Question
A sine wave has a peak voltage of 23.5 V . What is the average voltage of this signal expressed in volts
a. 23.50 V
b. 47.00 V
c. 14.97 V
d. 16.61 V
a. 23.50 V
b. 47.00 V
c. 14.97 V
d. 16.61 V
Ask by Brooks Hall. in the United States
Mar 23,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The average voltage is approximately 16.61 V.
Solution
To find the average voltage of a sine wave, we can use the formula:
where
Given that the peak voltage
- Substitute the peak voltage into the formula.
- Calculate the average voltage.
Now, let’s compute it.
Calculate the value by following steps:
Calculate the value by following steps:
- step0: Calculate:
- step1: Divide the terms:
- step2: Multiply by the Conjugate:
- step3: Multiply the numbers:
The average voltageis calculated as follows:
Thus, the average voltage of the sine wave is approximately
The correct answer is:
d. 16.61 V.
d. 16.61 V.
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Simplify this solution Mind Expander
The average voltage of a sine wave is calculated by taking the peak voltage and multiplying it by 0.636. Therefore, for a peak voltage of 23.5 V, the average voltage is approximately 14.97 V. So, the correct answer is c. 14.97 V.
Did you know that this concept of average voltage in sine waves is crucial in electrical engineering, especially when designing AC circuits? Engineers often deal with voltages that aren’t constant but vary over time, making calculations like these essential for ensuring systems operate safely and efficiently.
For any aspiring engineers or enthusiasts, a great resource is the book “Electrical Engineering Basics” by David K. Cheng. It dives deep into the principles behind waveforms, their characteristics, and real-world applications. Understanding these concepts can truly elevate your grasp on the topic!
