`n` identical cells are joined in series with two cells A and B with reversed polarities. EMF of each cell is E and internal resistance is r. Potential difference across cell A or B is (n > 4)

Options

A. `(2E)/(n)`
B. `2E(1-(1)/(n))`
C. `(4E)/(n)`
D. `2E(1-(2)/(n))`

Answer

To solve the problem of finding the potential difference across cell A or B when `n` identical cells are joined in series with two cells A and B with reversed polarities, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Configuration**:
- We have `n` identical cells in series, each with an EMF of `E` and an internal resistance of `r`.
- There are two additional cells A and B connected in reverse polarity.

2. **Calculate the Total EMF**:
- The total EMF contributed by the `n` cells is `nE`.
- The two cells A and B in reverse polarity will neutralize 2E from the total EMF.
- Therefore, the effective EMF in the circuit is given by:
\[ E_{\text{total}} = nE - 2E = (n - 2)E \]

3. **Calculate the Total Internal Resistance**:
- The total internal resistance from the `n` cells is `nr`.
- The internal resistances of cells A and B are not specified, so we assume they are negligible or included in the total resistance.

4. **Find the Current (I)**:
- Using Ohm's law, the current `I` flowing through the circuit can be calculated as:
\[ I = \frac{E_{\text{total}}}{R_{\text{total}}} = \frac{(n - 2)E}{nr} \]

5. **Calculate the Potential Difference Across Cell A**:
- The potential difference across cell A can be calculated using the formula:
\[ \Delta V_A = E + I \cdot r \]
- Substituting the value of `I` into the equation:
\[ \Delta V_A = E + \left(\frac{(n - 2)E}{nr}\right) \cdot r \]
- Simplifying this gives:
\[ \Delta V_A = E + \frac{(n - 2)E}{n} = E + \frac{(n - 2)E}{n} \]

6. **Combine the Terms**:
- Combine the terms to find a common expression:
\[ \Delta V_A = \frac{nE}{n} + \frac{(n - 2)E}{n} = \frac{nE + (n - 2)E}{n} = \frac{(2n - 2)E}{n} \]

7. **Final Expression**:
- Factor out the common terms:
\[ \Delta V_A = \frac{2E(n - 1)}{n} \]

### Final Answer:
The potential difference across cell A (or B) is:
\[ \Delta V_A = \frac{2E(n - 1)}{n} \]