Answer:
The correct option is H
Explanation:
From the question we are told that
The index of refraction of coating is [tex]n_1[/tex]
The index of refraction of material is [tex]n_2[/tex]
Generally the condition for constructive for a thin film interference is mathematically represented
[tex]2 * t = [ m + \frac{1}{2}] \frac{\lambda}{n_1 }[/tex]
Here t represents the thickness
For minimum thickness m = 0
So
[tex]2 * t =0 + \frac{1}{2}\frac{\lambda}{n_1 }[/tex]
=> [tex]t =\frac{\lambda}{4n_1 }[/tex]
Why is a flask is wider on the bottom than on the top? allows for a more precise measurement allows for better thermal equilibrium prevents spillage to hold a thermometer
Answer:
allows for better thermal equilibrium
Explanation:
Due to the cone shape, most of the liquid will be closer to the bottom than the top. The large surface area of the bottom allows for faster heating.
In the growth stage of a product's life cycle, demand has its own momentum through word of mouth and interactive marketing.
a. True
b. False
Answer:
Advertising, events and experiences, and personal selling all become more important in the maturity stage.
Explanation:
In the growth stage, demand has its own momentum through word of mouth and interactive marketing. hope this helps you :)
Two strings are respectively 1.00 m and 2.00 m long. Which of the following wavelengths, in meters, could represent harmonics present on both strings?
1) 0.800, 0.670, 0.500
2) 1.33, 1.00, 0.500
3) 2.00, 1.00, 0.500
4) 2.00, 1.33, 1.00
5) 4.00, 2.00, 1.0
Answer:
5) 4.00, 2.00, 1.0
Explanation:
wave equation is given as;
F₀ = V / λ
Where;
F₀ is the fundamental frequency = first harmonic
Length of the string for first harmonic is given as;
L₀ = (¹/₂) λ
λ = 2 L₀
when L₀ = 1
λ = 2 x 1 = 2m
when L₀ = 2m
λ = 2 x 2 = 4m
For First harmonic, the wavelength is 2m, 4m
For second harmonic;
L₁ = (²/₂)λ
L₁ = λ
When L₁ = 1
λ = 1 m
when L₁ = 2
λ = 2 m
For second harmonic, the wavelength is 1m, 2m
Thus, the wavelength that could represent harmonics present on both strings is 4m, 2m, 1 m
What quantity, combined with universal physical quantities, can be used to determine a particle's de Broglie wavelength
Answer:
The quantity that will be combined to determine a particle's de Broglie wavelength is ENERGY.
Explanation:
Energy of a particle is given by;
E = hf
Where;
f is frequency of the particle's wave = c/λ
[tex]E = \frac{hc}{\lambda}[/tex]
[tex]\lambda= \frac{hc}{E}[/tex]
Where;
λ is the particle's de Broglie wavelength
h is the Planck's constant = 6.626 x 10⁻³⁴ J/s (This is one of the universal physical quantities)
c is the speed of light, = 3 x 10⁸ m/s (This is also one of the universal physical quantities)
E is the energy of the particle.
Therefore, the quantity that will be combined to determine a particle's de Broglie wavelength is ENERGY.
The de Broglie wavelength of a particle can be calculated using energy and universal physical parameters.
Define wavelength.The wavelength of a wave signal conveyed in space or down a wire is the distance among identical points (consecutive crests) in adjacent cycles.
When two persons have the same overall mentality and hence can communicate successfully, this is an instance of wavelength.
The de Broglie wavelength of a particle can be calculated using energy and universal physical parameters.
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In empty space, which quantity is always larger for X-ray radiation than for a radio wave?
a) amplitude
b) wavelength
c) frequency
d) speed.
Answer:
C
Explanation:
LED light bulbs are more energy efficient, last longer, cost more, and have a smaller environmental impact from manufacture to recycling or disposal. The question is which costs less: incandescent, compact fluorescent (CFL), or LED lights?
(a) Ignore the time value of money. What is the average cost per hour for 25,000 hours of light-mg in a community with exist0.15/kWh electricity: for each choice?
(b) If the light is on 5%, 30%, or 60% of the time, how long until does it take for the 25,000 hours?
(c) Which type of light should a homeowner buy?
Answer:
a) Cost_incandescent = $ 375 , Cost _CFL = $ 75 , Cost_LED = $ 45
b) total = 20833 days , total_day = 3472 days , Total_days = 1736 d
c) LED
Explanation:
This problem is interesting to solve it, we must have a very important factor, such as the equivalence of the light emitted by the three systems, let's perform the calculation for a light intensity of 1000 lumen in the three bulbs.
consumed potence
incandescent 100W = fluorescent (CFL) 20W = Led 12 W
Now if we can solve your exercise
a) Let's find the power consumed by each type of bulb in the 25000 h
E = P t
incandescent
E_incandescent = 100 25000
E_incandescent = 2.5 105 Wh
E_incandescent = 2.5 103 kWh
Fluorescent (Low Power) CFL
E_CFL = 20 25000
E _DFL = 5 102 kWh
LED
E_LED = 12 25000
E_LED = 3 102 kwh
Let's use a direct rule of proportions (rule of three) for the cost of energy, if 1 kWh costs $ 0.15, the energy calculates how much it costs
incandescent
Cost_Incandescent = 2.5 103 kW / h ($ 0.15 / 1kWh)
Cost_incandescent = $ 3.75 102 = $ 375
CFL
Cost_CFL = 5 102 0.15
Cost _CFL = $ 75
LED
Cost_LED = 3 102 0.15
Cost_LED = $ 45
Here we do not take into account the possibility of burning incandescent bulbs and there is an extra replacement cost
b) for this part we use direct proportion rules
If the day has 24 hours and the light is on for 5%, how many days are 25000 hours?
for 5% = 0.05
hours on in a day
#_hoursdays = 24 hrs 0.05 = 1.2 hrs
total days
total = 25000 / 1.2
total = 20833 days
for 30% = 0.30
# _hoursday = 24 0.30 = 7.2 h
Total_days = 25000 h (1 day / 7.2 h)
total_day = 3472 days
for 60% = 0.602
#_hours = 24 0.60 = 14.4 h
Total _days = 25000h (1day / 14.4 h)
Total_days = 1736 d
c) you should decide between the CFL and the Led are much lower.
Between these two should take into account the cost of the bulbs, if we only take into account the cost of the energy consumed, the selection should be LED
An object–spring system undergoes simple harmonic motion. If the amplitude increases but the mass of the object is not changed, the total energy of the system:______.a. undergoes a sinusoidal change. b. decreases exponentially. c. decreases. d. doesn't change. e. increases.
Answer:
The correct answer is:
doesn't change (d)
Explanation:
The total energy in a system is the sum of Kinetic and Potential energies in a system, assuming that energy is not lost to an external procedure. Now, let us define what potential and kinetic energies are:
Potential Energy: this is energy at rest or stored energy
Kinetic Energy: this is energy in motion
In a simple harmonic motion of a mass-spring system, there is no dissipative force, hence the total energy is equal to the potential and kinetic energies. The total energy is not changed rather, it varies between potential and kinetic energies depending on the point at which the mass is. The kinetic energy is greatest at the point of lowest amplitude (highest velocity) and lowest at the point of greatest amplitude (lowest velocity), while potential energy is greatest at the point of highest amplitude (lowest velocity) and lowest at the point of smallest amplitude ( highest velocity). However, at every point, the sum of kinetic and potential energies equals total energy.
how high off the ground is a book that has 120 J of potential energy and a 4-kg mass ?
Answer:
3 m
Explanation:
PE = mgh
120 J = (4 kg) (10 m/s²) h
h = 3 m
The book is 3m high from the ground.
What is potential energy?The energy by virtue of its position is called the potential energy.
PE = mgh
where, g = 9.81 m/s²
Given is the mass of book m =4kg and the potential energy P.E = 120J, then the height is
120 J = (4 kg) (10 m/s²) h
h = 3 m
Thus, the book is 3m high from the ground.
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Calculate the period of a satellite orbiting the Moon, 98 kmkm above the Moon's surface. Ignore effects of the Earth. The radius of the Moon is 1740 kmkm.
Answer:
3.6*10^18s
Explanation:
To find the period of the satellite
We need to apply kephler's third law
Which is
MP² = (4π²/G) d³
d=semi-major axis which is the distance from center of moon = 98km+1740km = 1838km
where M= mass of the moon = 7.3x10^22kg
P=period
G=newtonian gravatational constant= 6.67x10^-11
To find the Period solve for P
P = √[(4π²/G M)xd³]
P=√(4 π²/6.67x10^-22*7.3x10^22kg) x (1.838x10^6m)³]
= 3.6*10^18s
A car traveling initially at 8.0 m/s accelerates to a velocity of 14 m/s in 2.0s. What is the average acceleration of the car?
Answer:
3.0 m/s²
Explanation:
Given:
v₀ = 8.0 m/s
v = 14 m/s
t = 2.0 s
Find: a
v = at + v₀
14 m/s = a (2.0 s) + 8.0 m/s
a = 3.0 m/s²
If the plane travels at 600 km/h for 2 hours, how far has it traveled?
Explanation:
Distance = speed × time
d = (600 km/hr) (2 hr)
d = 1200 km
Joe is hiking through the woods when he decides to stop and take in the view. He is particularly interested in three objects: a squirrel sitting on a rock next to him, a tree a few meters away, and a distant mountain. As Joe is taking in the view, he thinks back to what he learned in his physics class about how the human eye works.
Light enters the eye at the curved front surface of the cornea, passes through the lens, and then strikes the retina and fovea on the back of the eye. The cornea and lens together form a compond lens system. The large difference between the index of refraction of air and that of the aqueous humor behind the cornea is responsible for most of the bending of the light rays that enter the eye, but it is the lens that allows our eyes to focus. The ciliary muscles surrounding the lens can be expanded and contracted to change the curvature of the lens, which in turn changes the effective focal length of the cornea-lens system. This in turn changes the location of the image of any object in one's field of view. Images formed on the fovea appear in focus. Images formed between the lens and the fovea appear blurry, as do images formed behind the fovea. Therefore, to focus on some object, you adjust your ciliary muscles until the image of that object is located on the fovea.
A) Joe first focuses his attention (and his eyes) on the tree. The focal length of the cornea-lens system in his eye must be __________ the distance between the front and back of his eye.
a. greater than
b. less than
c. equal to
B) Joe's eyes are focused on the tree, so the squirrel and the mountain appear out of focus. This is because the image of the squirrel is formed ______ and the image of the mountain is formed _____.
a. between the lens and fovea / between the lens and fovea
b. between the lens and fovea / behind the fovea
c. behind the fovea / between the lens and fovea
d. behind the fovea / behind the fovea
C) Joe now shifts his focus from the tree to the squirrel. To do this, the ciliary muscles in his eyes must have _____ the curvature of the lens, resulting in a(n) _______ focal length for the cornea-lens system. Note that curvature is different from radius of curvature.
a. increased / increased
b. increased / decreased
c. decreased / increased
d. decreased / decreased
Answer:
A) correct answer is C, B) correct answer is b and C) The correct answer is b
Explanation:
In the exercises of geometric optics, the equation of the constructor tells us the location of the image.
1 / f = 1 / p + 1 / q
where f is the focal length of the cornea-crystalline system, p and q are the distances to the object and the image.
In this case, the distance to the image on the retina is constant, about 3 cm. Therefore depending on the distance to the object) p = the focal length must change
1 / q = 1 / f 1 / p
let's apply this expression to our case
A) indicates that the tree is at a medium distance
so that the image is formed on the retina THE SAME AS
correct answer is C
B) The squirrel is at a smaller distance (p ') than the tree (p), therefore if we substitute in the equation above we find that q must decrease. Consequently the image is in front of the retina
The mountain is very far, suppose in infinity, so the image is BEHIND THE RETINA
therefore the correct answer is b
C) The squirrel is very close so the curvature of the lens INCREASES, resulting in a DECREASE in the focal length
The correct answer is b
Water flows through a valve with inlet and outlet velocities of 3 m/s. If the loss coefficient of the valve is 2.0, and the specific weight of water is 9800 N/m3, the pressure drop across the valve is most nearly:
Answer:
The value is [tex]\delta P = 9000 \ Pa[/tex]
Explanation:
From the question we are told that
The inlet and outlet velocity is [tex]v = 3 \ m/s[/tex]
The loss coefficient is [tex]k = 2[/tex]
Th specific weight of water is [tex]w = 9800 \ N/m^3[/tex]
Generally the pressure drop across the valve is mathematically represented as
[tex]\delta P = \frac{1}{2} * k * \rho * v^2[/tex]
Here [tex]\rho[/tex] is the density which is mathematically represented as
[tex]\rho = \frac{w}{g}[/tex]
=> [tex]\rho = \frac{9800}{9.8}[/tex]
=> [tex]\rho = 1000 \ kg/m^3[/tex]
So
[tex]\delta P = \frac{1}{2} * 2* 1000 * 3^2[/tex]
[tex]\delta P = 9000 \ Pa[/tex]
During an earthquake, the top of a building oscillates with an amplitude of 30cm at 1.5Hz.
Part A What is the magnitude of the maximum displacement from the equilibrium of the top of the building? (in cm)
Part B What is the maximum velocity of the top of the building?(in cm/s)
Part C What is the maximum acceleration of the top of the building?(in cm/s^2
A.30cm
B.282.7cm/s
C.26655cm/s²
Explanation:
A. Maximum displacement= Amplitude= 0.3m
B.mum velocity=
2πAf= 2π x 1.5x30 =282.7cm/s
C. Maximum acceleration
= ( angular velocity)² A= (2πf)² A
=( 2 x 3.142 x 1.5)² x 30
2665.5cm/s²
Which of these changes will decrease the acceleration of an object? Select the two correct answers
increasing the applied net force
decreasing its mass
increasing its mass
decreasing the applied net force
Answer:
✔️From Newton's second law of motion we know that
✔️acceleration is inversely proportional to the mass of the body
✔️Here in this question increasing the mass of body will decrease its acceleration.
Explanation:
Hope it will help you :)
A truck pulls a block 8 meters across a level surface at a force of 216 N over the course of 12 seconds. How much power did the truck use
Answer:
work = 1728
Power = 134
Explaination:
by using the formula,
Work(W)= Force(F)×Distance(D)
andPower(P)= Work(W)/Time taken(T)
Amy runs 2 blocks south, then turns around and runs 3 blocks north. what is the distance and displacement
Answer: Distance= 5 blocks and displacement= -1 block
Explanation: distance is the total length of a journey while displacement is the shortest straight length of a journey!
What effect does the velocity of a rotating object have on the centripetal force exerted on it?
Answer:
The velocity of a rotating object and the centripetal force exerted on it are proportional to each other. Centripetal force is equal to mv /r. If the velocity increases, the centripetal force increases as well.
Explanation:
The velocity has the direct effect on the centripetal force. Hence, increasing the velocity, centripetal force also increases or vice - versa.
The given problem is based on the basic concept of centripetal force and fundamentals involved in the centripetal force. The centripetal force is a center seeking force which comes to play, when any object undergoes the rotational motion around the circular path.
The mathematical expression for the centripetal force is given as,
[tex]F= \dfrac{mv^{2}}{r}[/tex]
Here,
m is the mass of an object.
v is the velocity of an object undergoing the motion around the circular path.
r is the radius of curvature.
From the concept of centripetal force, the velocity of a rotating object and the centripetal force exerted on it are proportional to each other. Centripetal force is equal to mv /r. If the velocity increases, the centripetal force increases as well.
Thus, we can conclude that the velocity has the direct effect on the centripetal force. Hence, increasing the velocity, centripetal force also increases or vice - versa.
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Which of the following is not a way that astronomers can find how much dark matter there is in cluster of galaxies?
a. Using gravitational lensing effects to make a map of how much mass a cluster of galaxies contains.
b. Observe the radio waves coming from all dark matter; from the strength of the radio waves from each cluster, estimate the amount of dark matter needed to produce them.
c. Observing X-rays from the hot gas in the cluster, and using the amount of x-ray radiation to estimate the mass of the cluster.
d. Measuring how much slower galaxies in a rich cluster or supercluster are moving than the Hubble Law would predict.
e. Measuring the speeds with which the galaxies are moving around, to estimate the mass of the cluster needed to keep them from moving away.
Answer:
b. Observe the radio waves coming from all dark matter; from the strength of the radio waves from each cluster, estimate the amount of dark matter needed to produce them.
Explanation:
The universe is thought to be made up of 85% dark matters. Dark matter is called dark because it does not appear to interact with the electromagnetic field, which means it doesn't absorb, reflect or emit electromagnetic radiation, and is therefore difficult to detect. This means that option b is wrong since radio wave is an electromagnetic wave. Dark matter is a form of matter that makes up about a quarter of the total mass–energy density of the universe. Dark matter was theorized due a variety of astrophysical observations and gravitational effects that cannot be explained by accepted theories of gravity unless there were more matter in the universe than can be seen.
you have one 100 ohm resistor what size resistor must you hook up in parallel in order to have a resistance of 99.0
Answer:
The resistor to be hooked up must be 9900 [tex]\Omega[/tex]
Explanation:
Recall how resistors in parallel combine to render an equivalent resistor:
[tex]\frac{1}{R_e} =\frac{1}{R_1} +\frac{1}{R_2}[/tex]
So we need to find which resistor (R2) we need to combine in parallel with resistor R1 (100 [tex]\Omega[/tex]) in order to obtain an equivalent resistor Re (99 [tex]\Omega[/tex]) :
[tex]\frac{1}{99} =\frac{1}{100} +\frac{1}{R_2}\\\frac{9900\,R_2}{99} =\frac{9900\,R_2}{100} +\frac{9900\,R_2}{R_2}\\100\,R_2= 99\,R_2+9900\\R_2=9900\,\,\Omega[/tex]
Complete the following statement: (In Boyle's law), the volume of a gas ________ when the ________ decreases.
Answer:
In Boyle's law the volume of a gas increases when the pressure decreases.
Explanation:
Boyle's law states that at fixed mass of gas, the volume of a gas is inversely proportional to the gas pressure, provided temperature remain constant.
Mathematically it be expressed as;
P₁V₁ = P₂V₂
As the volume of a gas increases, the pressure decreases, or as the volume of the gas decreases, the pressure of the gas increases.
Therefore, in Boyle's law the volume of a gas increases when the pressure decreases.
A wheel that is rotating at 33.3 rad/s is given an angular acceleration of 2.15 rad/s 2. Through what angle has the wheel turned when its angular speed reaches 72.0 rad/s
Answer:
The angle through which the wheel turned is 947.7 rad.
Explanation:
initial angular velocity, [tex]\omega _i[/tex] = 33.3 rad/s
angular acceleration, α = 2.15 rad/s²
final angular velocity, [tex]\omega_f[/tex] = 72 rad/s
angle the wheel turned, θ = ?
The angle through which the wheel turned can be calculated by applying the following kinematic equation;
[tex]\omega_f^2 = \omega_i^2 + 2\alpha \theta\\\\\theta = \frac{\omega_f^2\ -\ \omega_i^2}{2\alpha } \\\\\theta = \frac{(72)^2\ -\ (33.3)^2}{2(2.15)}\\\\\theta = 947.7 \ rad[/tex]
Therefore, the angle through which the wheel turned is 947.7 rad.
Imagine that you are seeking treatment from a provider who offers complementary, alternative, or integrative treatment. Write at least one (1) question you would want to ask the provider about their education or credentials.
Explanation:
It is important to reach a decision only after noting the quality of responses received about the following pertinent questions;
1. What training program(s) have they gone through?
2. Do they have any licences?
3. Have they received any certifications from a recognized body?
4. Do they have any ongoing or past scientific research work?
5. Awards they've received, if any?
As this is a key decision of someone's life, making the decision on the basis of the provider's experience with similar cases and quality of service is the most important.
We should ask the following questions to the provider,
1. Does the practitioner have licenses for such practice?
2. Where did the practitioner receive their educational qualifications from and do they still learn to be up to date with the advanced treatments available in the market?
3. Was the practitioner awarded for any similar cases or handled similar cases?
4. For how long they have been practicing?
5. Does the practitioner have a membership of any organizations or professional societies?
6. Can the treatment be covered by the insurance?
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If i push a ball along the floor, which forces are acting upon the ball? Name atleast two forces and explain them !
Answer:
Hey there!
You are applying a force, pushing the ball, which makes the ball move forwards.
Friction is working in the opposite direction, slowing the ball down as it rolls on the floor.
Let me know if this helps :)
A cubic container holds 2,350 g of fresh water. Use density and the volume formula below to
compute the dimensions of the tank.
V = 93
Density of Water: 1.00 g/cm3
O 13 cm^3
13.20 cm
O 13.3 cm^3
13.3 cm
O 13 cm
Answer:
Each side is 13.3 cm long
Explanation:
Use the formula for density as the mass per unit of volume, to find the volume of the tank:
[tex]density=\frac{mass}{Vol} \\Vol=\frac{2350}{1} \,\,cm^3\\Vol=2350\,\,cm^3[/tex]
Now we can find the dimensions of the tank knowing that it is cubic, and therefore its volume is [tex]side^3[/tex]:
[tex]side^3=2350\,\,cm^3\\side=\sqrt[3]{2350} \,\,cm\\side\aprox13.3\,\,cm[/tex]
A 100-kg tackler moving at a speed of 2.6 m/s meets head-on (and holds on to) an 92-kg halfback moving at a speed of 5.0 m/s. Part A What will be their mutual speed immediately after the collision? Express your answer to two significant figures and include the appropriate units.
Given that,
Mass of trackler, m₁ = 100 kg
Speed of trackler, u₁ = 2.6 m/s
Mass of halfback, m₂ = 92 kg
Speed of halfback, u₂ = -5 m/s (direction is opposite)
To find,
Mutual speed immediately after the collision.
Solution,
The momentum of the system remains conserved in this case. Let v is the mutual speed after the collision. Using conservation of momentum as :
[tex]m_1u_1+m_2u_2=(m_1+m_2)V\\\\V=\dfrac{m_1u_1+m_2u_2}{(m_1+m_2)}\\\\V=\dfrac{100\times 2.6+92\times (-5)}{(100+92)}\\\\V=-1.04\ m/s[/tex]
So, the mutual speed immediately after the collision is 1.04 m/s but in opposite direction.
A small candle is 34 cm from a concave mirror having a radius of curvature of 22 cm. Where will the image of the candle be located? Follow the sign conventions.
Answer:
16.26 cm in front of the mirror
Explanation:
Using,
1/f = 1/u+1/v....................... Equation 1
Where f = focal focal length of the concave mirror, u = object distance, v = image distance.
make v the subject of the equation
v = fu/(u-f)................... Equation 2
Note: The focal length of a concave mirror is positive
Using the real- is- positive convention
Given: f = 22/2 = 11 cm, u = 34 cm.
Substitute into equation 2
v = (34×11)/(34-11)
v = 374/23
v = 16.26 cm.
The image will be formed 16.26 cm in front of the mirror.
pls help me solve dis
Answer:
9 Ω
Explanation:
The following data were obtained from the question:
Resistor 1 (R1) = 3 Ω
Resistor 2 (R2) = 3 Ω
Resistor 3 (R3) = 3 Ω
Resistor 4 (R4) = 3 Ω
Resistor 5 (R5) = 3 Ω
Resistor 6 (R6) = 3 Ω
Resistor 7 (R7) = 3 Ω
Resistor 8 (R8) = 3 Ω
Resistor 9 (R9) = 3 Ω
Resistor 10 (R10) = 3 Ω
Resistor 11 (R11) = 3 Ω
Resistor 12 (R12) = 3 Ω
Equivalent Resistance (R) =.?
From the above diagram,
Resistor 1, 2, 3, 4, 5 and 6 are in series connection and in parralle connections with Resistor 7, 8, 9, 10, 11 and 12 which are also in series connection.
Thus we shall determine the equivalent resistance of Resistor 1, 2, 3, 4, 5 and 6
This is illustrated below:
Resistance Ra = R1 + R2 + R3 + R4 + R5 + R6
Ra = 3 + 3 + 3 + 3 + 3 + 3
Ra = 18 Ω
Next, we shall determine the equivalent resistance of Resistor 7, 8, 9, 10, 11 and 12.
This is illustrated below:
Resistance Rb = R7 + R8 + R9 + R10 + R11 + R12
Rb = 3 + 3 + 3 + 3 + 3 + 3
Rb = 18 Ω
Thus, Ra and Rb are in parallel connections. The equivalent resistance between A and B can be obtained as shown below :
Ra = 18 Ω
Rb = 18 Ω
Equivalent resistance R =?
1/R = 1/Ra + 1/Rb
1/R = 1/18 + 1/18
1/R = 2/18
1/R = 1/9
Invert
R = 9 Ω
Therefore, the equivalent resistance between A and B is 9 Ω.
Parallel rays of monochromatic light with wavelength 582 nm illuminate two identical slits and produce an interference pattern on a screen that is 75.0 cm from the slits. The centers of the slits are 0.640 mm apart and the width of each slit is 0.434 mm. If the intensity at the center of the central maximum is 4.40×10^−4 W/m^2.
Required:
What is the intensity at a point on the screen that is 0.710 mm from the center of the central maximum?
Answer:
I = 0.56 10⁻⁴ W / m²
Explanation:
Double-slit interference is described by the expression
d sin θ = m λ
if we use trigonometry we can find the angle
tan θ= y / L
how the angles are small
tan θ = sin θ / cos θ = sin θ
sin θ = y / L
we substitute
d y / L = m λ
if we take into account that each slit also produces a diffraction phenomenon, the intensity distribution is the product of the intensity of the slits by the intensity of the diffraction process
I = I₀ cos² (d a) [(sin ba) / ba]²
a = π sin θ /λ
where the separation of the slits and b is the width of the slits
we substitute
I = I₀ [cos (d a)]² [sin ba /ba]²
a = π y / (L λ)
let's reduce the magnitudes to the SI system
λ = 582 nm = 582 10⁻⁹ m
L = 75.0 cm = 75.0 10⁻² m
d = 0.640 mm = 0.640 10⁻³ m
b = 0.434 mm = 0.434 10⁻³ m
Io = 4.40 10⁻⁴ W / m²
let's calculate for y = 0.710 mm = 0.710 10⁻³ m
a = π 0.710 10⁻³ / (75 10⁻² 582 10⁻⁹)
a = 5.11004 10³
I = 4.40 10⁻⁴ [cos (0.640 10⁻³ 5.11004 10³)]² (sin (0.434 10⁻³ 5.11004 10³) / (0.434 10⁻³ 5.11 10³)²
I = 4.40 10⁻⁴ cos² (3.2704) (sin 2.2178 / 2.2178)²
remember that the angles are in radians
I = 4.40 10⁻⁴ 0.9835 (0.79789 / 2.2178)²
I = 4.40 10⁻⁴ 0.9835 0.1294
I = 0.56 10⁻⁴ W / m²
A 5.0 V battery storing 43.0 kJ of energy supplies 1.5 A of current to a circuit. How much energy does the battery have left after powering the circuit for 1.0 h? A. 43 kJ B. 16 kJ C. 41 kJ D. 27 kJ
Answer:
B. 16 kJ
Explanation:
Energy = VIt.............. Equation 1
Where V = Voltage, I = Current, t = time
Given: V = 5.0 V, I = 1.5 A, t = 1 h = 3600 s.
Substitute these values into equation 2
E = 5.0(1.5)(3600)
E = 27000 J
E = 27 kJ.
Amount of energy left = 43 kJ - 27 kJ
Amount of energy left = 16 kJ.
Hence the right option is B. 16 kJ