RMS Current in an AC Generator with Doubled Rotational Speed

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Homework Help Overview

The discussion revolves around the behavior of rms current in an AC generator when the rotational speed of the coil is doubled. The original poster presents an equation for output voltage and attempts to analyze how changes in speed affect current through an inductor.

Discussion Character

  • Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants explore the relationship between voltage, reactance, and current, questioning how doubling the rotational speed impacts rms current. Some participants attempt to rearrange equations and analyze the implications of changing reactance.

Discussion Status

The discussion is active, with participants providing insights into the relationships between voltage, current, and reactance. There is a recognition that the current may remain unchanged despite changes in reactance, although this point is not universally accepted, leading to further questions and clarifications.

Contextual Notes

Participants express confusion regarding the constants and relationships in the equations, particularly in how reactance and current interact under varying conditions. There is an acknowledgment of the complexity of the problem without a clear resolution.

Terocamo
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Homework Statement


The output voltage of an a.c. generator is
\emph{V}=\emph{NBA}\omegasin(\omegat).
When the voltage is connected across an inductor, the rms current in the inductor is found to be 10mA. What will Be the rms current if the rotating speed of the coil inside the generator is doubled?

The Attempt at a Solution


I try to rearrange the equation, what i think is that the reactance of the inductor is constant so that if
Xc=\frac{NBA\omega}{\sqrt{2}Irms} (strangely i cannot get the root 2 shown in the faction)
Then \omega\proptoIrms
So if the rotational speed doubles the Irms also doubled.
But however the answer is the reactance change and the rms current remains at 10mA.
I don't understand how these kind of question can be solved cause there isn't any constant I can make use of in the question...
 
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Vmax = NABω and XL = ωL. Imax = Vmax/ωL = NAB/L.

When When the rotating speed doubles, Vmax = NAB(2ω) and XL= 2ωL

So Imax remains the same. Same is true for Irms.
 
I don't understand. How is the reactance doubles but not the current?
 
Terocamo said:
I don't understand. How is the reactance doubles but not the current?

Imax = Vmax/XL = NAB(2ω)/2ωL = NAB/L
 
oic the current is independent of rotation speed, thanks.
 

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