6. A sine wave has a peak value of 12 V. Determine the follow- ing values: a. rms b. peak-to-peak c. average
6. A sine wave has a peak value of 12 V. Determine the follow- ing values: a. rms b. peak-to-peak c. average
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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![**Problem 6:** A sine wave has a peak value of 12 V. Determine the following values:
a. RMS (Root Mean Square)
b. Peak-to-Peak
c. Average
*Solution Explanation:*
- **RMS (Root Mean Square):** The RMS value for a sine wave is calculated using the formula:
\[
\text{RMS} = \frac{\text{Peak Value}}{\sqrt{2}}
\]
Substitute the peak value of 12 V:
\[
\text{RMS} = \frac{12}{\sqrt{2}} \approx 8.49 \, \text{V}
\]
- **Peak-to-Peak:** The peak-to-peak value is simply twice the peak value.
\[
\text{Peak-to-Peak} = 2 \times 12 = 24 \, \text{V}
\]
- **Average Value:** For a complete cycle of a pure sine wave, the average value is zero. However, if considering only the positive half-cycle, the average value can be calculated by:
\[
\text{Average (half-wave)} = \frac{2 \times \text{Peak Value}}{\pi}
\]
Substitute the peak value of 12 V:
\[
\text{Average (half-wave)} \approx \frac{24}{\pi} \approx 7.64 \, \text{V}
\]
These values are useful in analyzing AC signals in electrical engineering.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fff3b2cf5-bb58-4668-82ab-a74bef1e0bab%2Fbc6e3c43-4203-418c-a39e-bd96cd99fed2%2Fi49awl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 6:** A sine wave has a peak value of 12 V. Determine the following values:
a. RMS (Root Mean Square)
b. Peak-to-Peak
c. Average
*Solution Explanation:*
- **RMS (Root Mean Square):** The RMS value for a sine wave is calculated using the formula:
\[
\text{RMS} = \frac{\text{Peak Value}}{\sqrt{2}}
\]
Substitute the peak value of 12 V:
\[
\text{RMS} = \frac{12}{\sqrt{2}} \approx 8.49 \, \text{V}
\]
- **Peak-to-Peak:** The peak-to-peak value is simply twice the peak value.
\[
\text{Peak-to-Peak} = 2 \times 12 = 24 \, \text{V}
\]
- **Average Value:** For a complete cycle of a pure sine wave, the average value is zero. However, if considering only the positive half-cycle, the average value can be calculated by:
\[
\text{Average (half-wave)} = \frac{2 \times \text{Peak Value}}{\pi}
\]
Substitute the peak value of 12 V:
\[
\text{Average (half-wave)} \approx \frac{24}{\pi} \approx 7.64 \, \text{V}
\]
These values are useful in analyzing AC signals in electrical engineering.
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