Hi every body I am stuck on question from the book Introductry circuits Analysis I tried to do the following To find T1 I need to count the time needed v to be 0 So my solution is : v = 200 Sin(2π1000t+60) 0= 200 Sin(360000+60) Sin(360000t+60) = 0 Sin־1 (0) = 360000t+60 t = 60/360000 = 0.16666 ms But the book I get the question from said that this answer is 1/3 ms ,, can you please tell me where is the mistake in my solution Thank you
Haven't used the TI but I suspect the problem is the mixing of radians and degrees in the equation. If the calculator can be set in radian mode try converting the 60° to radians first and then solve as you have already done. Hope that is the solution!
zaidqais, w*t = 2*pi*f*t= 2*pi*1000*t ===> f = 1000 Hz ===> P = 1 ms They want the time of (120/360) period = 1/3 period which is 1/3 ms = 0.333 ms. Ratch
First thank you for your replys I have a question in the solution i put it in my first post what is the mistake ? I suppose it must calculate T1 or not !! and in the equation Code ( (Unknown Language)): w*t = 2*pi*f*t= 2*pi*1000*t ===> f = 1000 kHz ===> P = 1 ms Pi is 180 degree or 3.14 ? note f = 1000 Hz and not 1000 kHz Thank you
OK - take your point - my reply not helpful keeping in mind that sin(x) = 0 at x=0 , pi [180°], 2 x pi [360°], etc solve v = 200 Sin(2π1000t+60) = 0 as you did! Consider the cases where Sin(2π1000t+60)= 0 , 180°, etc case 1: 200 Sin(2π1000t+60) = 0 2π1000t+60 = 0 (strictly 2π1000t + π/3 = 0) 360000t = -60 (using degrees) t = - 0.1667 ms - wrong solution as t is less than zero case 2: 2π1000t+60=180 (without being pedantic about radians) 360000t=180-60 t = (180-60)/360000 t = 0.333 ms (1/3 ms exactly) - first positive time at which function is zero - the required solution. t1
t_n_k, Why solve for 200 Sin(2π1000t+60) = 0 ? That was 1/6 ms previously. That is not what the problem asked. 2π1000t + π/3 = 0 , absolutely, no other way. When you introduce time into trig functions, then all frequencies and phase degrees have to be converted to radians. 2n1000t = -n/3 =====> t = -1/6 ms. Isn't that when the function was zero previously? You have to use radians with time. 2n1000t + n/3 = n ====> 2n1000t = 2n/3 ====> t = 1/3 ms, which is when the next zero value will occur. Arithmetic wrong, 2n1000t = 180-60 = 120 =====> t = 0.019099, which is off base because radians were not used. Ratch
t_n_k, Upon further reflection, I realize you were right and I was wrong. I did not realize that you were converting radians/sec into Hz/sec. Doing it that way you can work exclusively with Hz instead of radians. Sorry for the mixup. At least we both got the same answers. Ratch