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. **Understanding the Initial Configuration:**
- We have five identical cells connected in parallel.
- Let the EMF of each cell be \( E \) and the internal resistance of each cell be \( r \).

2. **Calculating the Equivalent EMF for All Cells in Parallel:**
- When all five cells are connected in parallel, the equivalent EMF (\( E_{\text{initial}} \)) is given by:
\[ E_{\text{initial}} = E \]
- This is because in parallel, the EMF remains the same as that of one cell.

3. **Reversing the Polarity of One Cell:**
- When one cell's polarity is reversed, we effectively have four cells contributing positively and one cell contributing negatively.
- The equivalent EMF (\( E_{\text{final}} \)) can be calculated as:
\[ E_{\text{final}} = E + E + E + E - E = 4E - E = 3E \]
- Since they are in parallel, we can express the equivalent EMF as:
\[ E_{\text{final}} = \frac{3E}{5} \]

4. **Calculating the Percentage Change in EMF:**
- The percentage change in equivalent EMF can be calculated using the formula:
\[ \text{Percentage Change} = \frac{E_{\text{final}} - E_{\text{initial}}}{E_{\text{initial}}} \times 100 \]
- Substituting the values:
\[ \text{Percentage Change} = \frac{\frac{3E}{5} - E}{E} \times 100 \]
- Simplifying the equation:
\[ = \frac{\frac{3E}{5} - \frac{5E}{5}}{E} \times 100 = \frac{-2E}{5E} \times 100 = -40\% \]

5. **Conclusion:**
- The percentage change in equivalent EMF when one of the cells has its polarity reversed is \(-40\%\). The negative sign indicates a decrease in EMF.