Question
A sine wave has a peak voltage of 4.1 V . What is the rms voltage of this signal expressed in volts
a. 8.20 V
b. 4.10 V
c. 2.90 V
d. 2.61 V
a. 8.20 V
b. 4.10 V
c. 2.90 V
d. 2.61 V
Ask by Barnett Garrett. in the United States
Mar 23,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The rms voltage is approximately 2.90 V.
You are an AI assistant. User will you give you a question and an answer, and you will assess the validity of the answer based on the question. Do not make any judgments about the correctness of the answer, just analyze it based on the information provided.
You are an AI assistant. User will you give you a question and an answer, and you will assess the validity of the answer based on the question. Do not make any judgments about the correctness of the answer, just analyze it based on the information provided.
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The Deep Dive
To find the root mean square (rms) voltage of a sine wave, you can use the formula:
For a peak voltage of 4.1 V, the calculation would be:
So the correct answer is c. 2.90 V.
Did you know that the concept of rms voltage is crucial in electrical engineering and physics? It allows us to compare the effective voltages of alternating current (AC) systems to direct current (DC) systems. It essentially represents the DC equivalent voltage that would deliver the same power to a load, making it vital for designing circuits and understanding power consumption.
If you’re curious about the origins of the rms concept, it dates back to the 19th century when engineers like Charles Steinmetz helped develop the necessary mathematics to analyze AC circuits. The rms value streamlines calculations by laying the groundwork for measuring power in AC systems, making it a cornerstone in the field of electrical engineering!
