*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 understand why the RMS (Root Mean Square) value of an AC signal produces the same power dissipation in a resistor as a DC voltage of the same value, we need to look at how power is calculated in resistive circuits.

### Correct Answer: C - The RMS value

- The power dissipated in a resistor is given by the formula:
  
  $$P = \frac{V^2}{R}$$

  where:
  - $P$ = power in watts
  - $V$ = voltage across the resistor
  - $R$ = resistance in ohms

- For a DC voltage, the voltage $V$ is constant. For an AC voltage, we use the RMS value because it represents the equivalent DC value that would produce the same power dissipation in the resistor.

- The RMS value of an AC voltage is calculated as:

  $$V_{RMS} = \frac{V_{peak}}{\sqrt{2}}$$

  This means that the RMS value is always less than the peak value for a sinusoidal waveform.

### Why the Other Choices are Incorrect:

- **A: The peak-to-peak value**
  - The peak-to-peak value measures the total voltage swing from the maximum positive to the maximum negative value. It does not represent the effective voltage that produces power in a resistor.

- **B: The peak value**
  - The peak value is the maximum voltage of the AC signal. While it is higher than the RMS value, it does not account for the average power dissipation in a resistor. The peak value would result in a higher power calculation than what would be dissipated by a DC voltage of the same value.

- **D: The reciprocal of the RMS value**
  - The reciprocal of the RMS value does not have a direct physical meaning in terms of power dissipation. It does not represent a voltage value that can be used to calculate power in a resistor.

### Summary

- The RMS value is the correct choice because it accurately reflects the effective voltage of an AC signal that results in the same power dissipation as a DC voltage of the same magnitude. 

- Remember, for AC signals, always use the RMS value when calculating power in resistive circuits!