Area under v vs t sinusoidal trace

In summary, the conversation discusses the relationship between the area under a squared waveform on an oscilloscope and the voltage root mean square (Vrms) value. It is explained that since the speaker does not have the ability to integrate, they are trying to determine if the area under the graph is proportional to Vrms^2. They also mention that Vrms is equal to 0.707 of the peak value in a sinusoidal wave and that AC power is equivalent to DC power. The conversation concludes with a question about the relationship between the area under the graph and Vrms^2.
  • #1
lavster
217
0
if I have a sinusoidal trace on an oscilloscope (v vs t) and I wanted to find the area under the wave form squared graph I could integrate the sqaured waveform with respect to t.

but since i don't have the integration facility... is it fair to say that the area under the graph is proprtional to vrms^2 ?

im confused to what vrms is? the average v^2 value (i know its Vpeak/2)

thanks
 
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  • #2
wiki has a pretty good article on rms

basically its 0.707 of the peak value
and from what I remember the rms power of an AC circuit ( average power) is the equivalent to the DC power
( did that make sense ?) :smile:

Dave
 
Last edited:
  • #3
lavster said:
im confused to what vrms is? the average v^2 value (i know its Vpeak/2)
thanks

An AC voltage of 10 volts rms ( no matter whether it is sinusoidal or not ) means that this AC voltage will heat up a resistor as a DC voltage of 10 volts.

Remember that the power transformed into heat is V^2 / R.

basically its 0.707 of the peak value
in a sinusoidal wave.

.. is it fair to say that the area under the graph is proprtional to vrms^2 ?
No, it is proportional to Vrms an also proportional to Vpeak ( because it is a sinuoidal wave ).
 

Related to Area under v vs t sinusoidal trace

1. What is the purpose of calculating the area under a v vs t sinusoidal trace?

The area under a v vs t sinusoidal trace is a measure of the total displacement of an object over a given time period. It can be used to determine the total distance traveled by an object or the amount of work done on the object.

2. How is the area under a v vs t sinusoidal trace calculated?

The area under a v vs t sinusoidal trace can be calculated by breaking the curve into smaller trapezoids, finding the area of each trapezoid, and then summing the areas of all the trapezoids. This method is known as the trapezoidal rule.

3. Can the area under a v vs t sinusoidal trace be negative?

Yes, the area under a v vs t sinusoidal trace can be negative. This can occur when the displacement of an object is in the opposite direction of its initial position. In this case, the area under the curve will be below the x-axis, resulting in a negative value.

4. How does the frequency of a sinusoidal trace affect the area under the curve?

The frequency of a sinusoidal trace does not directly affect the area under the curve. However, it can affect the shape and size of the curve, which in turn can impact the area calculation. A higher frequency may result in a curve with more peaks and valleys, leading to a larger area under the curve.

5. What are some real-world applications of calculating the area under a v vs t sinusoidal trace?

The area under a v vs t sinusoidal trace can be used in various fields, such as physics, engineering, and economics. For example, it can be used to calculate the work done on an object by a force, the amount of energy produced by a power generator, or the profits generated by a business over a period of time.

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