Root Mean Square Voltage Multiplied by \sqrt{}2: Explained

In summary, when the frequency of rotation of a coil in an AC generator is doubled, the peak voltage produced is also doubled. This results in an r.m.s. value of the voltage that is equal to V multiplied by \sqrt{}2. Although the equation for Vrms is typically Vo/\sqrt{}2, when doubling the frequency, the division becomes a multiplication due to the increase in peak voltage.
  • #1
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Homework Statement



An AC generator produces a voltage of peak value V. The frequency of rotation of the coil of the generator is doubled. The r.m.s. value of the voltage produced is

Homework Equations



The answer is V multiplied by [tex]\sqrt{}2[/tex] but I don't understand why.

The Attempt at a Solution



I know that Vrms = Vo/[tex]\sqrt{}2 [/tex]so how does a division become a multiplication?
 
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  • #2
Still looking at this. Does doubling the frequency mean V peak becomes 2 V peak?

In which case 2 V / [tex]\sqrt{}2[/tex] = V[tex]\sqrt{}2[/tex]

Is that right?
 
  • #3
Initially the peak voltage is V. What does doubling the frequency of rotation do to the voltage produced? So what is the new peak voltage in terms of V? Then work out the rms value for this new peak voltage.

edit: I was too late. Yes, I think that is right : )
 
  • #4
Thank you! :smile:
 

Related to Root Mean Square Voltage Multiplied by \sqrt{}2: Explained

1. What is Root Mean Square (RMS) Voltage?

Root Mean Square (RMS) Voltage is a measure of the average voltage of an alternating current (AC) signal. It is calculated by taking the square root of the mean of the squares of the individual voltage values over a given period of time. RMS voltage is often used as a more accurate representation of the actual voltage of an AC signal, as it takes into account the fluctuation of the voltage over time.

2. Why is the RMS value multiplied by \sqrt{}2?

The square root of 2 is a constant factor that is used to convert RMS voltage to peak voltage. This is because the peak voltage of an AC signal is 1.414 times higher than the RMS voltage. This conversion is necessary for accurately measuring and comparing the voltage of AC signals.

3. How is RMS voltage used in electrical circuits?

RMS voltage is used in electrical circuits to determine the power and energy consumption of devices. It is also used to calculate the effective voltage applied to a circuit, which is important for determining the safety and efficiency of the circuit.

4. Can the RMS value be used for both AC and DC signals?

No, the RMS value is only applicable to AC signals. DC signals do not have a fluctuating voltage, so there is no need to calculate an average value.

5. How does understanding RMS voltage help in analyzing and designing electrical systems?

Understanding RMS voltage is important in analyzing and designing electrical systems because it allows for more accurate calculations and predictions of power consumption, voltage drops, and other factors that affect the performance of the system. It also helps ensure the safety and efficiency of the system by providing accurate measurements and comparisons of voltage levels.

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