1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Finding Voltage As A Function of Peak Voltage

  1. Feb 21, 2012 #1
    1. The problem statement, all variables and given/known data



    I'm trying to understand how this website figured out that V = Vpk*(2/pi)*theta

    2. Relevant equations


    3. The attempt at a solution

    The only thing that comes to mind is that they're using the formula for the area of triangle. This doesn't seem to be the case though because:

    b = pi/2 h = Vpk

    A = (Vpk*pi)/4
  2. jcsd
  3. Feb 22, 2012 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    The red part is a straight line. In other words, V varies linearly with θ. That means it can be expressed it the form V = mθ + b where m is the slope of the line, and b is its y-intercept. We find b by finding the value of V when θ = 0. Since the plot clearly passes through the origin (0,0), it follows that 0 = m*0 + b. Or, 0 = b.

    That leaves the equation in the form V = mθ, where m is the slope. So all we need to do is find the slope of the red line. We can do that just by looking at it. Slope = rise/run. In this case, the rise is Vpk, because the line rises from V = 0 to V = Vpk. It does so over a horizontal distance of π/2, (since the line goes from θ = 0 to θ = π/2). So the run is π/2, and hence m = rise/run = Vpk/(π/2) = (2Vpk)/π. Substituting in this value for m, the equation of the line becomes:

    V = mθ = [(2Vpk)/π

    That's all there is to it. Really simple.
  4. Feb 28, 2012 #3
    Late response, but thanks tons for the response. I had spent HOURS trying to make sense of this; I think this is my lesson to reach out for help a little more often....
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook