To determine the RMS (Root Mean Square) voltage value of the DC output for a half-wave rectifier given an AC input, we need to understand the relationship between the RMS values of AC and DC in this context.
1. Given:
- The RMS value of the AC voltage input ([tex]\( V_{rms, AC} \)[/tex]) is 10 volts.
2. Formula for RMS value of DC output for a half-wave rectifier:
- The RMS value of the DC output ([tex]\( V_{rms, DC} \)[/tex]) for a half-wave rectifier can be calculated using the formula:
[tex]\[
V_{rms, DC} = \frac{V_{rms, AC}}{2}
\][/tex]
- This formula arises because a half-wave rectifier only lets through one-half of the AC cycle, thus its effective (RMS) output is half of the input's RMS value.
3. Calculation:
- Substitute the given RMS AC voltage into the formula:
[tex]\[
V_{rms, DC} = \frac{10 \text{ V}}{2}
\][/tex]
- Simplifying this gives:
[tex]\[
V_{rms, DC} = 5 \text{ V}
\][/tex]
Hence, the RMS voltage value of the DC output for a half-wave rectifier, when the input RMS AC voltage is 10 volts, is 5 volts.
Answer: None of the given options (A, B, C, D) are correct, as the correct value is 5 volts.
