Question 11.9: It is often necessary to convert from rms to peak value. Dev......
It is often necessary to convert from rms to peak value. Develop the formula.
Step-by-Step
Start with
RMS value = 0.707 × peak value (11-9)
Then invert:
Peak value =\frac{1}{0.707} × rms value = 1.414 × rms value
or V_{M}=1.414\ V_{rms}
I_{M}=1.414\ I_{rms}Verify this relationship by referring to Table 11-1.
| Table 11-1 Conversion Table for AC Sine Wave Voltage and Current | ||
| Multiply the Value
|
By
|
To Get the Value
|
| Peak | 2 | Peak-to-peak |
| Peak-to-peak | 0.5 | Peak |
| Peak | 0.637 | Average |
| Average | 1.570 | Peak |
| Peak | 0.707 | RMS (effective) |
| RMS (effective) | 1.414 | Peak |
| Average | 1.110 | RMS (effective) |
| RMS (effective) | 0.901 | Average |
Related Answered Questions
Question: 11.SP.7
Verified Answer:
To determine the phase angle, select a correspondi...
Question: 11.SP.8
Verified Answer:
Draw the sine waves with phase angles described. A...
Question: 11.SP.9
Verified Answer:
From Table 11-1,
V_{M} = 1.414\ V (...
Question: 11.SP.10
Verified Answer:
From Table 11-1,
I_{av} = 0.901\ I ...
Question: 11.SP.11
Verified Answer:
Use Eq. (11-9).
RMS value = 0.707 × peak value (1...
Question: 11.SP.12
Verified Answer:
Peak-to-peak amplitudes, measured between the maxi...
Question: 11.SP.13
Verified Answer:
The period T for a complete cycle is 4 μs (Fig. 11...
Question: 11.SP.14
Verified Answer:
By Ohm’s law,
I=\frac{V}{R_{L}}=\frac{120}{...
Question: 11.SP.15
Verified Answer:
For a parallel circuit, V_{T} = V_{1} = V_{...
Question: 11.SP.5
Verified Answer:
Write v=V_{M} \sin \theta ...