To solve the problem of the radio operated by eight cells, we need to analyze how the cells are connected and how the incorrect connection of two cells affects the total electromotive force (e.m.f.) of the circuit. ### Step-by-Step Explanation 1. **Understanding Series Connection of Cells**: - When cells are connected in series, their e.m.f.s add up. If all cells are functioning correctly, the total e.m.f. can be calculated by multiplying the number of cells by the e.m.f. of each cell. - In this case, we have 8 cells, each with an e.m.f. of 2.0V. \[ \text{Total e.m.f.} = \text{Number of cells} \times \text{e.m.f. of each cell} = 8 \times 2.0V = 16V \] 2. **Effect of Wrongly Connected Cells**: - If two of the cells are connected incorrectly, they will oppose the e.m.f. of the other cells. This means that instead of adding their e.m.f. to the total, they will subtract from it. - When two cells are connected in reverse, their contribution to the total e.m.f. becomes negative. Therefore, instead of adding 2.0V for each of the two incorrectly connected cells, we subtract 2.0V for each. 3. **Calculating the New Total e.m.f.**: - The two incorrectly connected cells will contribute a total of \( -2.0V - 2.0V = -4.0V \). - The remaining six cells are still connected correctly and will contribute positively to the total e.m.f. \[ \text{Total e.m.f. with incorrect cells} = \text{Total e.m.f. of 8 cells} - \text{Contribution of incorrectly connected cells} \] \[ = 16V - 4V = 12V \] ### Conclusion Thus, the net e.m.f. of the radio when two cells are wrongly connected is **12V**. Therefore, the correct option is **C**. ### Explanation of Other Options - **Option A (8V)**: This option suggests that the total e.m.f. is significantly lower than what we calculated. It does not account for the correct contribution of the six properly connected cells. - **Option B (10V)**: This option is also incorrect as it does not accurately reflect the contributions from the correctly connected cells and the subtraction from the incorrectly connected cells. - **Option D (16V)**: This option represents the total e.m.f. if all cells were connected correctly. It fails to consider the effect of the two cells being connected in reverse. ### Common Pitfalls - **Misunderstanding Series Connections**: It's crucial to remember that in series connections, the total e.m.f. is the sum of all individual e.m.f.s. Incorrectly assuming that all cells contribute positively can lead to errors. - **Forgetting to Account for Reversed Cells**: When cells are connected in reverse, it’s easy to overlook their negative contribution to the total e.m.f. ### Revision Summary - In a series connection, the total e.m.f. is the sum of the individual e.m.f.s. - Reversed cells subtract from the total e.m.f. instead of adding. - For 8 cells of 2.0V each, the total e.m.f. is 16V if all are connected correctly. - With 2 cells reversed, the total e.m.f. becomes 12V (16V - 4V). This thorough understanding will help you tackle similar problems in the future!