Five identical cells are connected in parallel. Now, polarity of one of the cells is reversed. Percentage change in equivalent emf will be

Options

A. -0.1
B. -0.2
C. -0.4
D. -0.6

Answer

To solve the problem of finding the percentage change in equivalent EMF when one of the five identical cells connected in parallel has its polarity reversed, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Configuration**:
- We have 5 identical cells connected in parallel. Let the EMF of each cell be \( E \) and the internal resistance of each cell be \( R \).

2. **Calculate Initial Equivalent EMF**:
- When all cells are connected in parallel, the equivalent EMF (\( E_{eq} \)) is simply the EMF of one cell, since they are identical and in parallel:
\[ E_{eq\_initial} = E \]

3. **Effect of Reversing One Cell**:
- When the polarity of one cell is reversed, its EMF becomes \(-E\). Thus, we now have:
- Four cells with EMF \( E \)
- One cell with EMF \(-E\)

4. **Calculate New Equivalent EMF**:
- The equivalent EMF can be calculated using the formula:
\[ E_{eq\_new} = \frac{E}{R} + \frac{E}{R} + \frac{E}{R} + \frac{E}{R} - \frac{E}{R} \]
- This simplifies to:
\[ E_{eq\_new} = \frac{4E - E}{R} = \frac{3E}{R} \]
- The total resistance in the parallel circuit remains:
\[ R_{eq} = \frac{R}{5} \quad \text{(since there are 5 identical resistances in parallel)} \]

5. **Final Equivalent EMF**:
- Therefore, the new equivalent EMF is:
\[ E_{eq\_new} = \frac{3E}{5} \]

6. **Calculate Percentage Change in EMF**:
- The change in EMF (\( \Delta E \)) is given by:
\[ \Delta E = E_{eq\_new} - E_{eq\_initial} = \frac{3E}{5} - E = \frac{3E - 5E}{5} = -\frac{2E}{5} \]
- To find the percentage change:
\[ \text{Percentage Change} = \left( \frac{\Delta E}{E_{eq\_initial}} \right) \times 100 = \left( \frac{-\frac{2E}{5}}{E} \right) \times 100 = -40\% \]

### Conclusion:
The percentage change in equivalent EMF when one cell's polarity is reversed is \(-40\%\), indicating a decrease in EMF.