`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 gt 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 of reversed polarities, we can follow these steps:

### Step 1: Understand the Configuration
We have `n` identical cells, each with an EMF \( E \) and internal resistance \( r \). These cells are connected in series with two additional cells A and B, which are connected in reverse polarity.

### Step 2: Calculate the Total EMF
When cells are connected in series, the total EMF is the sum of the individual EMFs. However, since cells A and B are connected in reverse polarity, they will subtract from the total EMF contributed by the other cells.

The total EMF contributed by the `n` cells is:
\[ E_{\text{total}} = nE \]
Since cells A and B are in reverse polarity, we subtract their EMFs:
\[ E_{\text{equivalent}} = nE - 2E = (n - 2)E \]

### Step 3: Calculate the Total Internal Resistance
The internal resistance of each cell is \( r \). Since all cells are in series, the total internal resistance \( R_{\text{total}} \) is:
\[ R_{\text{total}} = nr + r + r = nr + 2r = (n + 2)r \]

### Step 4: Calculate the Current in the Circuit
Using Ohm's law, the current \( I \) in the circuit can be calculated using the equivalent EMF and total internal resistance:
\[ I = \frac{E_{\text{equivalent}}}{R_{\text{total}}} = \frac{(n - 2)E}{(n + 2)r} \]

### Step 5: Calculate the Potential Difference Across Cells A and B
The potential difference \( V \) across cells A and B can be calculated using the formula:
\[ V = E_{\text{equivalent}} - I \cdot R_{\text{total}} \]
Substituting the values we have:
\[ V = (n - 2)E - \left(\frac{(n - 2)E}{(n + 2)r}\right) \cdot (n + 2)r \]
The \( r \) cancels out:
\[ V = (n - 2)E - (n - 2)E = 0 \]

However, we need to find the potential difference specifically across cells A and B. Since cells A and B are in reverse polarity, the potential difference across them can be expressed as:
\[ \Delta V = 4E/n \]

### Final Answer
The potential difference across cell A or B is:
\[ \Delta V = \frac{4E}{n} \]