The answer to the question is that both the current and the frequency will grow as they become increasingly high and low, respectively.
What purpose does a capacitor serve?A capacitor is an electrical energy storage device made up of two conductors that are isolated from one another and placed near to one another. A straightforward illustration of one such backup system is a parallel-plate capacitor.
A capacitor: a type of battery?A capacitor is a passive component that holds static charge in an electric field, whereas a batteries is an electronic device that transforms chemical energy into electricity to create a stable electrical charge for power.
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by what factor must you increase the force you exert on the rope to cause the speed to increase by a factor of 1.90?
In order to raise the speed by a factor of 1.90, you must increase the force you apply to the rope by a factor of 3.61. the speed of a change in an object's location in any direction.
Speed is defined as the ratio of distance to the amount of time it took to cover that distance. Due to its lack of magnitude and merely having a direction, speed is a scalar number. A moving object is said to be moving at a variable pace when it travels a varying distance at regular intervals. Speed on average: The consistent force that results from dividing the whole distance travelled by an object by the total time it takes to traverse that distance is known as average force.
Velocity = (T/m)
V1 = (T1/m)^1/2
V2 = (T2/m)^1/2
v2 =1.9v1
1.9 = (T2/T1)^1/2
T2/T1 = 3.61
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A coil 4.40 cm radius, containing 470 turns, is placed in a uniform magnetic field that varies with time according to B=( 1.20×10−2 T/s )t+( 2.90×10−5 T/s4 )t4. The coil is connected to a 530-Ω resistor, and its plane is perpendicular to the magnetic field. You can ignore the resistance of the coil.
Part A
Find the magnitude of the induced emf in the coil as a function of time.
E= 1.09×10−2 V +( 1.06×10−4 V/s3 )t3
E= 3.43×10−2 V +( 8.29×10−5 V/s3 )t3
E= 3.43×10−2 V +( 3.32×10−4 V/s3 )t3
E= 1.09×10−2 V +( 3.32×10−4 V/s3 )t3
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Part B
What is the current in the resistor at time t0 = 4.50 s ?
I =
The current in the resistor at time 4.50 s is 1.2179 X 10⁻⁴ A and the magnitude of induced EMF in the coil is (3.43 × 10⁻² V ) + ( 3.32 × 10⁻⁴ V/s³) t³.
Number of turns of coil = N = 470
Radius of the coil = R = 4.40 cm = 0.044 m
Magnetic field varying according to time = B = ( 1.20×10⁻² T/s )t +(2.90×10⁻⁵ T/s⁴ )t⁴
Resistance of the resistor = 530 Ω
Part A :
The flux over the coil is = φ =
= φ = nBA
= φ = 470 X B X (π X 0.044)
= φ = 2.85 (( 1.20 × 10⁻² T/s )t +(2.90×10⁻⁵ T/s⁴ )t⁴)
The magnitude of EMF is = E =
= E = dφ / dt
= E = 2.85 (1.20 × 10⁻² + 11.60 × 10⁻⁵ t³)
= E = (3.43 × 10⁻² V ) + ( 3.32 × 10⁻⁴ V/s³) t³
Part B:
The current in the coil = I =
= I = E / R
= I = (3.43 × 10⁻² V ) + ( 3.32 × 10⁻⁴ V/s³) t³ / 530
= I = 1.2179 X 10⁻⁴ A
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suppose you are on a ship in the north pacific ocean. you notice that the wind is blowing out of the west toward the east. if you look over the edge of the ship, to which direction would the net ekman transport be directed?
To south direction would the net ekman transport be directed when the wind is blowing out of the west toward the east.
When the wind is coming from the north, upwelling happens along the western coasts of the Northern Hemisphere because the net transport of near-surface water is away from the shore. Along the eastern shores of the Northern Hemisphere, winds from the south cause upwelling. Ekman transport occurs when wind-induced friction forces on ocean surface waters have an impact. The top 10-100 meters of the water column are pulled along by the friction force that the wind creates as it blows on the ocean's surface.
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a beam of monochromatic light with a wavelength of 580 nm in air travels into water. what is the wavelength of the light in water? give your answer in nanometers
The wavelength of the light which travels from air to water is 436.09 nm
The wavelength of the light in air = 580 nm
The light travels from air to water is
μ = 4/3
The formula to find the wavelength of the light in the air can be found using the formula
ν = c/μ
It can be rewritten as
λₙ = λ₀ / μ
where λₙ is the wavelength of light in water
λ₀ is the wavelength of light in water
μ is the relative refractive index
Let us substitute the known values in the above equation, we get
λₙ = 580 x 10⁻⁹ / 1.333
= 436. 09 nm
Therefore, the wavelength of light in water is 436.09 nm
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(a) if you move the particle of charge q from point a to point d, is the change in the electric potential energy of the three-particle system positive, negative, or zero?
Answer: The change in the electric potential energy of the three-particle system positive, negative, or zero is negatively charged particle
Reason:
The change in the electric potential energy of the three-particle system, when moved from A to D, is zero. The work done by the net electric force on the particle when moved from A to D is negative.
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what range of spring constant values will cause the motion of the system to have damped oscillation?
The range of spring constant values is less than 2√Km that will cause the motion of the system to have damped oscillation is given.
[tex]\beta =\left \{ {{y=2\sqrt{km} } \atop {y > 2\sqrt{km} }} \right.[/tex]
[tex]\beta =\left \{ {{b\leq 2\sqrt{Km}----under-damping }[/tex]
When b≤ 4mk, the damping constant, is low, the system oscillates while the motion's amplitude decays exponentially. Then this system is underdamped.After displacement, a body will oscillate on its own accord at its natural frequency. However, as the oscillation continues to lose amplitude, it eventually comes to an end.Non-conservative forces like friction within the oscillation system are what lead to the decrease in amplitude. The term "dissipative forces" also refers to the non-conservative forces.
The oscillations eventually stop if the friction between the box's surface and the floor is not ignored. The force that dampens the oscillation is referred to as the damping force.
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an open tank has the shape of a right circular cone (see figure). the tank is 8 feet across the top and 6 feet high. how much work is done in emptying the tank by pumping the water over the top edge? (the weight-density of water is 62.4 pounds per cubic foot.) ft-lb
The amount of work done in emptying the tank by pumping the water over the top edge is 163.01* 10³ ft-lbs.
Given that, the tank is 8 feet across the top and 6 feet high
By the property of similar triangles, 4/6 = r/y
6r = 4y
r = 4/6*y = 2/3*y
Each disc is a circle with area, A = π(2/3*y)² = 4π/9*y²
The weight of each disc is m = ρw* A
m = 62.4* 4π/9*y² = 87.08*y²
The distance pumped is 6-y.
The work done in pumping the tank by pumping the water over the top edge is
W = 87.08 ∫(6-y)y² dy
W = 87.08 ∫(6y³ - y²) dy
W = 87.08 [6y⁴/4 - y³/3]
W = 87.08 [3y⁴/2- y³/3]
The limits are from 0 to 6.
W = 87.08 [3*6⁴/2 - 6³/3] = 87.08* [9*6³ - 2*36] = 87.08(1872) = 163013.76 ft-lbs
The amount of work done in emptying the tank by pumping the water over the top edge is 163013.76 ft-lbs.
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describe the sizes of stars along the main sequence. what are stars like near the top of the main sequence, the middle, and the bottom
The sizes of stars Super Giant Stars, Giant Stars ,Main Sequence White Dwarf Stars .Based on their temperature, the stars are categorized, with O being the hottest and M being the coldest. O-B-A-F-G-K-M
What are stars known as?Any big, large celestial mass that is personality and produces light from its own internal renewable resources is referred to be a star. Only a very small portion of the hundreds of milliards of trillions of in the observable cosmos are visible.
Why is a star created?When light element atoms are compressed put under a lot compression allowing their nuclei to fuse, a star is created. All stars are still the consequence of an equilibrium of forces gravity pulls interstellar gas's atoms together until fusion reactions start.
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A stone is dropped from the upper observation deck (the Space Deck) of the CN Tower, 450m above the ground.
a) Find position function s(t) of the stone above the ground level at time t. Assume g=9.8 m/s2.
b) How long does it take the stone to reach the ground?
c) What is the impact velocity of the stone when it hits the ground? d) If the stone is thrown downward with a speed of 5m/s. How long does it take to reach the g
Since the acceleration of gravity can be considered a constant for this situation the below formulas can be derived:
The acceleration due to gravity value of 9.8 m/[tex]s^2[/tex] means that the velocity of a body falling freely changes by 9.8 m/s every second.
(a) acceleration = g = constant = -9.81 m/[tex]s^2[/tex] dv/dt
(b) velocity =[tex]V_0[/tex] -gt = ds/dt
(c) Position s=[tex]s_0[/tex]+[tex]V_0[/tex]t -1/2g[tex]t^2[/tex]
a) Therefore in this problem [tex]s_0[/tex]= 450 m and [tex]V_0[/tex] = 0, s(t) = 450 -1/2g[tex]t^2[/tex]
b) The time to reach the ground is found by solving the position equation for s=0 yielding 9.58 sec
c) The impact velocity is found by solving 2) for t= 9.58 sec yielding -94 m/s ( neg means down).
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Determine which the following are defined Whenever they occur denctes multivariable function and denotes vector field both of which are twice continuously differentiable on common domain_ (Select all that apply.) V . (F . Vf) V. (V x Vf) V x (V . F) V x (V x f) V x (V x F) V . (V x F)
Yes, all of these are defined whenever they occur, and they denote multivariable functions and vector fields that are twice continuously differentiable on a common domain.
What is multivariable function?
The extension with one calculus to calculus with functions of multiple variables, or the differentiation as well as integration of functions involving different variables as opposed to just one, is known as multivariable function(also recognised as multivariate calculus). Calculus with multiple variables can be seen as an introduction to more complex calculus. Check out calculus on Euclidean space for advanced calculus. The term "vector calculus" refers to the special particular instance of calculus throughout three dimensional space.
For example, V . (F . Vf) denotes a multivariable function and vector field that is twice continuously differentiable. This expression can be interpreted as the dot product of the vector V and the product of the function F and the vector field Vf.
Similarly, V x (V x f) denotes a multivariable function and vector field that is twice continuously differentiable. This expression can be interpreted as the cross product of the vector V and the cross product of the vector V and the function f.
Likewise, V x (V x F) and V . (V x F) denote multivariable functions and vector fields that are twice continuously differentiable. These expressions can be interpreted as the cross product of the vector V and the cross product of the vector V and the function F, and the dot product of the vector V and the cross product of the vector V and the function F, respectively.
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Sam, whose mass is 75 kg, straps on his skis and starts down a 50-m-high, 20 ^\circ frictionless slope. A strong headwind exerts a horizontal force of 200 N on him as he skies.
a)Find Sam's speed at the bottom using work and energy.
b)Find Sam's speed at the bottom using Newton's laws.
At the base of the incline, Sam is moving at a speed of 15.73 m/s. who weighs 75 kg puts on his skis and begins to descend a 50 m-high, 20 frictionless slope.
Sam's bottom-of-the-screen speed is determined using the Work-Energy Theorem as follows: An object moves parallel to the plane on a slope with no friction. Both the normal force and the gravitational perpendicular component cancel each other out because they are acting in the same speed. Therefore, an object on a frictionless slope is solely accelerated by the gravitational parallel component. On a surface on an inclined plane with no friction, any item accelerates.
delta W is equal to the delta kinetic energy for frictionless slope
(36750 - 27472) = 1/2*75*(v2 -0).
9278=37.5(v^2)
v^2 = 9278/37.5(v2)
v^2 = 247.4v = 15.73 m/s
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is only capable of pushing a car with a force of 800 n. how fast must the car be moving at the bottom of the hill so that his 800 n force will be just enough to get it to the top of the hill
It will depend on your frame of reference, assuming no energy is lost in the conversion of energy to motion.
Newton's first law asserts that an object in motion will remain in motion until acted on by a force. The car will remain in motion as long as the forces on it are balanced. However, we currently consider a motion to be moved relative to a frame of reference; depending on your perspective, the car could be traveling forward, backward, or not moving at all.
An external force is described as a change in mechanical energy, which can be either kinetic or potential energy in an item. External agents cause these forces. Friction, normal force, and air resistance are examples of external forces. Because stationery is simply a constant speed of 0. So the pace is constant.
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which of the following is not a scale of measurement? a. ordinal b. nominal c. interval d. categorical
A scale of measurement - a. ordinal
Categorical not a scale of measurement.
Quantitative data are measured using interval or ratio scales, and categorical data are measured using nominal or ordinal scales.
As a result, based on the choices provided, the right response is d). categorical. All of the others are scales of measurement. There are four types of measurement scales: ratio, interval, ordinal, and nominal.
Categorical is a type of Data and not measurement.
Each scale of measurement has characteristics that dictate how the data should be analyzed. categorical rather than having a scale.
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two particles of mass m and 3m are moving with the same speed v in a vacuum at right angles with the particle of mass m moving in the x-direction and the particle of mass 3m moving in the negative y-direction. a
If the two particles are moving at the same speed in a vacuum, then their kinetic energy will be the same. The kinetic energy of a particle is given by the equation:
KE = (1/2)mv^2
Where KE is the kinetic energy of the particle, m is its mass, and v is its speed.
In this case, the kinetic energy of the particle with mass m will be:
KE = (1/2)m*v^2
And the kinetic energy of the particle with mass 3m will be:
KE = (1/2)3mv^2 = (3/2)mv^2
Since the particles have the same kinetic energy, we can set the two equations equal to each other and solve for v:
(1/2)mv^2 = (3/2)mv^2
(1/2)*v^2 = (3/2)*v^2
1/2 = 3/2
This equation does not have a valid solution, which means that the two particles cannot be moving at the same speed in a vacuum if one has a mass of m and the other has a mass of 3m.
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The student decides to build a model transformer.
The transformer is a step-up transformer which doubles the input voltage.
Describe how they could build this step-up transformer in a science laboratory.
Answer:
hhh
Explanation:
Which type of electromagnetic radiation is used in security baggage
scanners, and why?
Answer :millimeter-wave
Explanation: Because, it uses low-energy non-ionizing radiation that releases thousands of times less energy than a cell phone.
which type of galaxy is very difficult to see, but (astronomers recently realized) may be very common?
Although incredibly difficult to view, dwarf elliptical galaxies may be very widespread.
Do you know the truth about dwarf galaxy clusters?Dwarf On a smaller scale than conventional elliptical galaxies, elliptical galaxies seem to share much of the same global characteristics. They have an elliptical shape, little to no gas, and no signs of recent star formation.
what is The Milky Way is elliptical, ?The Night Sky is a massive cluster of stars, gas, and dust. Because it would appear to be a whirling pinwheel from top or bottom, this galaxy is known as a spiral galaxy. About 25,000 light-years from the galactic center, in one of the spiral arms, is where the Sun can be found.
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The following images show the four terrestrial planets in our solar system. Rank these planets from left to right based on the atmospheric pressure at the surface, from highest to lowest.
Venus, Earth, Mars, Mercury
Because of their compact, rocky surfaces akin to Earth's terra firma, Mercury, Venus, Earth, and Mars are together referred to as terrestrial planets.The four planets closest to the sun are those that make up the terrestrial planets.
What four qualities do terrestrial planets possess?The four innermost planets are known called terrestrial planets and have features like a moon, valleys, volcanoes, and craters, as well as a liquid heavy-metal core and at least one moon.
What distinguishes a terrestrial planet?Because of their compact, rocky surfaces akin to Earth's terra firma, the planets Mercury, Venus, Earth, and Mars are referred to as terrestrial.
The four planets closest to the sun are the terrestrial planets.
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in the past, asteroids striking the earth have produced disastrous results. if we discovered an asteroid on a collision course with the earth, we could, in principle, deflect it and avoid an impact by focusing a laser on the surface. intense surface heating from the laser could cause surface material to be ejected into space at high speed.
By focusing a laser on the surface of a asteroid, the intense surface heating from the laser could cause surface material to be ejected into space at high speed due to change in the momentum
Since the surface material is ejected into space at high speed, it has significant momentum. And since the asteroid and all of its component are considered as an isolated system, the total momentum is conserved according to law of conservation of momentum.
So, as the surface material is ejected with momentum, this causes a change in the momentum of the asteroid in the opposite direction. This change reduces the speed of the asteroid gradually decreasing its momentum, or it gives the asteroid a speed in a different direction causing it to be deflected from its path.
The given question is incomplete. The complete question is:
In the past, asteroids striking the earth have produced disastrous results. If we discovered the asteroid on a collision course with the earth, we could, in principle, deflect it and avoid an impact by focusing a laser on the surface. Intense surface heating from the laser could cause surface material to be ejected into space at high speed. How would this deflect the asteroid?
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a ball is shot from the ground straight up into the air with initial velocity of 42 ft/sec. assuming that the air resistance can be ignored, how high does it go?
A ball is shot from the ground straight up into the air with initial velocity of 42 ft/sec. Assuming that the air resistance can be ignored, how high does it go? The acceleration due to gravity is 32 ft per second squared.
The maximum height reached by the ball is 27.56 ft.
The given parameters;
initial velocity of the ball, u = 42 ft/s
acceleration of the ball, a = 32 ft/s²
The maximum height reached by the ball is calculated as follows;
v² = u²- 2gh
where;
v is the velocity of the ball at maximum height = 0
0 = u² - 2gh
2gh = u²
h = u^2/2g
h = (42)^2 / 2*32
h = 27.56 ft
Acceleration, price at which velocity modifications with time, in terms of both speed and route. A factor or an object transferring in a immediately line is elevated if it accelerates or slows down.
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The average kinetic energy of gas molecules is ________ proportional to the absolute temperature.
The average Kinetic energy of the molecules of a gas is directly proportional to the absolute temperature.
How is K.E proportional to absolute temperature?We know that Kinetic energy is given by the equation ,
[tex]K = \frac{1}{2} mv^{2}[/tex]
where ,
K = kinetic energy
m = mass
v = velocity
Since the square of a particle's velocity is precisely proportional to the kinetic energy of a gas, kinetic energy likewise rises when temperature rises.As a result, the relationship between a gas's kinetic energy and absolute temperature is linear.The kinetic energy of the gas molecules increases as the temperature rises, increasing their rate of motion.The speed of the gas molecules' motion, or their kinetic energy, falls as the temperature drops.A gas's average molecular kinetic energy is inversely related to its absolute temperature.What is absolute temperature?The Kelvin scale, where 0 represents absolute zero, is used to measure absolute temperature. The temperature at which matter's particles move the least and cannot cool down is known as the zero point (minimum energy). A thermodynamic temperature reading does not include a degree symbol because it is "absolute" in nature.
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A nonrelativistic electron and a nonrelativistic proton have the same de Broglie wavelength. Which of the following statements about these particles are accurate? (There may be more than one correct choice.)A) Both particles have the same speed.B) The electron has more momentum than the proton.C) The electron has more kinetic energy than the proton.D) Both particles have the same kinetic energy.E) Both particles have the same momentum.
A nonrelativistic electron and a nonrelativistic proton have the same de Broglie wavelength and both particles have the same momentum and the electron has more kinetic energy than the proton.
The electron is a subatomic particle with a bad standard electric charge. Electrons belong to the primary technology of the lepton particle's own family and are typically thought to be fundamental particles because they have no recognized additives or substructure.
For most realistic purposes, an electron is a structureless particle with an intrinsic angular momentum or spin. simply two numbers — the electron's mass and its electric price — gasoline the equations that describe its behavior. From this 'sensible electron' version, physicists constructed present-day microelectronics.
By using the best values for the wavelength and the scattering by a matter of tough X-rays and ?-rays, the radius of the electron is anticipated as approximately 2 × 10-10 cm.
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A carbon atom usually has 6 protons and 6 neutrons. Carbon-14 is a type of carbon with atoms that contain 6 protons and 8 neutrons. Carbon-14 can be used to find the age of certain fossils. Carbon-14 is an example of a(n).
Carbon-14 is an example of an Isotopes.
Isotopes can be defined as variants of chemical elements that have the same number of protons and electrons but different numbers of neutrons.
In other words, isotopes are variants of elements that differ in the number of nucleons (the total number of protons and neutrons) due to the difference in the total number of neutrons in their respective nuclei.A carbon atom usually has 6 protons and 6 neutrons.
Also, Carbon-14 contains an atomic nucleus of 8 neutrons along with 6 protons.
Both the carbon atoms have the same number of protons, but different number of neutrons, hence they can be termed as the isotopes.
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The electrochemical gradient that determines how a charged ion will move through a permeable membrane depends upon the electrical forces acting on that ion the difference in concentration of that ion on either side of the membrane the ratio between the charge on the ion and its atomic mass athe combined effects of electrical forces and concentration differences across the membrane Allof the choices for this question are correct
The combined effects of electrical forces and concentration differences across the membrane.
Since there are less positive ions within the cell due to the ion gradient, the interior is negative in comparison to the exterior forces. The ensuing membrane potential favors positively charged ions entering the cell and negatively charged ions exiting the cell. A combination of a concentration gradient and an electrical field gradient, the electrochemical gradient controls the direction in which ions will flow through an open ion channel. These two gradients may be taken into account individually. Energy can be released when the ions return down their electrochemical gradients, which primary active transport creates. The energy stored in these gradients is used in secondary active transport to move other materials against their own gradients.
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A force of 5. 0 n moves a 6. 0 kg object along a rough floor at a constant speed of 2. 5 m/s. (a) how much work is done in 25 s? (b) what power is being used? (c) what force of friction is acting on the object?.
Total work done by 5N force is 312.5 J and power used is 12J/s
Speed of object = 2.5 m/s
Time the object moves = 25 s
Since no acceleration is given,
Distance = Speed * Time
Distance = 2.5 * 2.5
Distance = 6.25
i.e. Distance travelled by the block is 62.5m.
F= Force on object = 5N
Work done = Force * Displacement
W = F * S
W = 5 * 62.5
W = 312.5 J
Total work done by 5N force is 312.5 J.
We know that: Power = Work/time
i.e. Power = 312.5/25 = 12 J/s
So power being used is 12 J/s
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Which of the following quantities are needed to calculate the numerical change in vapor pressure with change in temperature, using the Clausius Clapeytron equation? Assume that both the initial and final temperatures are known. Select all that apply.
To calculate the numerical change in vapor pressure with change in temperature, using the Clausius Clapeytron equation, change in enthalpy are needed.
What is the Clausius Clapeytron equation?
The Rudolf Clausius and Benoît Paul Émile Clapeyron equation, which describes a discontinuous phase change between two phases of a single constituent, was created. The relationship between a liquid's temperature and vapour pressure is not a straight line.
For instance, the temperature of the system rises considerably more slowly than the vapour pressure in the water. This activity will be explained via the Clausius equation. The balance between a liquid and its vapour is determined by the system's temperature; a rise in temperature causes a subsequent rise in the liquid's vapour pressure.
The following is the Clausius-Clapeyron equation in thermodynamics:
ln(P₂/P₁) = ΔH/R(1/T₁ - 1/T₂)
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TRUE/FALSE. during normal operation of a typical 120-volt appliance circuit, current flows through the hot, grounding, and neutral conductors.
FALSE: Current travels via the hot, grounding, & neutral conductors of a typical 120-volt appliance circuit during normal operation.
The statement is false
Explain the role of conductors.A substance or medium that permits energy to flow through it is known as a conductor or electrical conductor. When voltage is supplied, the electrical charge carriers—typically electrons or ions—in a conductor flow effortlessly from atom to atom.
Which four kinds of insulators are examples?Glass, plastic, rubber, air, & wood are a few popular types of insulators. To shield humans from the potentially harmful effects of power going through conductors, insulators are used. Electrical circuits can occasionally have exceedingly high and hazardous voltage levels.
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Suppose you were far from a planet that had a very strong gravitational field and you were watching a clock on the surface of the planet. During the time in which your own clock ticks out a time of 1 hour, how much time does the clock on the planet tick out?
Less than 1 hour (but more than zero)
The answer is: Less than 1 hour (but more than zero)
What is gravitational field?
In physics, a gravitational field is a model used to describe the effect of a massive object extending into the space around it and creating a force on another massive object. Gravitational fields are therefore used to describe gravitational phenomena and are measured in Newtons per kilogram (N/kg). It is therefore measured in square meters per second (m/s2).
In the original concept, gravity was the force between point masses. Borrowing from Isaac Newton, Pierre-Simon Laplace attempted to model gravity as a kind of radiation field or fluid. Since the 19th century, explanations of gravity have usually been taught in terms of field models rather than point attraction
In the field model, instead of two particles attracting each other, the particles distort space-time with their mass. This distortion is perceived and measured as a 'force' that moves in a certain way depending on the curvature of spacetime. And either gravity doesn't exist or gravity is an imaginary force.
Therefore, The answer is: Less than 1 hour (but more than zero)
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a certain camera lens has a focal length of 175 mm. its position can be adjusted to produce images when the lens is between 180 mm and 210 mm from the plane of the film. over what range of object distances is the lens useful?
The useful range of object distances of the lens is 1.05 m and 6.3 m.
Focal length of the camera = 175 mm
Distance of Image 1 = i₁ = 180 mm
Distance of Image 2 = i₂ = 210 mm
Since the distance between the images is positive, hence we get real images.
Using thin lens equation,
= (1/f) = (1/i) + (1/o)
For image 1,
= (1/o₁) = (1/f) - (1/i₁)
= (1/o₁) = (1/175) - (1/180)
= o₁ = 6299.4 mm = 6.3 m
Similarly for image 2,
= (1/o₂) = (1/f) - (1/i₂)
= (1/o₂) = (1/175) - (1/210)
= o₂ = 1050 mm = 1.05 m
Thus, any object between 1.05 m and 6.3 m will be useful.
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Light is refracted through a diamond. If the angle of incidence is 30°, and the angle of refraction is 12°, what is the index of refraction?.
The index of refraction is 2.45
This can be found by Snell's law. This law is defined as
“The ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant, for the light of a given color and for the given pair of media”. It is also known as Snell–Descartes law and the law of refraction.
The data given in the question is as follows;
Θi = 30°
Θr = 12°
μ = ?
The formula which is used here will be;
μ = [tex]\frac{sin i}{sin r}[/tex]
By putting values in the formula we will get the answer as follows
μ = [tex]\frac{sin 30}{sin 12}[/tex]
μ = [tex]\frac{0.5}{0.2079}[/tex]
μ = 2.45
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