Sine Waves

Discussion in 'Homework Help' started by dennis.muller, Mar 7, 2008.

  1. dennis.muller

    Thread Starter Member

    Feb 5, 2008
    10
    0
    Circuit Analysis: Theory and Practice 4th Edition
    ISBN-10: 1-4180-3861-X
    Chapter #15 Question #29

    Determine equations for sine waves with the following:

    a. Vm = 170V, f = 60Hz
    b. Im = 40μA, T = 10ms
    c. T = 120μs, v = 10V at t = 12μs

    Here is my attampt at solving for question a:

    a. Vm = 170V, f = 60Hz

    v = Vm Sin θ
    v = 170V Sin 60Hz
    v = 147.2243186
    v = 147V

    Here is the answer in the back of my text book:

    a. v = 170 Sin 377t V

    Here is my attampt at solving for question b:

    b. Im = 40μA, T = 10ms

    f = 1/T
    f = 1/10ms
    f = 100Hz

    i = Im Sin θ
    i = 40μA Sin 100Hz
    i = 39.39231012
    i = 39.4μA

    Here is the answer in the back of my text book:

    i = 40μA Sin 628t μA

    Here is my attampt at solving for question c:

    c. T = 120μs, v = 10V at t = 12μs

    f = 1/T
    f = 1/120μs
    f = 8.33333333MHz

    θ = 360˚ x ft
    θ = 360˚ x 8.33333333MHz x 12μs
    θ = 36˚

    e = Em Sin θ
    Em = e/Sin θ
    Em = 10V/Sin 36
    Em = 17.01301617
    Em = 17V˚

    Here is the answer in the back of my text book:

    v = 17 Sin 54.4kt V

    So it looks like here i may have stumbled accross a correct answer i got 17V but What's this 54.4kt V?

    Clearly I'm lost, where do I begin? Is there a check list process to solving for wave sines? HELP!
     
  2. Dave

    Retired Moderator

    Nov 17, 2003
    6,960
    144
    When you define the sine equation:

    v = Vm Sin θ

    Remember θ = 2πft

    Note the answers for a) and b) in the textbook is expressed in terms of t because you don't have a time variable.

    Dave
     
  3. dennis.muller

    Thread Starter Member

    Feb 5, 2008
    10
    0
    Dave,

    Thank you, strange thing is i can't seem to find anything on this equation θ = 2πft in the chapter but i did find this equation θ = 360°xft but this equation only works when my calculator is in rads. So how do you know when to calculate in rads and when to calculate in degrees?

    Here is my attampt at solving the questions again:

    a. Vm = 170V, f = 60Hz

    θ = 2πft
    θ = 2π60Hzt
    θ = 376.9911184t
    θ = 377t V

    There For v = |170| Sin 377t V

    b. Im = 40μA, T = 10ms

    f = 1/T
    f = 1/10ms
    f = 100Hz

    θ = 2πft
    θ = 2π100Hzt
    θ = 628.3185307t
    θ = 628t V

    There For i = |40μA| Sin 628t μA

    c. T = 120μs, v = 10V at t = 12μs

    f = 1/T
    f = 1/120μs
    f = 8333.333333Hz

    θ = 2πft
    θ = 2π8333.333333Hzt
    θ = 52359.87756t
    θ = 52.35987756kt
    θ = 52.4kt V

    So if i understand correctly this θ answer is in rads, there for . . .

    θ = 52.4k x t
    θ = 52.4krads x 12μs
    θ = 36.02758616
    θ = 36°

    e = Em Sin θ
    Em = e/Sin θ
    Em = 10V/Sin 36°
    Em = 17.01301617
    Em = 17V˚

    There For v = |17| Sin 54.4kt V

    I also could use f in the equation θ = 360°ft, there for . . .

    θ = 360°ft
    θ = 360° x 833.333333Hz x 12μs
    θ = 35856

    e = Em Sin θ
    Em = e/Sin θ
    Em = 10V/Sin 35856
    Em = -17.01301617
    Em = -17V˚

    There For v = |-17| Sin 54.4kt V

    So which solution is correct for question 29c?
     
  4. Papabravo

    Expert

    Feb 24, 2006
    10,135
    1,786
    Would it be impertinent to mention that 360 degrees is the same thing as two pi radians.? We somtimes measure phase angle in degrees, but seldom do we measure frequency in degrees per second. We do measure frequency in radians per second, and we measure frequency in cycles per second aka revolutions per second or Hertz.
     
  5. dennis.muller

    Thread Starter Member

    Feb 5, 2008
    10
    0
    Thanks everyone for the clarification, i just couldnt grasp the relationships between θ, w, t, f, T in terms of degrees & radians. Just to summarize . . .

    θ = wt = 2πft = [(2π/T) x t]

    Example A : T = 5

    θ = wt = 2πft = [(2π/T) x t] = [(2π/5) X t] = [1.256 X t] = 1.3t rads

    Lets say t = 3ms, there for . . .

    θ = 1.3t = [1.3 x 3ms] = 0.22345354 = 223.1m°

    Example B : f = 5Hz

    θ = wt = 2πft = 2π5Hzt = 31.41592654 = 31.4 rads

    Lets say t = 3ms, there for . . .

    θ = 31.4t = [31.4 x 3ms] = 5.39726243 = 5.4°

    There for the following statment is TRUE . . .

    θ = w = 2πf = (2π/T) = RADIANS

    AND

    θ = wt = 360°ft = [(360°/T) x t] = DEGRESE

    I just needed a little more calculator 101 and I'm sure I'll fully understand the relationships once I can see the process.
     
    Last edited: Jun 8, 2008
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