1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Svetradugi [14.3K]
3 years ago
14

The op amp in this circuit is ideal. R3 has a maximum value of 100 kΩ and σ is restricted to the range of 0.2 ≤ σ ≤ 1.0. a. Calc

ulate the range of vO if vI = 40 mV. b. If σ is not restricted, at what value of σ will the operational amplifier saturate?

Physics
1 answer:
Firlakuza [10]3 years ago
8 0

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

You might be interested in
I will mark brainlist pls help and. Give right answers
Vera_Pavlovna [14]

I think its b. Answer:

Explanation:

7 0
3 years ago
Read 2 more answers
The mean free path of a helium atom in helium gas at standard temperature and pressure is 0.2 um.What is the radius of the heliu
ivolga24 [154]

Answer: 0.10233nm

Explanation:

The mean free path \lambda   of an atom is given by the following formula:

\lambda=\frac{RT}{\sqrt{2} \pi d^{2}N_{A}P}    (1)

Where:

\lambda=0.2\mu m=0.2(10)^{-6}m

R=8.3145J/mol.K is the Universal gas constant

T=0\°C=273.115K is the absolute standard temperature

d is the diameter of the helium atom

N_{A}=6.0221(10)^{23}/mol is the Avogadro's number

P=1atm=101.3kPa=101.3(10)^{3}Pa=101.3(10)^{3}J/m^{3} absolute standard pressure

Knowing this, let's find d from (1), in order to find the radius r of the helium atom:

d=\sqrt{\frac{RT}{\sqrt{2}\pi\lambda N_{A}P}}    (2)

d=\sqrt{\frac{(8.3145J/mol.K)(273.115K)}{\sqrt{2}\pi(0.2(10)^{-6}m)(6.0221(10)^{23}/mol)(101.3(10)^{3}J/m^{3})}}    (3)

d=2.0467(10)^{-10}m    (4)

If the radius is half the diameter:

r=\frac{d}{2}  (5)

Then:

r=\frac{2.0467(10)^{-10}m}{2}  (6)

r=1.0233(10)^{-10}m  (7)

However, we were asked to find this radius in nanometers. Knowing 1nm=(10)^{-9}m:

r=1.0233(10)^{-10}m.\frac{1nm}{(10)^{-9}m}=0.10233nm  (8)

Finally:

r=0.10233nm This is the radius of the helium atom in nanometers.

5 0
2 years ago
Juan makes an adjustment to an electromagnet that causes the electromagnet to lose some of its strength. What did Juan most like
vampirchik [111]
A: He reduced the number of loops in the wire.

Explanation: The fewer coils of solenoid there are around the magnet, the weaker the electromagnet is. FYI: The solenoid <em>is</em> the wire in the electromagnet.
5 0
3 years ago
Read 2 more answers
WILL GIVE BRAINLEST!!
polet [3.4K]
I think the answer is c
7 0
3 years ago
The Earth possesses an electric field of (average) magnitude near its surface. The field points radially inward. Calculate the n
IgorLugansk [536]

Answer:

Incomplete question

This is the complete question

The Earth possesses an electric field of (average) magnitude 150 near its surface. The field points radially inward. Calculate the net electric flux outward through a spherical surface surrounding, and just beyond, the Earth's surface.

Explanation:

Given that,

Electric field is 150N/C inward

i.e E = - 150 i

Then, electric flux (Φ) is given as

Φ=∮E.dA

Surface area of a sphere is

A=4πr²

dA=8πr dr

The area is outwardly i.e

dA=-8πr dr i

Φ=∮E.dA

Φ=∮-150 i • 8πr i dr from 0 to R

Φ= -1200π∮rdr. From 0 to R

Φ= -1200π r²/2. From 0 to R

Φ= -600π [R² -0²]

Φ= -600πR²

Where R is radius of earth which is 6,400,000m

Φ= -600πR²

Φ= -600π(6400000)²

Φ= -7.72×10^16 Nm²/C

7 0
3 years ago
Other questions:
  • If you touch the two terminals of a power supply with your two fingertips on opposite hands, the potential difference will produ
    13·1 answer
  • Describe the energy transformations that occur in a waterfall...
    12·2 answers
  • When operated on a household 110.0 V line, typical hair dryers draw about 1650 W of power. The current can be modeled as a long,
    6·1 answer
  • PLEASE HELP!!!!! How are energy and the amplitude of a wave related?
    13·1 answer
  • The apartment’s explosion, reportedly caused by a gas leak, produced a violent release of gas and heat. The heat increased the _
    12·2 answers
  • A student is holding a marble in his hand. What are the equal and opposite forces that are acting on it?
    10·1 answer
  • What is a substance?
    10·1 answer
  • What effect does a catalyst have on the energy of a reaction system? HELP ASAP PLZ!!
    10·1 answer
  • What describes the main benefit to organisms that reproduce sexually?
    10·2 answers
  • a steel ball rolls horizontally off the edge of a tabletop that is 1.0 m high. it strikes the floor at a point 2.0 m horizontall
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!