A simple pendulum is made from a 0.54-m-long string and a small ball attached to its free end. The ball is pulled to one side th
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Answer:
Explanation:
Un electrón tiene una carga negativa de y la masa total es igual al producto del número de electrones y esa carga unitaria. El número de electrones se obtiene al dividir la carga total por la carga unitaria. (An electron has a negative charge of
and the total mass is equal to the product of the qunatity of electrons and such unit charge. The quantity of electrons is found by diving the total charge by the unit charge):
I have attached the circuit image missing in the question.
Answer:
A) The range of vo is; -6.6V≤ vo ≤-1V
B) σ = 0.1861
Explanation:
A) First of all, Let VΔ be the voltage from the potentiometer contact to the ground.
Thus; [(0 - vg)/(2000)] +[(0 - vΔ)/(50,000)] = 0
So, [(- vg)/(2000)] +[(- vΔ)/(50,000)] = 0
Simplifying further; -25 vg - vΔ = 0
From the question, vg = 40mV = 0.04 V
So - 25(0.04) = vΔ
So: vΔ = - 1 V
Now, [vΔ/(σRΔ)] + [(vΔ - 0)/(50,000)] + [(vΔ - vo)/((1 - σ)RΔ))] = 0
So, multiplying each term by RΔ to get; [vΔ/(σ)] + [(vΔ x RΔ)/(50,000)] + [(vΔ - vo)/((1 - σ))] = 0
So RΔ = 100kΩ or 100,000Ω from the question.
So, substituting for RΔ, we get,
[vΔ/(σ)] + [2vΔ] + [(vΔ - vo)/((1 - σ))] = 0
Let's put the value of - 1 for vΔ as gotten before.
So, ( - 1/σ) - 2 + [(-1 - vo)/(1 - σ)] = 0
Now let's make vo the subject of the equation to get;
-1 - vo = (1 - σ)[2 + (1/σ)]
-1 - vo = 2 - 2σ + (1/σ) - 1
-vo = 1 + 2 - 2σ + (1/σ) - 1
-vo = 2 - 2σ + (1/σ)
vo = - 1 (2 - 2σ + (1/σ))
When σ = 0.2; vo = - 1(2 - 0.4 + 5) =
- 1 x 6.6 = - 6.6V
Also when σ = 1;
vo = - 1(2 - 2 + 1) = - 1V
Therefore, the range of vo is;
- 6.6V ≤ vo ≤ - 1V
B) it will saturate at vo = - 7V
So, from;
vo = - 1 (2 - 2σ + (1/σ))
-7 = - 1 (2 - 2σ + (1/σ))
Divide both sides by (-1)
7 = (2 - 2σ + (1/σ))
Now, subtract 2 from both sides to get; 5 = - 2σ + (1/σ)
Multiply each term by α to get;
5σ = - 2σ^(2) + 1
So 2σ^(2) + 5σ - 1 = 0
Solving simultaneously and picking the positive value , we get σ to be approximately 0.1861
