7. (20 points) Consider 1D electrostatic plasma oscillations w(k) in a warm plasma with a 1D electron distribution function given by f(0) = = VO 1 πυ2 + υδ Assume that k is real, but that w can be complex. (a) Sketch f(v) and show what is meant by the 'cold' and 'hot' plasma approx- imations. (b) Determine the algebraic dispersion relation for electron oscillations assum- ing that the ions are fixed. Consider separately the 'cold' and 'hot' limits.
Answers
a) Sketch of f(v) and Cold and hot plasma approximation. The distribution function f(v) is given by, f(v) = VO/ [πυ2 + υδ]. This is a typical bell-shaped distribution function for electrons which represents a warm plasma. Here, the cold and hot plasma approximation will be described.
Figure 1: Sketch of f(v)The cold plasma approximation occurs when temperature approaches zero and so f(v) will be very thin, high and narrow. In other words, it will approach a step function as shown in figure 1 below.
Figure 2: Sketch of the cold plasma approximation. The hot plasma approximation is when temperature is high enough that f(v) becomes a broad distribution. In this case, f(v) resembles a Gaussian as shown in figure 1.
Figure 3: Sketch of the hot plasma approximation
b) The algebraic dispersion relation for electron oscillations in a hot plasma approximation is given by, ω(k)2 = k2ε0n0 / m*[1 + 3/2 ωp2/ ωc2 ] Where ωp is the plasma frequency and ωc is the electron-cyclotron frequency.
Algebraic dispersion relation for electron oscillations. The general dispersion relation for the electron density waves is given by,ω(k)2 = k2ε0e / m*(n0 + Δn) where k is the wave number, ε0 is the permittivity of free space, e is the electron charge, m* is the effective electron mass, n0 is the equilibrium electron density and Δn is the electron density perturbation.
The algebraic dispersion relation for electron oscillations can be derived by considering the warm plasma model, 1D electron distribution function f(0) = VO/[πυ2 + υδ], and assuming the ions are fixed. For a cold plasma approximation, the dispersion relation is obtained by taking the limit as temperature approaches zero. In this case, the velocity distribution function is highly peaked and can be approximated by a step function. Consequently, the algebraic dispersion relation for electron oscillations in a cold plasma approximation is given by,ω(k)2 = k2ε0n0 / m*For the hot plasma approximation, the dispersion relation is obtained by taking the limit as temperature approaches infinity. In this case, the velocity distribution function is broad and can be approximated by a Gaussian.
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Related Questions
in an array-based heap, assuming heap entries start at index 1, the right child of node n is at index
Answers
In an array-based heap, assuming heap entries start at index 1, the right child of node n is at index 2n + 1.
In different wording: How is the index of the right child calculated in an array-based heap starting at index 1?In an array-based heap where the heap entries start at index 1, the index of the right child of a node can be calculated using the formula 2n + 1, where n represents the index of the parent node. This formula ensures that the right child is located at a position one index higher than the left child. By multiplying the parent node index by 2 and adding 1, we can determine the index of the right child in the array representation of the heap.
Array-based heap: An array-based heap is a data structure used to represent a binary heap. In this representation, the elements of the heap are stored in an array. Each node in the heap has a parent-child relationship, and the index-based calculations help to efficiently navigate and manipulate the heap. The formulas for determining the indices of the left and right children are essential for maintaining the heap structure and performing operations such as insertion and deletion.
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X + worksheet/questions?ald=25241606&wld 3215 MG Calculate Speed X What is the average speed of a car that travels 200 miles in 5 hours? miles per hour (just write the number) Type your answer in below.
Answers
Answer:
40 miles per hour
Explanation:
Average speed = distance ÷ time
= 200 ÷ 5
= 40
Show that the scalar potential of a static, infinitesimally short dipole with the electric dipole moment p=q1 located at r
′
in vacuum is given by φ(r)=
4πϵ
0
∣r−r
′
∣
3
p⋅(r−r
′
)
where r denotes the observation point. Based on this result, derive the scalar potential of a polarized dielectric with a polarization intensity of P(r) and a volume of V enclosed by a surface of S.
Answers
The scalar potential of a polarized dielectric with polarization intensity P(r) and a volume of V enclosed by a surface of S is given by:
φ(r) = (1/4πϵ₀) * (P ⋅ (r - r')) / |r - r'|^3,
Where r denotes the observation point and r' denotes the position of an infinitesimally small volume element within the dielectric.
To derive the scalar potential of a polarized dielectric, we'll start with the expression for the scalar potential of a static, infinitesimally short dipole in a vacuum. The electric potential at a point r due to an infinitesimally short dipole with electric dipole moment p located at r' is given by:
φ(r) = (1/4πϵ₀) * (p ⋅ (r - r')) / |r - r'|^3.
Now let's consider a polarized dielectric with polarization intensity P(r) and a volume V enclosed by a surface S. The polarization intensity is defined as the dipole moment per unit volume. The total dipole moment of the polarized dielectric is given by the volume integral:
p = ∫ P(r) dV,
where the integral is taken over the volume V.
Using this dipole moment in the expression for the scalar potential, we have:
φ(r) = (1/4πϵ₀) * ∫ (P(r') ⋅ (r - r')) / |r - r'|^3 dV.
Since P(r') represents the dipole moment density at position r', we can rewrite it as P(r') = p' / V,' where p' is the dipole moment of an infinitesimally small volume element dV' centered at r' and V' is the volume of that element. Now the expression for the scalar potential becomes:
φ(r) = (1/4πϵ₀) * ∫ [(p' / V') ⋅ (r - r')] / |r - r'|^3 dV.
Since p' = P(r') dV', we can substitute it in the integral:
φ(r) = (1/4πϵ₀) * ∫ [(P(r') dV') / V' ⋅ (r - r')] / |r - r'|^3 dV.
Notice that dV' cancels out in the expression:
φ(r) = (1/4πϵ₀) * ∫ [P(r') / V' ⋅ (r - r')] / |r - r'|^3 dV.
The integral ∫ P(r') / V' dV' equals the average value of P(r') over the volume V, which we denote as P.
Therefore, we can simplify the expression as follows:
φ(r) = (1/4πϵ₀) * (P ⋅ (r - r')) / |r - r'|^3.
This is the scalar potential of a polarized dielectric.
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When a 9.00 V voltage is applied to a resistor, it drives 0.325 A of current through the resistor. How much power does the resistor use? (Unit = W)
Can someone please explain how to do this question.
Answers
Answer: 2.925
Explanation: :)
Answer:
2.925
Explanation:
the measurement of the amount of kinetic energy particles have
Answers
The measurement of the amount of kinetic energy particles have is typically described by their temperature.
The measurement of the amount of kinetic energy particles have is typically described by their temperature. Temperature is a measure of the average kinetic energy of the particles in a substance or system.
In a gas, for example, the temperature reflects the average speed or kinetic energy of the gas molecules. The higher the temperature, the greater the average kinetic energy of the particles. Conversely, at lower temperatures, the average kinetic energy decreases.
The kinetic energy of an individual particle can be calculated using the equation:
Kinetic Energy = \((1/2) * mass * velocity^2,\)
Where mass is the mass of the particle and velocity is its speed.
However, when referring to the measurement of the amount of kinetic energy particles have collectively, temperature is the commonly used parameter.
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Hello people ~
A hollow metal sphere of radius 5 cm is charged so that the potential on its surface is 10 V. The potential at the centre of the sphere is
(a) 0 V
(b) 10 V
(c) Same as at point 5 cm away from the surface
(d) Same as at point 25 cm away from the surface
Answers
Answer:
10V
Explanation:
Hollow sphere means two spherical surfaces inside
So charge on the surface =Charge at any point in sphere i.e voltage remains constant.
So
potential at centre=Potential at surface=10V
Option B is correct
HELP IM TIMED. ILL MARK BRAINLIEST PLSSSSSS.
A model rocket accelerates at 15.3 m/s2 with a force of 44 N.
Calculate the mass of the rocket. Round your answer to the nearest tenth of a kg.
The mass of the rocket is kg.
Fill in the blank above. Also what is the formula to find the mass. Include that in the answer pls.
Answers
Answer:
According to Newton's Second Law of Motion :
Where,
F = Force Applied
m = Mass of the object
a = Acceleration
Now, we will use this law to solve this question.
Given :
Acceleration or a = 15.3 m/s²
Force = 44 N
Mass = ?
Substitute, the given values in the formula.
F = ma
⇒ m = F/a
m = 44/15.3
m = 2.9 kg
Answer:
7.0 n
Explanation:
gravitational potential energy is converted to kinetic __ energy when the object begins to move
Answers
Gravitational potential energy is converted to kinetic (Motion) energy when the object begins to move.
What is the gravitational potential energy movement about?The energy gained from this change in position is stored within the body as gravitational potential energy if a ball is raised from the ground to a height above the earth. The gravitational potential energy is then converted into kinetic energy when the ball hits the earth.
Therefore, the way an object falls, its gravitational potential energy is said to be transformed or altered into the kinetic energy of motion.
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what started that people thought the earth was flat
Answers
Answer:
The flat Earth model is an archaic conception of Earth's shape as a plane or disk. Many ancient cultures subscribed to a flat Earth and due to this people still belive earth is flat but scientist proven earth is round .
Explanation:
calculate the time taken to raise the temperature of 1.5 kg of water in a kettle from 15°C to 100°C given that specific heat capacity of water is 4200 J/kg/K and the heater is rated 250V , 2kW
Answers
Answer:
270 s or 4.5 min
Explanation:
First find the amount of heat needed:
q = mCΔT
q = (1.5 kg) (4200 J/kg/K) (100 − 15) K
q = 535,500 J
q = 535.5 kJ
Power is energy per time.
P = E / t
2 kW = 535.5 kJ / t
t = 270 s
A 2 kg box of taffy candy has 40j of potential energy relative to the ground. Its height above the ground is
Answers
Answer:
2.04m
Explanation:
PE=mgh
h= PE/mg
h= 40/2(9.82)
h=40/19.64
h=2.04
Answer:
\(20m\)
Explanation:
Formula to find the potential energy is,
Potential Energy = mgh
Here,
m = mass
g = gravitational field
h = height
According to the question, we have to find the height.
Usually, we get g is \(10ms^{-2}\)
Let us solve for the answer now.
\(P.E. =mgh\\40J =2kg*10ms^{-2} *h\\40 = 20h\\\frac{40}{20}= \frac{20h}{20} \\20m=h\)
Hope this helps you.
Let me know if you have any other questions :-)
HELPPPPPPPPPPP PLEASEEEEEEEEEEE
Complete this sentence. The solubility of a sample will ____________ when the size of the sample increases.
stay the same
decrease
increase
be unable to be determined
the answer is not decrease
Answers
The solubility of the sample will decrease
the process of heating a pot of water from room temperature to boilling temperature to boilling temperature is an endothermic process
T/F
Answers
The given statement "The process of heating a pot of water from room temperature to boiling temperature is an endothermic process" is true because it accurately reflects the thermodynamics involved in heating water.
Is the process of heating water endothermic?When heating a pot of water from room temperature to boiling temperature, the process is indeed endothermic. In an endothermic process, energy is absorbed from the surroundings to increase the internal energy of the system.
In this case, heat energy is transferred to the water molecules, causing them to gain kinetic energy and eventually reach the boiling point. As the water absorbs heat, it undergoes a phase change from a liquid to a gas. This requires energy input, resulting in an endothermic process.
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What kinds of stars have either no habitable zones or very inferior ones
Answers
A parallel plate capacitor has plates of area 2.0 à 10-3 m2 and plate separation 1.0 à 10-4 m. Air fills the volume between the plates. What potential difference is required to establish a 3.0 μC charge on the plates?A) 9.3 à 102 VB) 2.4 à 104 VC) 1.7 à 104 VD) 6.9 à 103 VE) 3.7 à 105 V
Answers
The potential difference required to establish a 3.0 μC charge on the plates is approximately 169.49 V, which is closest to option (C) 1.7 × 10^4 V. Therefore the correct option is option C.
The capacitance of a parallel plate capacitor with A-sized plates separated by d and air between them is given by:
C = ε0 * A / d
where 0 is the open space permittivity (8.85 10-12 F/m).
The charge Q on a capacitor is proportional to the capacitance C and potential difference V as follows:
Q = C * V
Rearranging this equation yields:
V = Q / C
When we substitute the provided values, we get:
\(C = (1.77 10-8 F) = (8.85 10-12 F/m) * 2.0 10-3 m2 / (1.0 10-4 m)\)
\(Q = 3.0 × 10^-6 C\)
V = (3.0 × 10^-6 C) / (1.77 × 10^-8 F)
= 169.49 V
As a result, the potential difference necessary to charge the plates to 3.0 C is roughly 169.49 V, which is close to option (C) 1.7.
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What notecard word is defined: a substance or particles that a wave travel through.
outer space
electromagnetic
medium
mechanical
Answers
Answer:
medium
Explanation:
A substance or particle that wave travel through is called medium. There are two main types of such medium, some contains particles and some are vacuums.
Waves can travel through a vacuum which contains no particles. Some can also contain particles. Waves can interact in different ways with the medium.What is static friction?
A. Friction that acts when an object is not moving
B. Friction that exerts no force
O C. Friction that opposes air resistance
D. Friction that acts on a sliding object
Answers
Answer:
the awsner is d because friction is caused by two objects touching
Answer:
It’s friction that acts when an object is not moving
Explanation:
PLZ HELP!!! Detailed PLZ!
A man is standing on a building 30 m high holding a 1 kg rock. What is the potential
energy of the rock? The man drops the rock. What is the kinetic energy of the rock
the instant before it hits the ground? g=9.8m/s^2
Answers
Answer:
Potential Energy = 294J, Kinetic Engergy = 48.02J
Explanation:
We have these formulas:
Potential Energy = mass * gravitational force * height (m) = 1 * 9.8 * 30 = 294(J)
Kinetic Energy = 1/2 * mass * velocity^2 = 1/2 * 1 * 9.8^2 = 48.02 (J)
As the rock falling at an acceleration of 9.8m/s^2 which means for each second, the rock increases 9.8m/s. I think we are missing time to find the instantaneous velocity, the formula is (initial displacement - final displacement)/ (initial time - final time) which will directly give the final answer for you.
what is the state of the electrical charge when a neuron is at resting potentia
Answers
When a neuron is at resting potential, the state of the electrical charge is negative inside the neuron compared to the outside
Because of an unequal distribution of ions like potassium (K+) and chloride (Cl-) inside and outside the neuron, the interior of the neuron is negatively charged at resting potential. The membrane of the neuron is selectively permeable, permitting certain ions to pass while preventing others from doing so. A gradient in electrochemistry results from this.
Ion channels, notably the sodium-potassium pump, which actively transfers sodium ions (Na+) out of the neuron and potassium ions (K+) into the neuron, are responsible for maintaining the resting potential. As a result, the neuron produces an excess of negative charge within and an excess of positive charge outside.
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The parachutists are not hurt when they jump out of an airplane, why?
Answers
A worker assigned to the restoration of the Washington Monument is checking the condition of the stone at the very top of the monument. A nickel with the mass of 0.005 kg is in her shirt pocket. What is the kinetic energy (KE) of the nickel in her shirt pocket at the top of the monument?
Answers
Answer:
Your answer is: K.E = 8.3 J
Explanation:
If the height (h) = 169.2 meters (m) and the mass (m) is 0.005 kilograms (kg) the total energy will be kinetic energy which is equal to the potential energy.
K.E = P.E and also P.E equals to mgh
Then you substitute all the parameters into the formula ↓
P.E = 0.005 × 9.81 × 169.2
P.E = 8.2908 J
So your answer is 8.2908 but if you round it is K.E = 8.3
A pitching machine throws a 0.148kg baseball to the left at 26m/s. A batter then hits the baseball directly back at 39m/s. What is the change in momentum of this baseball
Answers
Let us assume that the initial direction of the ball, i.e., from the pitching machine to the batter as the negative direction, and the final direction of the ball is the positive direction.
Given,
The mass of the baseball, m=0.148 kg
The initial velocity of the baseball, u=-26 m/s
The final velocity of the baseball, v=39 m/s
The momentum of the ball before the batter hits it is given by,
\(p_1=mu\)On substituting the known values,
\(\begin{gathered} p_1=0.148\times-26 \\ =-3.848\text{ kg}\cdot\text{m/s} \end{gathered}\)The momentum of the ball after the batter hits it is given by,
\(p_2=mv\)On substituting the known values,
\(\begin{gathered} p_2=0.148\times39 \\ =5.772\text{ kg}\cdot\text{m/s} \end{gathered}\)The change in the momentum is given by,
\(\Delta p=p_2-p_1\)On substituting the known values,
\(\begin{gathered} \Delta p=5.772-(-3.848) \\ =9.62\text{ kg}\cdot\text{m/s} \end{gathered}\)Thus the change in the momentum of baseball is 9.62 kg·m/s
Amir bought a lamp with a design attached to it that casts a shadow when the lamp is lit, as shown below. He wants to carryout an experiment using this lamp to find out the factors that effect the size of the shadow.
The effect of which factors can he actually find out using only this lamp?
Answers
The effect of the factors which he can he actually find out using only this lamp to determine the size of shadow is the light intensity and type of object.
What is Experiment?
This forms part of the scientific methods and is referred to as a procedure which is used to support or refute an hypothesis.
The size of the shadow is dependent on factors such as the light intensity and the type of object. Since the lamp produces the light in which the intensity can be gotten and the type of material it is in contact with then it therefore the correct choices.
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at the surface of earth, an object is suspended by two cords. one cord is horizontal and one cord is at an angle to the horizontal, as shown in the figure above. the tension in the horizontal cord is th . if the assembly is moved to the surface of a planet with the same average density and twice the radius of earth, the new tension in the horizontal cord will be
Answers
The tension in the horizontal cord remains the same, regardless of the radius of the planet.
The tension in the horizontal cordAssuming that the object is stationary, forces acting on it are:
Gravity: This force pulls the object downwards, towards the center of the planet.
Tension in the horizontal cord: This force acts horizontally and is equal to "th".
Tension in the angled cord: This force acts at an angle to the horizontal and can be broken down into two components: one perpendicular to the horizontal (which balances out the force due to gravity in that direction), and one parallel to the horizontal (which adds to the force due to tension in the horizontal cord).
Since the object is stationary, the force due to tension in the angled cord must be equal and opposite to the sum of the forces due to gravity and tension in the horizontal cord.
T cosθ = mg (perpendicular component)
T sinθ + th = 0 (parallel component)
We can solve for T in terms of th and θ using the second equation:
T = -th / sinθ
what happens when we move the assembly to a planet with twice the radius of the Earth. Using the formula for the acceleration due to gravity at the surface of a planet of radius R and mass M:
g' = G M / R^2
where G is the gravitational constant, we can find that the new acceleration due to gravity is:
g' = (8GMe) / (2Re)^2 = (8/4^2)g = 0.5g
where "e" and "Re" are the mass and radius of the Earth, respectively, and we have used the fact that the gravitational constant and average density are the same for both planets.
to find the new tension in the horizontal cord:
T' = -th / sinθ = -th / sinθ
So the tension in the horizontal cord remains the same, regardless of the radius of the planet.
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which of the following spectroscopy methods does not involve the interaction of organic molecules with electromagnetic radiation?
Answers
The following spectroscopy method does not involve the interaction of organic molecules with electromagnetic radiation:
Mass Spectrometry (MS): Mass spectrometry is a technique that analyzes the mass-to-charge ratio of ions. It does not directly involve the interaction of organic molecules with electromagnetic radiation. Instead, it involves the ionization of molecules and the measurement of their mass-to-charge ratios using magnetic and electric fields.
On the other hand, the following spectroscopy methods do involve the interaction of organic molecules with electromagnetic radiation: Ultraviolet-Visible Spectroscopy (UV-Vis): UV-Vis spectroscopy measures the absorption or transmission of ultraviolet and visible light by organic molecules.
Infrared Spectroscopy (IR): IR spectroscopy measures the absorption or emission of infrared light by organic molecules. It provides information about the molecular vibrations and functional groups present in the molecules.
Nuclear Magnetic Resonance Spectroscopy (NMR): NMR spectroscopy measures the absorption of radiofrequency radiation by atomic nuclei in organic molecules. It provides information about the molecular structure, connectivity, and environment of the nuclei.
It's important to note that different spectroscopy methods have their own applications and provide complementary information about organic molecules.
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It is determined that a certain light wave has a wavelength of 3.012 ×10−12 m. The light travels at 2.99 ×108 m/s. What is the frequency of the light wave? (Round your answer to three significant figures.)
Answers
Answer:
Explanation:
velocity=frequency*wavelength
velocity = 2.99*10^8 m/s
frequency = ?
wavelength = 3.012*10^-12
2.99*10^8m/s = (f)(3.012*10^-12)
f=9.58*10^19 Hertz
racing on a flat track, a car taking 5.5 s to round a curve of a radius of 56 m. what is the centripetal acceleration of the car?
Answers
The centripetal acceleration of the car is 1.85 m/s²
The speed at which anything moves around a circle is known as its centripetal acceleration. Centripetal acceleration is the acceleration experienced by any object that is travelling in a circle and whose acceleration vector is directed toward the center of the circle.
To find the centripetal acceleration of the car, we can use this following formula:
Centripetal acceleration = v²/r
In this case, we are given that:
The time that car was taking = 5.5 s
The radius of the car (r) = 56 m
The velocity of the car (v) = distance : time = 56 m : 5.5 s = 10.18 m/s
Hence, the centripetal acceleration:
Centripetal acceleration = 10.18² / 56
Centripetal acceleration = 1.85 m/s²
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A 7.50 kg bowling ball moving6.42 m/s strikes a 1.60 kg bowlingpin at rest. After, the pin moves14.8 m/s at a -47.0° angle. Whatis the y-component of the ball'sfinal velocity?y-component (m/s)Enter
Answers
let the bowling ball initially is moving along the x-axis,
The whole process can be represented as,
Before the collision the net kinetic energy of the balls is,
\(K_{iy}=\frac{1}{2}\times m_1\times(v_1\cos (90^o))^2+\frac{1}{2}\times m_2\times(0)^2\)where the values of the variables are given as,
\(\begin{gathered} m_1=7.5\text{ kg} \\ v_1=6.42ms^{-1} \\ m_2=1.6\text{ kg} \end{gathered}\)As the value of cos(90) is zero.
Substituting the known values,
The value of the net kinetic energy with the velocity along the y-axis before the collision is,
\(K_{iy}=0\)The velocity of the second ball is at rest in the initial state, thus its value is taken as zero.
After the collision of the balls, the net kinetic energy is,
\(\begin{gathered} K_{fy}=\frac{1}{2}\times m_1\times(v^{\prime}_1\sin (\alpha))^2+\frac{1}{2}\times m_1\times(v^{\prime}_2\sin (-47^o))^2 \\ K_{fy}=\frac{1}{2}\times m_1\times(v_{1fy})^2+\frac{1}{2}\times m_1\times(v^{\prime}_2\sin (-47^o))^2 \end{gathered}\)Negative sign here indicating the direction of the final balls motion will be opposite to the each other.
The values of the variables are given as,
\(v^{\prime}_2=14.8ms^{-1}\)Substituting the known values,
The value final kinetic enegry of the balls with velocity along the y-axis is,
\(\begin{gathered} K_{fy}=\frac{1}{2}\times7.5\times(v_{1fy})^2+\frac{1}{2}\times1.6\times(14.8\times\sin (360^o-47^o)^2 \\ K_{fy}=3.75\times(v_{1fy})^2-93.72 \end{gathered}\)Here 360 degree is used because the pin ball direction is downward of the positive x-axis.
Then by the law of conservation of energy along the y-axis,
\(\begin{gathered} K_{iy}=K_{fy} \\ 0=3.75\times(v_{1fy})^2-93.72 \\ (v_{1fy})^2=\frac{93.72}{3.75} \\ (v_{1fy})^2=25 \\ v_{1fy}=5ms^{-1} \end{gathered}\)Thus, the y component of the final velocity of the bowling ball of mass m1 is 5 meter per second.
describe the location of nonmetals on the periodic table
Answers
3 resitor is connected in series to a 6 resior and a 12-v battery.what is the current in each of the resistors ? what is the voltage drop across each resitor?
Answers
The current in each resistor is 4 A, 2 A, and 4 A, respectively. The voltage drop across each resistor is 12 V.
When three resistors are connected in series with a six resistor and a 12-volt battery, the total resistance of the series circuit is R = R1 + R2 + R3 + ...
The current flowing through the circuit is the same at every point. So, if we want to know the current flowing through each resistor, we need to use Ohm's law, I = V/R, where V is the voltage of the battery and R is the resistance of each resistor.
I1 = V/R1 = 12/3 = 4 AI2 = V/R2 = 12/6 = 2 AI3 = V/R3 = 12/3 = 4 A. The voltage drop across each resistor can be calculated using Ohm's law, V = IR.
V1 = I1R1 = 4 x 3 = 12 VV2 = I2R2 = 2 x 6 = 12 VV3 = I3R3 = 4 x 3 = 12 V.
Therefore, the current in each resistor is 4 A, 2 A, and 4 A, respectively. The voltage drop across each resistor is 12 V.
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