Calculating Vrms: Homework Equations & Solutions Explained

In summary, Vrms stands for root mean square voltage and is important in calculations because it takes into account the varying voltage levels in an AC circuit. The formula for calculating Vrms is Vrms = (Vmax / √2) and for circuits with multiple voltages, the Vmax values are averaged and plugged into the formula to get the final Vrms value. Vrms is different from Vp, which is the peak voltage and only shows the maximum voltage level. Vrms is used in practical applications such as power transmission and distribution, electronics, and electrical safety standards.
  • #1
kostoglotov
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Homework Statement



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Homework Equations



The Attempt at a Solution


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Shouldn't I use [itex]V_{rms} = \sqrt{\frac{1}{T}\int_T v^2 dt}[/itex]?

Which would be

[tex]\sqrt{\frac{100}{2\pi}\int_0^{2\pi/100}(20+60cos(100t))^2dt}[/tex]

This equals [itex]\approx 79.88 V[/itex]

The answer is given as [itex]\approx 46.9V[/itex] and the solution manual shows the following working

[tex]\sqrt{20^2 + \frac{60^2}{2}}[/tex]

Why do they apply that solution and not the one I used?
 
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  • #2
You might want to check your integration. I find that the integral matches the manual's result.
 
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Related to Calculating Vrms: Homework Equations & Solutions Explained

What is Vrms and why is it important in calculations?

Vrms stands for root mean square voltage and it is a measure of the average voltage in an alternating current (AC) circuit. It is important in calculations because it takes into account the varying voltage levels in an AC circuit and gives a more accurate representation of the overall voltage.

What is the formula for calculating Vrms?

The formula for calculating Vrms is: Vrms = (Vmax / √2), where Vmax is the maximum voltage in the AC circuit.

How do you calculate Vrms for a circuit with multiple voltages?

To calculate Vrms for a circuit with multiple voltages, you would first find the Vmax for each voltage using the formula Vmax = Vp / √2, where Vp is the peak voltage. Then, you would find the average of all the Vmax values and plug it into the formula Vrms = (Vmax / √2) to get the final Vrms value.

What is the difference between Vrms and Vp?

Vp stands for peak voltage and it is the maximum voltage in an AC circuit, while Vrms is the root mean square voltage and it takes into account the varying voltage levels in an AC circuit. Vrms is a more accurate representation of the overall voltage in a circuit, while Vp only shows the maximum voltage level.

How is Vrms used in practical applications?

Vrms is used in many practical applications, such as in power transmission and distribution, where it is used to calculate the voltage levels needed for efficient power transmission. It is also used in electronics, as it is a more accurate measure of the voltage that components in a circuit are exposed to. Additionally, Vrms is used in electrical safety standards to determine safe voltage levels for humans.

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