistance can be calculated.

### Step 2: Calculate Total EMF and Resistance for Correctly Connected Cells
If all cells were connected correctly, the total EMF (\( E_{total} \)) and total internal resistance (\( R_{total} \)) would be:
- Total EMF:
\[ E_{total} = 6E \]
- Total Internal Resistance:
\[ R_{total} = 6r \]

### Step 3: Analyze the Incorrect Connections
When two cells are connected incorrectly (i.e., their polarities are reversed), we need to consider the effect of this reversal. Let's assume the first two cells are connected incorrectly.

- The two incorrectly connected cells will effectively subtract their EMF from the total. Therefore, the contribution of these two cells to the total EMF will be:
\[ E_{wrong} = -E - E = -2E \]

### Step 4: Calculate the New Total EMF
Now, we can find the new total EMF by adding the contributions of all cells:
\[ E_{new} = (4E) + (-2E) = 2E \]

### Step 5: Calculate the Total Internal Resistance
The internal resistance remains the same because all cells are still in series. Therefore, the total internal resistance is:
\[ R_{new} = 6r \]

### Final Result
The equivalent EMF and internal resistance of the combination is:
- Equivalent EMF: \( 2E \)
- Equivalent Internal Resistance: \( 6r \)

### Summary
Thus, the final answer is:
- Equivalent EMF = \( 2E \)
- Equivalent Internal Resistance = \( 6r \)

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