Rearrange formula and work out phase angle

In summary, the conversation discussed the values of amplitude and frequency, as well as obtaining the phase angle for a sinusoidal wave. It was mentioned that the phase angle can be obtained by plugging in a value for t, reading off the y value from the graph, and solving the equation. The ambiguity in evaluating ##\arcsin## was also addressed, and it was suggested to use two points for more accuracy. Finally, there was a disagreement about the correct method for obtaining the phase angle.
  • #1
leejohnson222
76
6
Homework Statement
work out what ip, f and phase angle is, then rearrange the formula to make t the subject and find out at what point in time does 6.78 amp occur
i = Ipsin (2pi f t - phase angle)

so far i think Ip = 10 f = 1000hz
struggling with the phase angle
Relevant Equations
i = Ipsin (2pi f t - phase angle)
so far i think Ip = 10 f = 1000hz
struggling with the phase angle
 
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  • #2
Screenshot 2023-02-08 at 13.39.52.png
 
  • #3
I confirm your amplitude and frequency values.
To get the phase angle, plug in a value for t, read off the y value from the graph and solve the equation. You will need to do that for at least two points because of the ambiguity in evaluating ##\arcsin##.
 
  • #4
Shouldn't the amplitude have units?
haruspex said:
To get the phase angle, plug in a value for t, read off the y value from the graph and solve the equation. You will need to do that for at least two points because of the ambiguity in evaluating ##\arcsin##.
Can the phase angle not be obtained by noting that at t = 0 the sinusoidal is at a minimum?
 
  • #5
kuruman said:
Shouldn't the amplitude have units?

Can the phase angle not be obtained by noting that at t = 0 the sinusoidal is at a minimum?
I should have written "you may have to". I was trying to be general.
 
  • #6
i could be very wrong here, but i worked out the angle to be 90 degrees ?
i full cycle of the wave is 0.001 s and the delay from 0 is 0.00025 s
360 x 0.00025 / 0.001 = 90
 
  • #7
That's not what @haruspex suggested ... but I agree.

Easy:
##I = I_p\sin (2\pi f t - \phi)\quad ## pick ##t=0## and solve ##\sin(-\phi)=-1\ ##

Personally, I prefer to imagine the graph for ##\phi = 0## and conclude that a shift of ##-{\pi\over 4}## to the right yields the given graph. Therefore ##\ -\phi=-{\pi\over 4}##

##\ ##
 

1. How do I rearrange a formula?

Rearranging a formula involves isolating a specific variable on one side of the equation. This can be done by using algebraic operations such as addition, subtraction, multiplication, and division. The goal is to get the variable you want to solve for on one side of the equation and all other variables and constants on the other side.

2. What is the phase angle in a formula?

The phase angle in a formula represents the angular difference between two waves or signals. It is typically measured in degrees or radians and can be positive or negative depending on the direction of the wave or signal.

3. How do I calculate the phase angle?

To calculate the phase angle, you need to know the frequency and time period of the wave or signal. The formula for calculating phase angle is phase angle = (360 * time period * frequency) / 360. This will give you the phase angle in degrees. If you want the phase angle in radians, you can use the formula phase angle = (2 * pi * time period * frequency) / (2 * pi).

4. Can I use a calculator to work out the phase angle?

Yes, most scientific calculators have a function for calculating the phase angle. Look for a button labeled "phase" or "angle" on your calculator. If you are using a graphing calculator, you can also use the "phase" function in the "math" menu.

5. Why is it important to rearrange formulas and work out phase angle?

Rearranging formulas allows us to solve for a specific variable and manipulate equations to better understand the relationship between different variables. Working out the phase angle is important in fields such as physics and engineering, where understanding the phase difference between waves or signals is crucial in designing and analyzing systems and circuits.

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