Explanation:
When the modulation index of an AM wave is changed from 0 to 1, there is a significant change in the transmitted power. Let's understand this in detail.

Modulation Index:
The modulation index of an AM wave determines the extent of modulation applied to the carrier wave. It is defined as the ratio of the peak amplitude of the modulating signal to the peak amplitude of the carrier wave.

Effect of Modulation Index on Transmitted Power:
When the modulation index is changed from 0 to 1, the transmitted power increases by 50%. This can be explained by considering the power calculation of an AM wave.

Power Calculation:
The power of an AM wave can be calculated as the sum of the carrier power and the sideband powers.

- Carrier Power: The power of the carrier wave is proportional to the square of its amplitude.
- Sideband Power: The power of the sidebands is proportional to the square of their amplitudes.

Effect of Modulation on Carrier and Sidebands:
When the modulation index is 0, there is no modulation applied to the carrier wave. In this case, the carrier wave remains at its original amplitude, and there are no sidebands. Therefore, the transmitted power is solely the power of the carrier wave.

When the modulation index is 1, the modulating signal fully modulates the carrier wave. This results in the generation of two sidebands that carry the information. The amplitude of the carrier wave is varied based on the modulating signal, resulting in an increase in its peak amplitude. As a result, the power of the carrier wave increases.

Additionally, the power of the sidebands is also generated due to modulation. The sidebands have their own power, which adds to the total transmitted power.

Overall Increase in Transmitted Power:
Therefore, when the modulation index is changed from 0 to 1, the power of the carrier wave increases along with the power of the sidebands. This overall increase in power results in a 50% increase in the transmitted power.

Conclusion:
In summary, when the modulation index of an AM wave is changed from 0 to 1, the transmitted power increases by 50%. This is because the modulation fully modulates the carrier wave, increasing its power, and also generates sidebands that contribute to the total power.