Answer:
Approximately [tex]2.7\times 10^{4}\; \rm kg \cdot m \cdot s^{-1}[/tex].
Explanation:
The two colliding objects would be stuck to each other if the collision is perfectly inelastic. While kinetic energy is conserved only in elastic collisions, momentum is conserved in all types of collisions. Therefore, the momentum of the truck and the car right after the collision will be equal to the vector sum of their momentum right before the collision.
Momentum of the car right before the collision:
[tex]\vec{p}(\text{car, before}) = m \cdot \vec{v} = 800\; \rm kg \times 18\; \rm m \cdot s^{-1}= 14400\; \rm kg \cdot m \cdot s^{-1}[/tex].
Momentum of the truck right before the collision:
[tex]\vec{p}(\text{truck, before}) = m \cdot \vec{v} = 1500\; \rm kg \times 15 \; \rm m \cdot s^{-1} = 22500\; \rm kg \cdot m \cdot s^{-1}[/tex].
Note that these two momentum are perpendicular to each other. The magnitude of their vector sum should be found using the Pythagorean theorem:
[tex]\begin{aligned}&\left|\vec{p}(\text{sum, before})\right| \\ &= \left|\vec{p}(\text{car, before}) + \vec{p}(\text{truck, before})\right| \\ &= \left(\sqrt{14400^2 + 22500^2}\right)\; \rm kg \cdot m \cdot s^{-1} \approx 2.7\times 10^{4}\; \rm kg \cdot m \cdot s^{-1} \end{aligned}[/tex].
Because momentum is conserved, the sum of the momentum of the car and the truck right after the collision should be equal to the sum right before the collision. In other words:
[tex]\vec{p}(\text{sum, after}) = \vec{p}(\text{sum, before})[/tex].
Therefore:
[tex]\left|\vec{p}(\text{sum, after})\right| = \left|\vec{p}(\text{sum, before})\right| \approx 2.7 \times 10^{4}\; \rm kg \cdot m \cdot s^{-1}[/tex].
Three identical point charges, Q = 2 PC, are placed at the vertices of an equilateral triangle as shown in the figure. The length of each side of the triangle is d
= 2 m. Determine the magnitude and direction of the total electrostatic force on the charge at the top of the triangle.
Answer:
The total force on the charge at the top of the triangle is approximately
[tex]1.56\,\,10^{-14}\,\,N[/tex]
Explanation:
Please look at the attached image to follow the explanation.
Since all charges are of the same positive value, the force exerted on the top charge by the other two are going to be on the line that joins the top charge with each of the other vertices of the triangle, pointing away from the top charge (illustrated by green vectors of the same length in the image).
We need to find the x and y components of these force vectors in order to find the resultant force by combining the x components among themselves, and the y components among themselves. Notice that the angle needed is in all cases [tex]60^o[/tex].
The x- components include the cosine of [tex]60^o[/tex], while the y components include the sine of [tex]60^o[/tex].
Notice as well that the x-components cancel each other (they have the same magnitude but point in opposite directions), while the y-components are both of the same value but pointing in the same direction (pointing up).
Then we just need to multiply by two the y component of one of the forces to find this total force.
Now, the magnitude of the forces in question are given by Coulomb's Law:
[tex]F_C=k\,\frac{q_1\,\,q_2}{d^2} =9\,\,10^9\,\frac{2\,\,10^{-12}\,\,2\,\,10^{-12}}{2^2} =9\,\,10^{-15}\,\,N[/tex]
therefore we can calculate what the y-component of this is using:
[tex]F_y=F\,sin(60^o)=9\,\,10^{-15} \,\frac{\sqrt{3} }{2} \\[/tex]
and twice this value becomes:
[tex]2\, \,F_y=(2)\,\,9\,\,10^{-15} \,\frac{\sqrt{3} }{2}=9\,\,\sqrt{3} \,\,10^{-15}\approx 1.56\,\,10^{-14}\,\,N[/tex]
A skateboarder lands on all four wheels after riding a railing. If the skateboarder has a weight of 990 and the area on the bottom of a single wheel is 0.0005m^2, what pressure does the skateboard put on the ground?
Explanation:
Pressure = force / area
P = 990 N / (4 × 0.0005 m²)
P = 495,000 Pa
A 12.0-g sample of carbon from living matter decays at the rate of 162.5 decays/minute due to the radioactive 14C in it. What will be the decay rate of this sample in 1000 years? What will be the decay rate of this sample in 50000 years?
Answer:
a)143.8 decays/minute
b)0.41 decays/minute
Explanation:
From;
0.693/t1/2 = 2.303/t log (Ao/A)
Where;
t1/2=half-life of C-14= 5670 years
t= time taken to decay
Ao= activity of a living sample
A= activity of the sample under study
a)
0.693/5670 = 2.303/1000 log(162.5/A)
1.22×10^-4 = 2.303×10^-3 log(162.5/A)
1.22×10^-4/2.303×10^-3 = log(162.5/A)
0.53 × 10^-1 = log(162.5/A)
5.3 × 10^-2 = log(162.5/A)
162.5/A = Antilog (5.3 × 10^-2 )
A= 162.5/1.13
A= 143.8 decays/minute
b)
0.693/5670 = 2.303/50000 log(162.5/A)
1.22×10^-4 = 4.61×10^-5 log(162.5/A)
1.22×10^-4/4.61×10^-5 = log(162.5/A)
0.26 × 10^1 = log(162.5/A)
2.6= log(162.5/A)
162.5/A = Antilog (2.6 )
A= 162.5/398.1
A= 0.41 decays/minute
A cheetah can accelerate from rest to a speed of 27.0 m/s in 6.75 s. What is its acceleration (in m/s2)?
Explanation:
we use the formula, Vf=Vi+at
since the cheetah accelerated from rest, it's initial speed is 0, 27=0+a (6.75), a=4 m/s2
Relative to the frame of the observer making the measurement, at what speed parallel to its length is the length of a meterstick 60 cm?
Answer:
The speed of the observer is 2.4 x 10^8 m/s
Explanation:
The standard length of a meter stick is 100 cm
we are to calculate at what speed parallel to the length the length reduces to 60 cm.
This is a relativistic effect question. We know that the length will contract to this 60 cm following the equation below
[tex]l = l_{0}\sqrt{1 - \beta ^{2} }[/tex]
where
[tex]l[/tex] is the new length of 60 cm
[tex]l_{0}[/tex] is the original length which is 100 cm
[tex]\beta[/tex] is the the ratio v/c
where
v is the speed of the observer
c is the speed of light = 3 x 10^8 m/s
substituting values, we have
60 = [tex]100\sqrt{1 - \beta ^{2} }[/tex]
0.6 = [tex]\sqrt{1 - \beta ^{2} }[/tex]
we square both side
0.36 = 1 - [tex]\beta ^{2}[/tex]
[tex]\beta ^{2}[/tex] = 1 - 0.36 = 0.64
β = [tex]\sqrt{0.64}[/tex] = 0.8
but β = v/c
v/c = 0.8
substituting value of c, we have
v = 0.8 x 3 x 10^8 = 2.4 x 10^8 m/s
(The figure model is attached below in a picture) For the figure above there is no friction between block A and the ramp. The mass of block A is 5.6kg. The ramp is 37.383198° from horizontal. Block A is being pulled up the ramp with a constant velocity by a line that is parallel to the ramp. What is the mass of block B?
Give a variable legend for this problem. The model for this problem:
mB (Mass of block B) =__________________________________ Answer________________________________
Is it possible for a radioactive nucleus to decay two times and end up as the same element as the original?
Answer:
Yes, it is possible for a radioactive nucleus to decay two times and end up as the same element as the original
Explanation:
Radioactive decay of nucleus is the process by which an unstable atomic nucleus loses energy by radiation. The energy loss may be from an excited nucleus, which may be emitted as a gamma ray in a process called gamma decay or due to a mass deficit whenever the nucleus decays according to the energy-mass relationship. Whenever a radioactive nucleus decays, new nucleus may be formed in a "transmutation decay", usually into an element of a lower atomic mass than the mother element. Another type of radioactive decay results in products that vary, appearing as two or more "fragments" of the original nucleus with a range of possible masses. This decay is called "spontaneous fission" and it usually happens when a large unstable nucleus decays into two (or occasionally three) smaller daughter nuclei, with an emission of gamma rays, neutrons, or other particles.
You hold a spherical salad bowl 50 cm in front of your face with the bottom of the bowl facing you. The salad bowl is made of polished metal with a 44 cm radius of curvature.
(a) Where is the image of your 5.0-cm-tall nose located?
(b) What are the image’s size, orientation, and nature (real or virtual)?
Answer:
a) q = 39.29 cm , b) h ’= - 3.929 cm the image is inverted and REAL
Explanation:
For this exercise we will use the equation of the constructor
1 / f = 1 / p + 1 / q
where f is the focal length of the salad bowl, p and q are the distance to the object and the image
The metal salad bowl behaves like a mirror, so its focal length is
f = R / 2
f = 44/2
f = 22 cm
a) Suppose that the distance to the object is p = 50 cm, let's find the distance to the image
1 / q = 1 / f - 1 / p
1 / q = 1/22 - 1/50
1 / q = 0.0254
q = 39.29 cm
b) to calculate the size of the image we use the equation of magnification
m = h’/ h = - q / p
h ’= - q / p h
h ’= - 39.29 / 50 5
h ’= - 3.929 cm
the negative sign means that the image is inverted
as the rays of light pass through the image this is REAL
Which statement describes a force acting on an object?
A.a person sees a rolling ball toward him
B. A magnet pulls a nail toward it
C. A piece of charcoal burns in a grill.
D.A car is parked on the street
Answer: B. A magnet pulls a nail towards it
Explanation: Out of the list of answers, this is the only answer where a force is acting on an object. the act of the magnet pulling on the nail is the force, and the nail is the object.
The speed of a boat is often given in knots. If a speed of 5 knots were expressed in the SI system of units, the units would be:____________.
Answer:
0.514 m/s
Explanation:
The knot is a unit of nautical speed used in maritime navigation.
1 knot is equal to one nautical mile per hour,
1 nautical mile per hour = 1.852 km/h
The basic SI system of units of speed is in 'm/s'
1.852 km/h = (1.852 x 1000)/3600 = 0.514 m/s
determine the maximum angle theta for which the light rays incident on the end of the optical fiber of radius 1 mm are subhect to the total internal reflection along the walls of the fiber. assume that the fiber has an index of refraction od 1.2 and that the outside medium is air. note that the rays refracts when entering the fiber g
Answer:
Explanation:
Let the critical angle be C .
sinC = 1 / μ where μ is index of refraction .
sinC = 1 /1.2
= .833
C = 56°
Then angle of refraction r = 90 - 56 = 34 ( see the image in attached file )
sin i / sinr = 1.2 , i is angle of incidence
sini = 1.2 x sinr = 1.2 x sin 34 = .67
i = 42°.
The elements within a group tend to share
A. similar chemical properties and characteristics
B. similar atomic weights
c. similar atomic numbers
D. similar atomic symbols
Answer: A. similar chemical properties and characteristics
PLEASEE I NEED HELP FAST!!! .Study the scenario.A small container of water with a low temperature is poured into a large container of water with a higher temperature. Which choice correctly explains what happens to the thermal energy of these systems? A)The smaller container of water has more thermal energy than the larger container, and some of that energy is transferred to the warmer water in a process known as heating. B)The larger container of water has more thermal energy and some of that energy is transferred to the colder water in a process known as heating. C)The larger container of water has more heat and thermal energy than the smaller container. Some heat and thermal energy is transferred to the smaller container of water. D)The smaller container of water has more heat and thermal energy than the larger container. Some heat and thermal energy is transferred to the larger container of water.
Answer:
that best describes the process is C
Explanation:
This problem is a calorimeter process where the heat given off by one body is equal to the heat absorbed by the other.
Heat absorbed by the smallest container
Q_c = m ce ([tex]T_{f}[/tex]-T₀)
Heat released by the largest container is
Q_a = M ce (T_{i}-T_{f})
how
Q_c = Q_a
m (T_{f}-T₀) = M (T_{i} - T_{f})
Therefore, we see that the smaller container has less thermal energy and when placed in contact with the larger one, it absorbs part of the heat from it until the thermal energy of the two containers is the same.
Of the final statements, the one that best describes the process is C
since it talks about the thermal energy and the heat that is transferred in the process
If the speed of a car is 20m/s .How long does it take to cover a distance of 1km?
Answer: 50 seconds
Explanation:
1km=1000m
Distance/speed=time
1000/20=50
50 seconds
Explanation:
Hey, there!!
Here,
speed (s)= 20m/s
distance (d)= 1km
= 1000m
now,
we have formula,
[tex]t = \frac{d}{s} [/tex]
putting value,
[tex]t = \frac{1000m}{20m/ s } [/tex]
cancelling the like terms,
[tex]t = 50s[/tex]
Therefore, the time is 50s.
Hope it helps...
What amount of heat is required to increase the temperature of 75.0 grams of gold from 150°C to 250°C? The specific heat of gold is 0.13 J/g°C.A. 750 joulesB. 980 joulesC. 1300 joulesD. 1500 joulesE. 2500 joules
Answer:
980 J, B
Explanation:
Given that.
mass of substance, m = 75 g
initial temperature of system, θ1 = 150° C
final temperature of system, θ2 = 250° C
specific heat capacity, c = 0.13 J/gC
Q = mcΔθ, where
Q = quantity of heat required in J
m = mass of substance in G
c = specific heat capacity of substance in J/gC
Δθ = change in temperature °C
Δθ = θ2 - θ1
Δθ = 250° C - 150° C
Δθ = 100° C
now that we have all our values, what we do next is to substitute and apply all in the initial formula given
Q = mcΔθ
Q = 75 * 0.13 * 100
Q = 7500 * 0.13
Q = 975 J
Thus, we can say they amount of heat required to increase the temperature of 75g of gold, from 150° - 250° is 975 J, which is approximately, 980 J.
Option B
Answer:
980 B for plato
Explanation:
A nearsighted woman has a far point of 180 cm . Part A. What kind of lens, converging or diverging, should be prescribed for her to see distant objects more clearly?Part B. What power should the lens have?
Explanation:
It is given that,
A nearsighted woman has a far point of 180 cm.
The object distance for nearsightedness is infinity, u = ∞
The image distance is, v = -180 cm
Using lens formula,
[tex]\dfrac{1}{f}=\dfrac{1}{v}-\dfrac{1}{u}\\\\\dfrac{1}{f}=\dfrac{1}{(-180)}-\dfrac{1}{\infty}\\\\f=-180\ cm\\\\f=-1.8\ m[/tex]
For nearsightedness, a diverging lens is used.
Power of the lens,
P = 1/f
[tex]P=\dfrac{1}{-1.8}\\\\P=-0.56\ D[/tex]
So, the power of the lens is -0.56 D.
The power of lens to be prescribed is 3.5 D.
A person that is far sighted can see far objects clearly but not nearby objects. The farpoint of a normal eye is infinity. Far sightedness is corrected by the use of a convex lens. The near point of the normal eye is 25 cm.
We have that;
u = 25 cm
v = -180 cm
1/f = 1/u - 1/v
1/f = 1/25 - 1/180
1/f = 0.04 - 0.0056
f = 29 cm
Power of lens = 100/f = 100/29 = 3.5 D
Learn more about lens: https://brainly.com/question/1195122
what will you use to measure the length of a copper wire of 50cm long?
Answer:
BS33
Explanation:
its a cable length meter used for measuring length of all kinds of wires.
The uncertainty in position of a proton confined to the nucleus of an atom is roughly the diameter of the nucleus. If this diameter is d = 7.8×10−15 m, what is the uncertainty in the proton's momentum?
Answer:
0.135E-19kgm/s
Explanation:
Using the uncertainty principle, we find
Dp = h / (4π Dx)
= (6.63×10-34Js)/4π(3.90×10-15m) = 0.135×10-19kg m/s
Refraction in ocean waves is identical to refraction in sound and energy waves in that it involves movement through a different medium.a. Trueb. False
Answer:
True
Explanation:
Refraction is the change in the speed, wavelength and direction of a wave as it crosses the boundary between two different media of different densities.
Hence, refraction always involves the movement of a wave from one medium to another. This is the key point to be remembered whether we are discussing refraction in ocean waves or sound waves.
An unmanned spacecraft has been sent to another planet to detect other life forms that might be quite different from those on Earth. If the probe could only send back one still picture, which property or properties of life would be observable in a picture?
Answer:
The presence of water
Explanation:
Any evidence of water that might appear on the still photo would be a clear indication of life on the planet. This is because scientists believe that for life to thrive elsewhere as it has done here on Earth, it needs water. Water is necessary for fertilization of reproductive cells for some organism, and for others it is where their developing young starts life from. For most, all life biochemical system needs a certain level of moisture to function properly.
Suppose the moon was twice as a massive as it is. Would the month be Select one: a. half as long bthe same c. twice as long d. 1/4 as long e. 4 times as long
Answer:
The correct answer is B
Explanation:
The lunar month is the time it takes for the moon to go around the Earth, for this we use Newton's second law where the force is the universal force of attraction
F = ma
the universal attractive force is
F = G M_earth m_moon / r²
Accelerations centripetal acceleration
a = w² r
the angular velocity is for the movement is
w = 2π / T
Where T is the period of revolution; let's substitute
G M_eath m_moon / r² = m_moon (2π /T)² r
G M_earth = 4π² / T² r³
T² = (4π² / G M_eart) r³
Let's analyze this equation we see that it does not depend on the mass of the Luma, therefore the period is the same
The correct answer is B
What is the maximum number of electrons in an atom that can have the following quantum numbers?
a. n = 3, m1 = -2;
b. n = 4, l = 3;
c. n = 5, l = 3, ml = 2;
d. n = 4, l = 1 ml = 0.
Answer:
Explanation:
a ) n = 3, m1 = -2
when n = 3 , l = 0 , 1 , 2 .
when l = 2 , one electron may have m = -2 .
two electrons with s = + 1/2 and - 1/2 may have m = -2 .
So only two electrons may have the configuration of n = 3 , m = -2 .
b ) n = 4, l = 3
when , n = 4 and l = 3 , m may have values -3 , -2 , -1 , 0 , 1 , 2 , 3 . Each m have two electrons with s = + 1/2 and - 1/2 .
So altogether there are 7 x 2 = 14 electrons that have configuration of n = 4, l = 3 .
c ) n = 5, l = 3, ml = 2
Similar to case of a ) , only two electrons with s = + 1/2 and - 1/2 may have configuration of n = 5, l = 3, ml = 2
d ) n = 4, l = 1 ml = 0.
In this case also only two electrons may have configuration of
n = 4, l = 1 ml = 0. with s = + 1/2 and - 1/2 .
(a) The maximum number of electrons in an atom that have n = 3, ml = -2 is two electrons.
(b) The maximum number of electrons in an atom that have n = 3, ml = -2 is 14 electrons.
(c) The maximum number of electrons in an atom that have n = 5 l = 3, ml = 2 is two electrons.
(d) The maximum number of electrons in an atom that have n = 4 l = 1 , ml = 0 is two electrons.
The given parameters:
n = 3, ml = -2n = 4, l = 3n = 5, I = 3, ml = 2n = 4, I = ml = 0The maximum number of electrons in an atom that have n = 3, ml = -2
the quantum number = 3the maximum number of electron = 2The maximum number of electrons in an atom that have n = 4, l = 3
the quantum number = 4the maximum number of electron = (2 x 3) + 1 = 7The orbital is 7 which corresponds to f-orbital and the maximum number of electrons = 14;
The maximum number of electrons in an atom that have n = 5 l = 3, ml = 2
the quantum number = 5the maximum number of electrons = 2The maximum number of electrons in an atom that have n = 4 l = 1 , ml = 0
the quantum number = 4the maximum number of electrons = 2Learn more about quantum number of electrons here: https://brainly.com/question/11575590
Q2: W A soccer ball is kicked off the ground at an angle
of 40 degrees at a speed of 40mls.
co Find The maximum height that the ball will reach
Answer:
1metre
Explanation:
height gained is equal to speed multiplied by angle
Calderas and craters are similar because they are both landforms that show the removal of land at the surface above an area due to volcanic activity.a) trueb) false
Answer:
True
Explanation: A calderas is a large volcanic crater, especially one formed by a major eruption leading to the collapse of the mouth of the volcano.
A Crater is a volcanic crater is an approximately circular depression in the ground caused by volcanic activity. It is typically a bowl-shaped feature within which occurs a vent or vents.
If three forces are equal and their resultant force is zero, then measure of its internal angle is: a)0° b)90° c)60° d)45° Fill in the blanks, tell me which one is right. a or b or c or d
Answer:
edqr3fr =wdmmwfmnl[=kvlfkgvb
Explanation:bcz idk
Me BeLIves iT iS ZeRo So A
A toy uses a spring to shoot an arrow with a suction cup on the end. The toy shoots a 34.2 g arrow and gives it a speed of 5.50 m/s. If the efficiency of the toy is 69.0%, how much elastic potential energy was stored in the spring? Show all your work.
Answer:
0.750 J
Explanation:
69% of the elastic energy is converted to kinetic energy.
0.69 EE = KE
0.69 EE = ½ mv²
EE = mv² / 1.38
EE = (0.0342 kg) (5.50 m/s)² / 1.38
EE = 0.750 J
A refracting telescope has a 1.48 m diameter objective lens with focal length 15.4 m and an eyepiece with focal length 3.28 cm. What is the angular magnification of the telescope
Answer:
m = 469.51
Explanation:
Given that,
The diameter of a refracting telescope is 1.48 m
Focal length of the objective lens is 15.4 m
Focal length of an eyepiece is 3.28 cm
We need to find the angular magnification of the telescope. The ratio of focal length of objective lens to the focal length of the eye piece is called angular magnification of the telescope. So,
[tex]m=\dfrac{f_o}{f_e}\\\\m=\dfrac{15.4}{3.28\times 10^{-2}}\\\\m=469.51[/tex]
So, the angular magnification of the telescope is 469.51.
The magnetic field perpendicular to a single 16.7-cm-diameter circular loop of copper wire decreases uniformly from 0.750 T to zero.
If the wire is 2.25 mm in diameter, how much charge moves past a point in the coil during this operation? The resistivity of copper is 1.68Ã10â8Ωâm.
Express your answer to three significant figures and include the appropriate units.
Answer:
1.24 C
Explanation:
We know that the magnitude of the induced emf, ε = -ΔΦ/Δt where Φ = magnetic flux and t = time. Now ΔΦ = Δ(AB) = AΔB where A = area of coil and change in magnetic flux = Now ΔB = 0 - 0.750 T = -0.750 T, since the magnetic field changes from 0.750 T to 0 T.
The are , A of the circular loop is πD²/4 where D = diameter of circular loop = 16.7 cm = 16.7 × 10⁻²m
So, ε = -ΔΦ/Δt = -AΔB/Δt= -πD²/4 × -0.750 T/Δt = 0.750πD²/4Δt.
Also, the induced emf ε = iR where i = current in the coil and R = resistance of wire = ρl/A where ρ = resistivity of copper wire =1.68 × 10⁻⁸ Ωm, l = length of wire = πD and A = cross-sectional area of wire = πd²/4 where d = diameter of wire = 2.25 mm = 2.25 × 10⁻³ m.
So, ε = iR = iρl/A = iρπD/πd²/4 = 4iρD/d²
So, 4iρD/d² = 0.750πD²/4Δt.
iΔt = 0.750πD²/4 ÷ 4iρD/d²
iΔt = 0.750πD²d²/16ρ.
So the charge Q = iΔt
= 0.750π(Dd)²/16ρ
= 0.750π(16.7 × 10⁻²m 2.25 × 10⁻³ m)²/16(1.68 × 10⁻⁸ Ωm)
= 123.76 × 10⁻² C
= 1.2376 C
≅ 1.24 C
The magnetic field inside a 5.0-cm-diameter solenoid is 2.0 T and decreasing at 4.60 T/s. Part A What is the electric field strength inside the solenoid at a point on the axis
Complete Question
The magnetic field inside a 5.0-cm-diameter solenoid is 2.0 T and decreasing at 4.60 T/s.
Part A What is the electric field strength inside the solenoid at a point on the axis?
Part B
What is the electric field strength inside the solenoid at a point 1.50 cm from the axis?
Answer:
Part A
[tex]E = 0 \ V/m[/tex]
Part B
[tex]E_{15} = 0.0345 \ V/m[/tex]
Explanation:
From the question we are told that
The diameter of the solenoid is [tex]d = 5.0 \ cm = 0.05 \ m[/tex]
The magnetic field is [tex]B = 2.0 \ T[/tex]
The rate of the change of the magnetic field is [tex]\frac{dB}{dt} = 4.60 \ T/s[/tex]
The radius of the solenoid is mathematically represented as
[tex]R = \frac{ d}{2}[/tex]
substituting values
[tex]R = \frac{ 5.0 *10^{-2}}{2} = 0.025 \ m[/tex]
Generally the of the solenoid is mathematically represented as
[tex]E = \frac{ r}{2} * |\frac{dB}{dt} |[/tex]
Now at the point on axis is r = 0 given that the axis is the origin so
[tex]E = \frac{ 0}{2} * |\frac{dB}{dt} |[/tex]
[tex]E = 0 \ V/m[/tex]
Now the electric field strength inside the solenoid at a point 1.50cm from the axis is mathematically represented as
[tex]E_{15} = \frac{ 15*10^{-2 }}{2} * |4.60 |[/tex]
[tex]E_{15} = 0.0345 \ V/m[/tex]
If R = 20 Ω, what is the equivalent resistance between points A and B in the figure?
Answer:
Option C. 70 Ω
Explanation:
Data obtained from the question include:
Resistor (R) = 20 Ω
From diagram given ABOVE, we observed the following
1. R and R are in parallel connections.
2. 2R and 2R are in parallel connections.
3. 4R and 4R are in parallel connections.
Next, we shall determine the equivalent resistance in each case.
This is illustrated below:
1. Determination of the equivalent resistance for R and R parallel connections.
R = 20 Ω
Equivalent R = (R×R) /(R+R)
Equivalent R = (20 × 20) /(20 + 20)
Equivalent R = 400/40
Equivalent R = 10 Ω
2. Determination of the equivalent resistance for 2R and 2R parallel connections.
R = 20 Ω
2R = 2 × 20 = 40 Ω
Equivalent 2R = (2R×2R) /(2R+2R)
Equivalent 2R = (40 × 40) /(40 + 40)
Equivalent 2R = 1600/80
Equivalent 2R = 20 Ω
3. Determination of the equivalent resistance for 4R and 4R parallel connections.
R = 20 Ω
4R = 4 × 20 = 80 Ω
Equivalent 4R = (4R×4R) /(4R+4R)
Equivalent 4R = (80 × 80) /(80 + 80)
Equivalent 4R = 6400/160
Equivalent 4R = 40 Ω
Thus, the equivalence of R, 2R and 4R are now in series connections. We can obtain the equivalent resistance in the circuit as follow:
Equivalent of R = 10 Ω
Equivalent of 2R = 20 Ω
Equivalent of 4R = 40 Ω
Equivalent =?
Equivalent = Equivalent of (R + 2R + 4R)
Equivalent = 10 + 20 + 40
Equivalent = 70 Ω
Therefore, the equivalent resistance between point A and B is 70 Ω.