`32` cells each of emf `3V` are connected in series and kept in a not External the combination shown as emf `84 V` How many number of cells are connected reversely?

Explanation

To solve the problem of how many cells are connected reversely in a series of 32 cells, each with an EMF of 3V, we can follow these steps:

### Step 1: Calculate the total EMF if all cells are connected in the same polarity.
If all 32 cells are connected in the same polarity, the total EMF (E_total) can be calculated as:
\[ E_{\text{total}} = N \times E \]
Where:
- \(N = 32\) (total number of cells)
- \(E = 3V\) (EMF of each cell)

Substituting the values:
\[ E_{\text{total}} = 32 \times 3 = 96V \]

### Step 2: Identify the actual total EMF given in the problem.
The problem states that the combination has an actual EMF of 84V.

### Step 3: Determine the difference in EMF.
Now, we find the difference between the total EMF if all cells were connected in the same polarity and the actual EMF:
\[ \text{Difference} = E_{\text{total}} - E_{\text{actual}} = 96V - 84V = 12V \]

### Step 4: Relate the difference in EMF to the number of cells connected in reverse polarity.
When cells are connected in reverse polarity, their EMF effectively reduces the total EMF. Each cell connected in reverse polarity reduces the total EMF by twice its EMF (since it opposes the EMF of the other cells).

Let \(M\) be the number of cells connected in reverse polarity. The reduction in EMF due to these cells can be expressed as:
\[ \text{Reduction} = 2M \times E \]
Where \(E = 3V\).

Setting this equal to the difference we calculated:
\[ 2M \times 3 = 12 \]

### Step 5: Solve for \(M\).
Now, we can solve for \(M\):
\[ 6M = 12 \implies M = \frac{12}{6} = 2 \]

### Conclusion
Thus, the number of cells connected reversely is \(M = 2\).

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