*Question E9B07:
What is the difference in radiated power between a lossless antenna with gain and an isotropic radiator driven by the same power?*  

*Correct Answer is  C: They are the same*  

### AI Response: (may contain errors)  

The correct answer to the question is that the power radiated from a lossless antenna with gain and an isotropic radiator driven by the same power is the same in terms of total radiated power.

### Explanation of the Correct Answer:
- **Isotropic Radiator**: An isotropic radiator is a theoretical point source that radiates power equally in all directions. It has a gain of 0 dBi (decibels relative to an isotropic radiator).
- **Directional Antenna with Gain**: A lossless directional antenna has gain, which means it focuses the radiated power in a specific direction. However, the total power radiated remains the same as the input power.

When both antennas are driven by the same input power, the total radiated power (in watts) is equal. The gain of the directional antenna does not increase the total power; it only redistributes it in a specific direction.

### Why the Other Choices are Incorrect:
- **Choice A**: "The power radiated from the directional antenna is increased by the gain of the antenna."
  - This is incorrect because while the gain of the antenna increases the power density in a specific direction, it does not increase the total power radiated. The total power remains the same as the input power.

- **Choice B**: "The power radiated from the directional antenna is stronger by its front-to-back ratio."
  - This is misleading. The front-to-back ratio describes how much more power is radiated in the forward direction compared to the backward direction, but it does not imply that the total power radiated is greater than that of an isotropic radiator.

- **Choice D**: "The power radiated from the isotropic radiator is 2.15 dB greater than that from the directional antenna."
  - This is incorrect because it misrepresents the relationship between the two. The isotropic radiator serves as a reference point (0 dBi), and the directional antenna's gain is relative to this. The total power remains equal, regardless of the gain.

### Useful Formulas and Rules of Thumb:
- **Total Power**: The total power radiated by both antennas is equal to the input power, regardless of gain.
- **Antenna Gain**: Gain is expressed in dBi (decibels relative to an isotropic radiator) and does not affect total power:
  $$ P_{total} = P_{input} $$

In summary, while the directional antenna may radiate more power in a specific direction due to its gain, the total power radiated remains the same as that of an isotropic radiator when both are fed the same input power.