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!

 

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

 

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?

 

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.

 

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.