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

In summary, a rotating voltage phasor is a graphical representation of an AC voltage that shows its amplitude and phase over time. It is used in AC circuits for analysis and problem solving, and is related to a sine wave as a snapshot at a specific point in time. The direction of rotation does not affect the phase angle, and it cannot be used to represent DC voltage.
  • #1
Deathfish
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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



-

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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  • #2
[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]
 

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

1. What is a rotating voltage phasor?

A rotating voltage phasor is a graphical representation of an alternating current (AC) voltage that shows the amplitude and phase of the voltage over time. It is typically represented by a vector that rotates counterclockwise at a constant speed, with the length of the vector representing the amplitude of the voltage and the angle of the vector representing the phase of the voltage.

2. How is a rotating voltage phasor used in AC circuits?

Rotating voltage phasors are used to analyze and solve problems in AC circuits, such as calculating voltage and current values at specific points in time. They also help to visualize the relationship between voltage and current, and can be used to determine the power and energy in an AC circuit.

3. What is the relationship between a rotating voltage phasor and a sine wave?

A rotating voltage phasor can be thought of as a snapshot of a sine wave at a specific point in time. As the voltage phasor rotates, it traces out a sine wave, with the amplitude and phase of the phasor corresponding to the amplitude and phase of the sine wave at that point in time.

4. How does the direction of rotation of a voltage phasor affect its phase angle?

The direction of rotation of a voltage phasor does not affect its phase angle, as the angle is determined by the position of the phasor on the complex plane. However, the direction of rotation does affect the sign of the phase angle, with counterclockwise rotation resulting in a positive phase angle and clockwise rotation resulting in a negative phase angle.

5. Can a rotating voltage phasor be used to represent DC voltage?

No, a rotating voltage phasor is specifically used to represent AC voltage, as it shows the changes in amplitude and phase over time. DC voltage is constant and does not change over time, so it cannot be represented by a rotating voltage phasor.

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