Suppose we want to determine how many of the bits in a twelve-bit unsigned number are equal to zero. Implement the simplest circ
uit that can accomplish this task.
1 answer:
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Answer:
A) 11.1 ms
B) 5.62 Ω
Explanation:
L ( inductance ) = 10 mH
Vcc = 14V
<u>A) determine the required on time of the switch such that the peak energy stored in the inductor is 1.2J </u>
first calculate for the current ( i ) using the equation for energy stored in an inductor hence
i = ----- ( 1 )
where : W = 1.2j , L = 10 mH
Input values into equation 1
i = 15.49 A
Now determine the time required with expression below
i( t ) = 15.49 A
L = 10 mH, Vcc = 14
hence the time required ( T-on ) = 11.1 ms
attached below is detailed solution
B) <u>select the value of R such that switching cycle can be repeated every 20 ms </u>
using the expression below
τ = ---- ( 2 )
but first we will determine the value of τ
τ = t-off / 5 time constants
= (20 - 11.1 ) / 5 = 1.78 ms
Back to equation 2
R = L / τ
= (10 * 10^-3) / (1.78 * 10^-3)
= 5.62 Ω
Answer:
Explanation:
Previous concepts
Angular momentum. If we consider a particle of mass m, with velocity v, moving under the influence of a force F. The angular momentum about point O is defined as the “moment” of the particle’s linear momentum, L, about O. And the correct formula is:
Applying Newton’s second law to the right hand side of the above equation, we have that r ×ma = r ×F =
MO, where MO is the moment of the force F about point O. The equation expressing the rate of change of angular momentum is this one:
MO = H˙ O
Principle of Angular Impulse and Momentum
The equation MO = H˙ O gives us the instantaneous relation between the moment and the time rate of change of angular momentum. Imagine now that the force considered acts on a particle between time t1 and time t2. The equation MO = H˙ O can then be integrated in time to obtain this:
Solution to the problem
For this case we can use the principle of angular impulse and momentum that states "The mass moment of inertia of a gear about its mass center is ".
If we analyze the staritning point we see that the initial velocity can be founded like this:
And if we look the figure attached we can use the point A as a reference to calculate the angular impulse and momentum equation, like this:
And if we integrate the left part and we simplify the right part we have
And if we solve for we got:
