Rotating Voltage Phasor: Frequency of Sinusoidal Voltage at 3/4 Peak Value

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SUMMARY

The frequency at which a sinusoidal voltage reaches 3/4 of its peak value 2.5 ms after the zero crossing is definitively calculated to be 54 Hz. The calculation involves determining the angle corresponding to 3/4 of the peak value using the arcsine function, followed by applying the formula for frequency derived from the angle and time. The correct answer is option (a) 54 Hz, confirmed through the use of trigonometric relationships and time period calculations.

PREREQUISITES
  • Understanding of sinusoidal waveforms and their properties
  • Knowledge of trigonometric functions, specifically arcsine
  • Familiarity with frequency and period relationships in oscillatory systems
  • Basic skills in solving equations involving angular measurements
NEXT STEPS
  • Study the derivation of frequency from sinusoidal voltage equations
  • Learn about the properties of sinusoidal functions and their graphical representations
  • Explore the application of trigonometric identities in electrical engineering contexts
  • Investigate the effects of phase shifts on sinusoidal waveforms
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Electrical engineering students, educators teaching AC circuit analysis, and professionals involved in waveform analysis and signal processing.

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Homework Statement



At what frequency does a sinusoidal voltage reach 3/4 of its peak value 2.5ms after the zero crossing?

a) 54 Hz
b) 56 Hz
c) 58 Hz
d) 47 Hz


Homework Equations



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The Attempt at a Solution



[tex]\frac{3}{4}[/tex] x 90 = 67.5
2.5ms / 67.5 x 360 = 1/75
Period is 1/75
Therefore Frequency is 75 Hz (?)
 
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[tex]3/4 = sin(\theta)\to \theta = arcsin(3/4)[/tex]
then
[tex]\theta = 2 \pi f t \to f = \frac{\theta}{2 \pi t} = \frac{arccsin(3/4)}{2 \pi 2.5ms} = 54 Hz[/tex]
 

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