*Question G5B07:
What value of an AC signal produces the same power dissipation in a resistor as a DC voltage of the same value?*  

*Correct Answer is  C: The RMS value*  

### AI Response: (may contain errors)  

To determine which value of an AC signal produces the same power dissipation in a resistor as a DC voltage of the same value, we need to understand the concept of RMS (Root Mean Square) voltage.

1. **Correct Answer: The RMS value**

   - The RMS value of an AC signal is the effective value that represents the equivalent DC voltage in terms of power dissipation. In other words, an AC voltage with an RMS value of $V_{\text{RMS}}$ will dissipate the same amount of power in a resistor as a DC voltage of the same magnitude.
   - The formula for power dissipation in a resistor is the same for both AC and DC when using RMS values:  
     $$P = \frac{V_{\text{RMS}}^2}{R}$$  
     where $P$ is the power, $V_{\text{RMS}}$ is the RMS voltage, and $R$ is the resistance.

2. **Why the other choices are incorrect:**

   - **A: The peak-to-peak value**  
     The peak-to-peak value is the total voltage swing from the maximum positive to the maximum negative value of the waveform. It does not directly relate to power dissipation because it does not account for the time the waveform spends at each voltage level.

   - **B: The peak value**  
     The peak value is the maximum instantaneous voltage of the waveform. While it indicates the highest voltage reached, it does not represent the average power dissipation over time.

   - **D: The reciprocal of the RMS value**  
     The reciprocal of the RMS value is not a meaningful quantity in the context of power dissipation. It does not relate to how power is calculated in a resistor.

3. **Useful Formula:**

   - The RMS value for a sinusoidal AC voltage is calculated as:  
     $$V_{\text{RMS}} = \frac{V_{\text{peak}}}{\sqrt{2}}$$  
     where $V_{\text{peak}}$ is the peak voltage of the waveform.

Understanding RMS is crucial for comparing AC and DC circuits in terms of power dissipation.