What is the phase angle for a given complex voltage and current?

In summary, the phase angle is a measure of the relative position or timing of two periodic waveforms at a given point in time. It is different from frequency, which measures the number of cycles a wave completes in one second. Phase angle plays a crucial role in wave interference and is calculated by determining the time difference between two waves or by using trigonometric functions. It has many real-life applications in fields such as physics, engineering, and telecommunications.
  • #1
lifeonfire
14
0

Homework Statement



If a complex voltage and current are related by the expression v(t) = ( - 1 + j (3)^(1/2) ) i(t)
What is the phase angle? Note j = sqrt(-1)

Homework Equations





The Attempt at a Solution



So is the phase angle simply tan inverse (sqrt (3) / -1 )??
Or do I assume that i = I e^(jwt) and then proceed from there?
 
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  • #2
hi lifeonfire! :smile:

(have a square-root: √ :wink:)
lifeonfire said:
So is the phase angle simply tan inverse (sqrt (3) / -1 )??

yes :smile:
 

Related to What is the phase angle for a given complex voltage and current?

1. What is the definition of phase angle?

The phase angle is a measure of the relative position or timing of two periodic waveforms at a given point in time. It is typically measured in degrees or radians and represents the difference in the starting point of two waves.

2. How is phase angle different from frequency?

Frequency refers to the number of cycles a wave completes in one second, while phase angle refers to the relative position of two waves at a specific point in time. Frequency is measured in Hertz (Hz) and is a measure of the wave's speed, while phase angle is measured in degrees or radians and is a measure of the wave's position.

3. What is the significance of phase angle in wave interference?

Phase angle plays a crucial role in wave interference, where two or more waves combine to form a new wave. The resulting wave will depend on the phase difference between the individual waves. If the waves are in phase (with the same phase angle), they will constructively interfere and create a larger amplitude. If the waves are out of phase (with opposite phase angles), they will destructively interfere and cancel each other out.

4. How is phase angle calculated?

Phase angle can be calculated by first determining the period of the wave (the time it takes to complete one cycle) and then finding the difference in the starting point of two waves in terms of time. This time difference is then converted into degrees or radians using the formula 360 degrees = 2π radians. Alternatively, phase angle can also be calculated by comparing the amplitude and frequency of two waves using trigonometric functions.

5. What are some real-life applications of phase angle?

Phase angle is used in various fields such as physics, engineering, and telecommunications. It is important in understanding wave interference and can be used to analyze and optimize signal processing in communication systems. Phase angle is also used in electrical circuits to measure the relative timing of voltage and current, which is essential in designing electronic devices.

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