*Question T0C03:
How does the allowable power density for RF safety change if duty cycle changes from 100 percent to 50 percent?*  

*Correct Answer is  C: It increases by a factor of 2*  

### AI Response: (may contain errors)  

To understand how the allowable power density for RF safety changes with duty cycle, we need to consider the relationship between duty cycle and average power.

1. **Correct Answer Explanation (C: It increases by a factor of 2)**:
   - The duty cycle is the fraction of time that a signal is "on" compared to the total time. A 100% duty cycle means the signal is always on, while a 50% duty cycle means the signal is on half the time.
   - The allowable power density is based on the average power over time. When the duty cycle is reduced, the average power decreases, allowing for a higher instantaneous power level without exceeding safety limits.
   - Specifically, if you reduce the duty cycle from 100% to 50%, the average power is halved, which allows the peak power to be increased by a factor of 2 while still maintaining the same average power density. Thus, the allowable power density increases by a factor of 2.

2. **Incorrect Choices Explanation**:
   - **A: It increases by a factor of 3**: This is incorrect because the relationship between duty cycle and power density does not support a factor of 3 increase. The factor is specifically 2 when going from 100% to 50%.
   - **B: It decreases by 50 percent**: This is incorrect because the average power density does decrease with a lower duty cycle, but the question asks about allowable power density, which actually increases due to the reduced average power.
   - **D: There is no adjustment allowed for lower duty cycle**: This is incorrect because regulations do allow for adjustments in allowable power density based on duty cycle changes, specifically allowing for higher peak power levels at lower duty cycles.

3. **Useful Formulas/Rules of Thumb**:
   - The average power ($P_{avg}$) can be calculated as:
     $$P_{avg} = P_{peak} \times \text{Duty Cycle}$$
   - For a 100% duty cycle, $P_{avg} = P_{peak}$. For a 50% duty cycle, $P_{avg} = \frac{1}{2} P_{peak}$.
   - This relationship shows that as the duty cycle decreases, the average power decreases, allowing for a higher peak power while still adhering to safety limits.

In summary, when the duty cycle is reduced from 100% to 50%, the allowable power density increases by a factor of 2, making option C the correct answer.