A ray of light traveling in air strikes the surface of a liquid. if the angle of incidence is 29.7◦ and the angle of refraction is 16.3◦ , find the critical angle for light traveling from the liquid back into the air. answer in units of ◦

Answers

Answer 1
When light moves from a medium with higher refractive index to a medium with lower refractive index, the critical angle is the angle above which there is no refracted ray, and it is given by:
[tex]\theta_c = \arcsin ( \frac{n_r}{n_i} )[/tex] (2)
where [tex]n_r[/tex] is the refractive index of the second medium and [tex]n_i[/tex] is the refractive index of the first medium.

We can find the ratio [tex]n_r / n_i[/tex] by using Snell's law:
[tex]n_i \sin \theta_i = n_r \sin \theta_r[/tex] (1)
where
[tex]\theta_i[/tex] is the angle of incidence
[tex]\theta_r[/tex] is the angle of refraction

By using the data of the problem and re-arranging (1), we find
[tex] \frac{n_r}{n_i} = \frac{\sin \theta_i}{\sin \theta_r} = \frac{\sin 16.3^{\circ}}{\sin 29.7^{\circ}} =0.566 [/tex]

and if we use eq.(2) we can now find the value of the critical angle:
[tex]\theta_c = \arcsin ( \frac{n_r}{n_i} ) = \arcsin (0.566) = 34.5^{\circ}[/tex]

Related Questions

Temperatures of four liquid substances are shown in the chart.

Which statement is best supported by the data in the chart?

A) Substance X will transfer thermal energy to substance Y mainly through radiation if they are mixed.
B) Substance Y will transfer thermal energy to substance Z through conduction if they are mixed.
C) Substance X will transfer thermal energy to substance W through radiation if they are placed near each other.
D) Substance W will transfer thermal energy to substance X through conduction if they are mixed.

Answers

For those of you taking the course on Edge, the right answer is D.

Answer: D) Substance W will transfer thermal energy to substance X through conduction if they are mixed.

Explanation:  Thermal energy is the energy possessed by an object by virtue of its temperature. It is transferred from a hotter object to a colder object till both the bodies attain the same temperature.

Radiation occurs when  thermal energy is transferred by electromagnetic waves. Conduction occurs when thermal energy is transferred when two objects are in direct contact.

Thus Substance W at a temperature of [tex]40^0C[/tex] will transfer thermal energy to substance X at a temperature of [tex]37^0C[/tex] through conduction if they are mixed as they are in direct contact.

When a front wheel drops off the roadway you should?

Answers

braking and returning suddenly to the roadway

When a front wheel drops off the roadway, stay calm, maintain a firm grip on the steering wheel, slow down gradually, and carefully steer back onto the road while checking for traffic.

When a front wheel drops off the roadway while you are driving, there are several steps you should follow to safely regain control:

Stay calm: Avoid any sudden movements or panicking, which can worsen the situation.

Hold the steering wheel: Keep a firm grip on the steering wheel to maintain control of the vehicle.

Decelerate gradually: Slowly lift your foot off the accelerator to decrease speed, but do not brake suddenly as this can cause further loss of control.

Slowly steer back: Gradually steer the vehicle back onto the roadway once you have slowed down sufficiently.

Check for traffic: Always ensure it is safe to merge back onto the road by checking for other vehicles.

By following these steps, you can safely recover from your front wheel dropping off the roadway and minimize the risk of an accident.

What is the wavelength (angstroms) of a photon that has an energy of 4.38 x 10-18 j?

Answers

The relationship between energy and frequency of a photon is given by
[tex]E=hf[/tex]
where E is the energy, h is the Planck constant and f is the photon frequency. By re-arranging the equation and using the photon energy, we can calculate its frequency:
[tex]f= \frac{E}{h}= \frac{4.38 \cdot 10^{-18} J}{6.6 \cdot 10^{-34}Js}=6.64 \cdot 10^{15} Hz [/tex]

Then we know that the photon travels at speed of light, c, so we can find its wavelength by using
[tex]\lambda= \frac{c}{f}= \frac{3 \cdot 10^8 m/s}{6.64 \cdot 10^{15}Hz}=4.52 \cdot 10^{-8} m [/tex]

And since 1 A (angstrom) corresponds to [tex]10^{-15} m[/tex], the wavelength expressed in angstroms is
[tex]\lambda= \frac{ 4.52 \cdot 10^{-8} m}{10^{-15} m/A} = 4.52 \cdot 10^7 A [/tex]

Answer: The relationship between energy and frequency of a photon is given by E = h*f.

E is the energy, h is planck constant and f is the frequency and f= c/λ.

But i want wavelength, so i write this equation as E= h*c/λ.

now

c=3.8[tex]*10^{8}[/tex]

E =4.38*[tex]10^{-18} [/tex]  [tex]\frac{m^{2}*kg }{s^{2} }[/tex]

where i replaced joules for  [tex]\frac{m^{2}*kg }{s^{2} }[/tex]

h = 6.62607004 *[tex]10^{-34}[/tex][tex]\frac{m^{2}*kg }{s }[/tex]

then λ = h*c/E =  [tex]\frac{6.62607004 *10^{-34}*3.8*10^{8}m/s}{4.38*10^{-18} \frac{m^{2}*kg }{s^{2} }}[/tex] = 5.7*[tex]10^{-8}[/tex]  m

But you want the solution in angstroms, so 1  meter is [tex]10^{10}[/tex] angstroms

so λ  = 5.7*[tex]10^{2}[/tex]  = 570 angstrom

Which is a characteristic that makes electromagnetic waves and water waves different

Answers

We know that a wave is a disturbance that transfers energy through matter or space There are two main types of waves: Mechanical and Electromagnetic. Water waves are mechanical. A mechanical wave is an oscillation of matter to transfers energy, but you always need a medium (substance such as: solid, liquid, gas, plasma) to transport it. The medium for water waves is, in fact, the water. For example, ripple in water is a surface wave. On the other hand, electromagnetic waves don't need a medium to transport, they can do it through the empty space. Then, this is the major characteristic that makes these two types of waves different.

Each line on a speed-lock cutting head tool arm knob moves the cutting tip ______ in or out.

Answers

It is to be noted that each line on a Speed-Lock cutting head tool arm knob moves the cutting tip .0025” in or out.

The question pertains to the movement of the cutting tip on a Speed-Lock cutting head tool arm knob.  A Speed-Lock cutting head tool arm knob likely refers to a component in a machining or cutting tool system, facilitating adjustments.

The statement "Each line on a Speed-Lock cutting head tool arm knob moves the cutting tip .0025” in or out" suggests that each line corresponds to a movement of 0.0025 inches for the cutting tip.

Therefore, the correct answer is option B, indicating that each line on the knob moves the cutting tip by 0.0025 inches.

Full Question:

Although part of your question is missing, you might be referring to this full question:

Q6. Each line on a Speed-Lock cutting head tool arm knob moves the cutting tip ______ in or out.

A. .001”

B. .0025”

C. .010”

D. .020”

Which term does not identify a vector quantity?

Answers

Here are a few:

-->  €
-->  £
-->  ¢
-->  ¥
-->  Ü
-->  Δ
-->  Σ
-->  Φ
-->  π
-->  Ω
-->  ω
-->  √
-->  ∞
-->  $
-->  °C
-->  °F

A girl throws a rock horizontally, with a velocity of 10 m/s, from a bridge. it falls 20 m to the water below. how far does the rock travel horizontally before striking the water, assuming negligible air resistance?

Answers

Before you begin, you need to first figure out what your problem gives you and what you need to look for.
Given:
vix=10m/s
dy= 20m

What you are looking for is horizontal distance or dx.

The formula for vertical distance is:
[tex]dx=vi_{x}t[/tex]

Where:
dx= horizontal distance
vix= initial horizontal velocity
t=time

But when you look at your problem, you do not have time. Now for time, you need to use the formula:

[tex]t= \sqrt{ \frac{2dy}{g} } [/tex]

g in this equation is a constant. It is the acceleration due to gravity which has the value of 9.8m/s^2.

Now we first need to get time:
[tex]t= \sqrt{ \frac{2dy}{g} } [/tex]
[tex]t= \sqrt{ \frac{2(20m}{9.8m/s^{2}} } [/tex]
[tex]t= \sqrt{ 4.08163265} [/tex]
[tex]t=2.02s [/tex]


Now that you have time, all you need to do is insert that into our equation for horizontal distance. 

[tex]dx=vi_{x}t[/tex]
[tex]dx=(10m/s)(2.02s)[/tex]
[tex]dx=20.20m[/tex]

The horizontal distance of the rock will be 20.20m.
Final answer:

The rock strikes the water after traveling approximately 20.3 meters horizontally. This is calculated using principles of physics related to projectile motion, with the separate vertical and horizontal movements taking place simultaneously and independently.

Explanation:

The physics problem you've described deals with the concept of projectile motion. In this scenario, the horizontal and vertical movements of the rock can be analyzed separately. The vertical displacement doesn't affect the horizontal one given the negligible air resistance.

First, let's find the time it takes for the rock to hit the water below. We can use the equation of motion, d = 0.5*g*t², where g is the acceleration due to gravity (9.8 m/s²), and d is the vertical displacement (20 m). Solving for t, we get approximately 2.03 seconds.

Then, to find the horizontal distance that the rock traveled, we use the formula for velocity (v = d/t), rearranged to solve for distance: d = v*t. Here, v is the initial velocity of the rock (10 m/s) and t is the previously calculated time (2.03 seconds). Completing the calculation, we find that the horizontal distance the rock travels before striking the water is approximately 20.3 meters.

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Help please!!!!!!!!!!!!!!!!!!!!

Answers

Looks like you need to review through the lesson and take notes as it tells you in the lesson what each of these are.

A 100 kg bag of sand has a weight on 100 N. When dropped its acceleration is what?

Answers

100N describes the weight of the sandbag, while 100kg is the mass of the sandbag.

To calculate acceleration, divide your weight by the mass, thus the accleration is:

[tex]100N/100kg = 1(m/s^2)[/tex]

Answer:

Gravity.

Explanation:

If you are holding the bag of sand, the only acceleration in the system is gravity, because is a vertical movement. So, [tex]a = 9.81 \frac{m}{s^{2} }[/tex]

We are assuming that is vertical movement because is say ''dropped'', which is a term used in Free-fall models, where acceleration is constant.

The height of the washington monument is measured to be 170 m on a day when the temperature is 30.0°c. what will its height be in meters on a day when the temperature falls to −16.0°c? although the monument is made of limestone, assume that its thermal coefficient of expansion is the same as marble's.

Answers

This is a case of linear expansion. The general expression of linear expansion is given by:

ΔL = αLΔT, ΔL = change in length or height, α = coefficient of linear thermal expansion, ΔT = Change in temperature.
In the current case;
α = 2.5*10^-6 /°C (for Marble)
L = 170 m at 30.0°C
ΔT = 30 - (-16) = 46°C

Substituting;
ΔL = 2.5*10^-6 *170*46 = 0.01955 m

Height at -16°C = 170 - 0.01955 = 169.98 m

what is the atomic number z of 73li?

Answers

I think thats a trick question on the periodic table there is no Z, theres Zi which is zinc but no Z

[tex] ^7 _3 {Li} [/tex] means that the element is Lithium (Li), 7 corresponds to its mass number (sum of protons and neutrons), 3 corresponds to its atomic number (number of protons in the nucleus).


The problem asks for the atomic number (Z) of this isotope: based on what we said previously, the answer is 3.

a roller coaster slows as it travels up a hill
a) speed
b) velocity
c) acceleration

Answers

think the answer should be C
Final answer:

As the roller coaster ascends the hill, it experiences a decrease in speed which affects its velocity, leading to what we describe as negative acceleration or deceleration.

Explanation:

When a roller coaster is traveling up a hill, it begins to slow down due to the force of gravity opposing its motion. This is a scenario of negative acceleration or deceleration.

Speed refers to how fast an object is moving without concerning the direction. In this case, the speed of the roller coaster decreases as it climbs the hill.

Velocity includes both the speed and direction of an object's motion. Here, the velocity also decreases as the speed decreases and the direction is upwards.

Acceleration refers to the rate of change of velocity. When the roller coaster slows down while moving up, it is undergoing negative acceleration or deceleration.

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What kind of movement does the heat within the core and mantle directly generate?

Answers

Heat within the earth generates convection currents in the mantle. Convection currents represent the circular motion of molten rocks in the mantle driven by heat from the core. This circular motion is what drives the plates and creates the theory of plate tectonics which states that the earth crust is divided into plates that float on the semi-molten mantle below. 

When an object moves at a very high speed relative to an observer, its measured length in the direction of motion is contracted. t true?

Answers

Your statement is not completely correct.
When an object is moving towards the observer, its measured wavelength decreases,(it is not correct if measured length) because the waves are compressed.
That's true. It doesn't even need to be very high speed, although the effect is too small to measure at low speeds.

A spring with a spring constant of 1.8 × 102 n/m is attached to a 1.5 kg mass and then set in motion.

a.what is the period of the mass-spring system?

b.what is the frequency of the vibration

Answers

k = 1.8 x 10^2
m = 1.5kg
T = ?
f =?
T = (2π) sqrt(m/k)
T = (2π) sqrt(1.5/(1.8x 10^2)) = .5732s

F = 1/T
F = 1÷.5732=1.744Hz

Part A: The time period of the mass-spring system is 0.573 seconds.

Part B: The frequency of the vibration of the mass-spring system is 1.75 Hz.

Time Period and Frequency

Given that the mass of the spring is 1.5 kg and the spring constant is 1.8 × 10^2 n/m.

Part A

The period of the mass-spring system is given by the formula.

[tex]T=2\pi\sqrt{\dfrac {m}{k}}[/tex]

Where m is mass and k is spring constant.

Substituting the values in the above equation, we get the time period.

[tex]T = 2 \times 3.14 \times \sqrt{\dfrac {1.5}{ 1.8 \times 10^2}}[/tex]

[tex]T = 0.573 \;\rm s[/tex]

Hence the time period of the mass-spring system is 0.573 seconds.

Part B

The frequency of the vibration is given below.

[tex]f = \dfrac {1}{T}[/tex]

[tex]f = \dfrac {1}{0.573}[/tex]

[tex]f = 1.75 \;\rm Hz[/tex]

Hence the frequency of the vibration of the mass-spring system is 1.75 Hz.

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which is a necessary part input for all heat engines?


A) Steam to act as a working substance

B) An energy source, such as fuel or electrticity

C) A device to generate electrticity

D) Luiqid water to act as a working substance

Answers

I believe the answer is B. An energy source such as fuel or electricity.
For example an energy source such as fuel or electricity. For example a heat source generates thermal energy that brings the working substance to the high temperature state. the working substance generates work in the working body of the engine while transferring heat to the colder sink until it reaches a low state of temperature.

Why is newton's first law of motion sometimes called the lae of inertia?

Answers

Newton's 1st law of motion states that an object at rest stays at rest and an object in uniform motion along a straight line stays in motion unless acted upon by an unbalanced force. 
This law talks about the tendency of an object to resist any change in its state of rest or uniform motion, this is called Inertia. Thus Newton's 1st law of motion is also called the Law of Inertia

Final answer:

Newton's first law of motion, also known as the law of inertia, states that an object at rest remains at rest and an object in motion remains in motion unless acted upon by an external force.

Explanation:

Newton's first law of motion states that a body at rest remains at rest or, if in motion, remains in motion at a constant velocity unless acted on by a net external force. This law is also known as the law of inertia. Inertia is the tendency of an object at rest to remain at rest or, if moving, to remain in motion at constant velocity. Inertia is related to an object's mass.

The largest tides occur at _____.

1. new moon
2. full moon
3. first quarter
4. last quarter
5. solar eclipse
6. lunar eclipse

This is a multiple answer question.

Answers

Lunar solar full that is all your welcome my friend ha ha

The largest tides occur at full moon, solar eclipse, and lunar eclipse. Thus, the correct option is B, E, and F.

What are solar and lunar eclipses?

Eclipses are of two types: Solar and Lunar eclipse. A solar eclipse occurs when the moon enters between the sun and the earth, which its shadow on the earth's surface.

A lunar eclipse occurs when the earth is moved between the sun and the moon and the Earth leaves its shadow on the moon. The tides form in seas because of the gravitational force of the moon.

The gravity of the moon makes the tides or waves in the seas or oceans. The full moon has more gravitation force and hence, larger tides are formed. The largest tides are also formed by solar and lunar eclipses.

When the sun is aligned with the moon during the eclipse, the sun is also pulling in the same direction resulting in the largest tides. The gravitational pull of the sun and moon increases the tides in ocean surfaces on Earth.

Thus, the largest tides occur at Full moon, solar and lunar eclipse. The correct options are B, E, and F.

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If we start with 1.000 g of cobalt-60, 0.675 g will remain after 3.00 yr. this means that the of is _____

Answers

Cobalt-60 is undergoing a radioactivity decay.

The formula of the decay is n=N(1/2)∧(T/t).
Where N ⇒ original mass of cobalt
           n ⇒ remaining mass of cobalt after 3 years
          T ⇒ decaying period
           t ⇒ half-life of cobalt.

So,
0.675 = 1 × 0.5∧(3/t)
log 0.675 = log 0.5∧(3/t)
3/t = log 0.675 ÷log 0.5
 3/t= 0.567

t = 3÷0.567
  = 5.290626524

the half-life of Cobalt-60 is 5.29 years. 

           

Sound from source a has twice the frequency of sound from source
b. compare the wavelengths of sound from the two sources.

Answers

are you asking me or telling me

A group of friends is celebrating New Years when one of them pulls out a gun and fires it into the air. One of the bullets comes down and strikes another member of the group in the head, killing him. What is the cause of death?
A) homicide
B) accidental
C) gunshot wound
D) cerebral hemorrhage

Determine the manner of death based on the following description:

Man shot during robbery. Man stabilizes. Develops pneumonia, followed by kidney failure, liver failure, and finally death. He had prior lung and heart disease, and probably would have survived if not for these diseases.
A) accident
B) homicide
C) natural
D) suicide

The following situations are presented to a medical examiner. In which situation is the medical examiner most likely to gather more evidence before determining the manner of death?
A) 18-year-old male recovered in alley with gunshot wound to back of head
B) 25-year-old

Answers

1. Would be C. It were a shot made by a gun, it makes sense.
(But it were also unintentional, I'm leaning towards B as well..but more on C)

2.  C, he wasn't intentionally meant to die by the gunshot wound, he developed illnesses then and died later of them! (Followed by his already had illnesses)

3. A, a younger body is more healthy and easier to find the cause of death, while an older individual could be much harder and already have many problems.

(I'm just using processes of text evidence)

Answer:

1. C

2. C

3. A

Explanation:

1. In the given question the cause of death is gunshot. because of gunshot on the head wound develops and person died. So here answer would be option c: gunshot wound.

2.In this question man survived after gunshot(maybe his immunity reduced) and after sometime he develops pneumonia, kidney failure and liver failure, here cause of death is these diseases so cause is natural. option c would be the right answer.

3. For a medical examiner most likely to gather more evidences before determining the manner of death would be a 18-year-old boy. Because his body is completely developed and full of immunity( in normal cases).

a summer thunderstorm has begun! it’s raining. lighting cracks through air. a few seconds later you hear booms of thunder. why do you see the lighting before you hear the thunder?

Answers

Light travels faster than sound
Lightning comes before sound, other wise said, light travels faster than sound 

Hope this helps.


in order to produce a current in a cell, the terminals must what?

a. have a potential difference
b. be exposed to light
c. be in a liquid
d. be at two different temperatures

Answers

A. They must have a potential difference
Potential difference is voltage and voltage is basically the thing that causes current to flow

A 500g sample of Potassium-40 is left to decay radioactively. After 3.9 x 109 years, about how many grams of Potassium-40 are expected to remain? [The half-life of Potassium-40 is 1.3 x 109 years.]

Answers

The answer is 62.5 grams
it is 62.5g i know for a fact i major and a teacher i'm science  and math

An exothermic reaction ___ energy.

A) releases

B) absorbs

C) creates

D) decreases

Answers

Well, an exothermic reaction is a reaction, that involves the release of heat. So your answer would be A, "releases".

Good luck!

How does lubricating a machine affect the output work from that machine? how would the input and output forces be affected?

Answers

lubricating a machine will make it more efficient and it will reduce the friction between the parts meaning that less energy will be transferred and dissipated into the surroundings as heat.
the in put and out put force may increase as it's easier for the machine to work due to less friction

By lubricating its components, a machine can operate more effectively and send less energy to the environment as heat by reducing friction between its parts.

Due to the machine's simplicity of use and less friction, the input and output forces might both increase.

What is lubrication?

To reduce wear and tear and friction in a contact between two surfaces, lubrication is a procedure or technique that uses a lubricant. The area of tribology includes the study of lubrication as a discipline.

Solid body interactions are decreased through the design of lubrication mechanisms, such as fluid-lubricated systems, which carry the given load either entirely or partially by hydrodynamic or hydrostatic pressure (and consequently friction and wear). Different lubrication regimes can be recognized depending on how far the surfaces have separated.

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The graph indicates what about the relationship between wavelength and frequency

Answers

We can't see the graph.
But is has to show that wavelength and frequency are inversely
proportional.  In other words, their product is constant.
That's because their product is the speed of the wave.
If the graph doesn't show that, then the graph is wrong.

Wavelength and frequency of awave are in inverse proportion. Therefore, the graph   showing as the frequency increases, wavelength decreases.

What is wavelength?

Wavelength of an electromagnetic wave is the distance between its two consecutive troughs or two consecutive crusts. Wavelength of a wave indicates how much distance it can cover.

Frequency of an electromagnetic wave is the number of cycles or waves get in one second. Thus its unit is s-1. Frequency of first last some radiations in the spectrum that are UV, gamma, x-ray etc are higher and they have shorter wavelength.

High frequency waves are more energetic whereas longer wavelength  is associated with less energy. The relation between frequency v and wavelength lambda is written as follows:

[tex]v = \frac{c}{\lambda}[/tex]

Where c is the speed of light.

As per this relation frequency is inversely proportional to the wavelength. Hence they are in inverse relation.

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A violin string that is 50.0 cm long has a fundamental frequency of 440 Hz. What is the
speed of the waves on this string?

Answers

For a standing wave on a string, the wavelength is equal to twice the length of the string:
[tex]\lambda=2 L[/tex]
In our problem, L=50.0 cm=0.50 m, therefore the wavelength of the wave is
[tex]\lambda = 2 \cdot 0.50 m = 1.00 m[/tex]

And the speed of the wave is given by the product between the frequency and the wavelength of the wave:
[tex]v=\lambda f = (1.00 m)(440 Hz)=440 m/s[/tex]

Answer:

30800 m/s

Explanation:

correct answer

The molar enthalpy of fusion for water is 6.008 kj/mol. what quantity of energy is released when 253g of liquid water freezes? (molar mass of water is 18.02 g/mol)

Answers

During freezing, energy is released by the mass of water without change in temperature. Such energy will also be required if the same mass of water has to be melted.

Then,

Number of moles = mass/molar mass = 253/18.02 =14.04 moles

Energy released = moles*molar enthalpy of fusion = 14.04*6.008 = 84.35 kJ

The current through inductance L is given by I=I0e−t/τ
A.) Find an expression for the potential difference ΔVL across the inductor.
B.) Evaluate ΔVL at t=0s , if L=15mH , I0=36mA , and τ=1.1ms
C.) Evaluate ΔVL at t=1ms , if L=15mH , I0=36mA , and τ=1.1ms
D.) Evaluate ΔVL at t=2ms , if L=15mH , I0=36mA , and τ=1.1ms
E.) Evaluate ΔVL at t=3ms , if L=15mH , I0=36mA , and τ=1.1ms

Answers

Final answer:

The potential difference (voltage) across the inductor is given by VL = L*(dI/dt), which for this specific question evaluates to VL = -L*I0*(e^-t/τ) / τ. Applying the given values at different time intervals, we can find VL values at t=0s, t=1ms, t=2ms, and t=3ms.

Explanation:

The current through an inductor is given by I=I0e−t/τ. Let's answer your questions one by one:

A) The potential difference (voltage) across the inductor is given by VL = L*(dI/dt). For this particular problem, it would be VL = -L*I0*(e^-t/τ) / τ. This equation results from the fact that the rate of change of current through an inductor is related to the voltage across it.

B) At t=0s, VL would evaluate to -L*I0 / τ.

C) At t=1ms, VL would evaluate to -L*I0*(e^-1) / τ.

D) At t=2ms, VL would evaluate to -L*I0*(e^-2) / τ.

E) And finally, at t=3ms, VL would evaluate to -L*I0*(e^-3) / τ.

These calculations use the given constants L=15mH, I0=36mA, and τ=1.1ms.

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Final answer:

The potential difference across the inductor is given by the equation VL = -L*I0*e^(-t/τ)*(1/τ). Plugging in L=15mH, I0=36mA, and τ=1.1ms, evaluations for t=0, 1ms, 2ms, and 3ms yield -0.49V, -0.27V, -0.15V, and -0.08V respectively.

Explanation:

The potential difference across the inductor, ΔVL, can be determined by using Faraday's law which states that the EMF in a circuit is equal to the rate of change of magnetic flux. In this case, it corresponds to:

VL = L*(dI/dt) = L * d/dt [I0*e^(-t/τ)] = -L*I0*e^(-t/τ)*(1/τ)

From this equation, the potential difference can be evaluated at different times.

At t=0s: ΔVL = -L*I0*1/τ = - (15x10^-3)*(36x10^-3)/1.1x10^-3 = - 0.49 V At t=1ms: ΔVL = -L*I0*e^(-t/τ)*(1/τ) = - (15x10^-3)*(36x10^-3)*e^(-1/1.1)(1/1.1x10^-3) = -0.27 V At t=2ms: ΔVL = - (15x10^-3)*(36x10^-3)*e^(-2/1.1)(1/1.1x10^-3) = -0.15 V At t=3ms: ΔVL = - (15x10^-3)*(36x10^-3)*e^(-3/1.1)(1/1.1x10^-3) = -0.08 V

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