a) Three impedance coils, each having a resistance of 20 ohms and a reactance of 15 ohms, are connected in star to a 400 V, 3 phase, 50 Hz supply. Calculate

i. the line current

ii. power supplied

iii. the power factor

iv. If three capacitors, each of the same capacitance, are connected in delta to the same supply so as to form parallel circuit with the above impedance coils, calculate the capacitance of each capacitor to obtain a resultant power factor of unity.

v. Draw the phasor diagrams for the system before and after power factor correction.

The molar specific heat of the mixture at constant volume, when one mole of a monoatomic gas is mixed with three moles of a diatomic gas, is 2.25r. The correct option is b.

The molar specific heat at constant volume (Cv) is a measure of the amount of heat required to raise the temperature of one mole of a substance by one degree Celsius while keeping the volume constant.

For a monoatomic gas, the molar specific heat at constant volume is given by Cv = (3/2)R, where R is the molar gas constant.

For a diatomic gas, the molar specific heat at constant volume is given by Cv = (5/2)R.

When one mole of a monoatomic gas is mixed with three moles of a diatomic gas, the total moles of gas in the mixture is four. The molar specific heat of the mixture at constant volume can be calculated by taking the weighted average of the molar specific heats of the individual gases, based on their respective mole ratios.

In this case, the mixture consists of one mole of the monoatomic gas and three moles of the diatomic gas, giving a mole ratio of 1:3. Using the weighted average formula, the molar specific heat of the mixture is calculated as:

Cv_mixture = (1/4) × (Cv_monoatomic) + (3/4) × (Cv_diatomic)

= (1/4) × (3/2)R + (3/4) × (5/2)R

= (3/8)R + (15/8)R

= (18/8)R

= 2.25R

Therefore, the molar specific heat of the mixture at constant volume is 2.25R. The correct option is b.

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Answer: 267 m

Explanation:

2.99x10^8 m/s

———————-

1.12 x 10^6 Hz

Answer:

5.25m to 52.5 Decimeters (10x)

5.25m to 5250 Millimeters (1000x)

For the book to move in the direction of the movement arrow, a force in the direction of the desired movement must be applied causing the forces to be unbalanced.

option D is the correct answer.

Newton's first law of motion states that an object at rest or uniform motion in a straight line will continue in that path unless it is acted upon by an external force and it will move in the direction of the applied force.

Also, from Newton's second law of motion, which states that the force applied to an object is directly proportional to the product of mass and acceleration of the object.

Mathematically, Newton's second law of motion is written as;

F (net) = ma

F - Ff = ma

where;

Thus, for the book to move, the force of friction must be overcame by the applied force and this create an unbalanced force acting on the book. Also, the book will move in the direction of the net force acting on it.

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The expression for the charge on the capacitor as a function of time  is \(q(t) = q_0e^{-\frac{t}{RC} }\).

Q = It

lnQ = -t/RC

ln(q - q₀) = -t/RC

\(q-q_o = e^{-\frac{t}{RC} }\\\\q = q_0e^{-\frac{t}{RC} }\\\\q(t) = q_0e^{-\frac{t}{RC} }\)

where;

Thus, the expression for the charge on the capacitor as a function of time  is \(q(t) = q_0e^{-\frac{t}{RC} }\).

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The distance from the central maximum to the fourth maximum in the interference pattern, when the double slits are illuminated with light of wavelength 440 nm, can be determined using the formula for the position of the nth maximum in a double-slit experiment:

y = n * λ * L / d
Given:
λ1 = 550 nm (wavelength of light for the third maximum)
y3 = 2.0 cm (distance from the central maximum to the third maximum)
λ2 = 440 nm (wavelength of light for the fourth maximum)
Using the formula, we can calculate y4:
y4 = 4 * λ2 * L / d
Substituting the given values into the equation:
y4 = 4 * (440 nm) * L / d
Therefore, the distance from the central maximum to the fourth maximum is given by 4 times the product of the wavelength (440 nm) and the distance L divided by the distance between the double slits (d). However, the values of L and d are not provided in the question, so the exact distance cannot be determined without that information.

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The displacement of a spring is directly proportional to the applied force. The displacement of the given spring is 50.45 m.

\(F = kx\)

Where,

\(F\) - force applied = 88 N

\(k\) - spring constant = 440 N/m

\(x\) - displacement = ?

Put the values in the formula,

\(88 = 440 \times x\\\\x = \dfrac {440 }{88}\\\\x = 50.45 \rm \ m\)

Therefore, the displacement of the given spring is 50.45 m.

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The linear expansivity of the metal is 4.44 × \(10^{-6}\) /°C.

What is Temperature?

Temperature is a measure of the degree of hotness or coldness of a substance or object, expressed in terms of a numerical scale. It is a physical property that determines the direction of heat transfer between two bodies in thermal contact. The most commonly used scales for temperature measurement are Celsius, Fahrenheit, and Kelvin.

Linear expansivity is defined as the change in length per unit original length per degree Celsius change in temperature.

Let the initial length of the metal be L1 = 15.01 m and the change in temperature be ΔT = 60°C.

The final length of the metal is L2 = 15.05 m.

The change in length of the metal is:

ΔL = L2 - L1

ΔL = 15.05 m - 15.01 m

ΔL = 0.04 m

The linear expansivity α can be calculated as:

α = ΔL / (L1 ΔT)

α = 0.04 m / (15.01 m × 60°C)

α = 4.44 ×\(10^{-6}\) /°C

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Explanation:

The simplest kinetic model is based on the assumptions that: (1) the gas is composed of a large number of identical molecules moving in random directions, separated by distances that are large compared with their size; (2) the molecules undergo perfectly elastic collisions (no energy loss) with each other and with the ...

Answer: 73 m/s

Explanation:

Answer: 73 M/S

Explanation:Did the work

Answer:

Explanation:

The color of the object is reflected by the object other colors are absorbed by the object.

Here object appears in red color so red color is reflected by the object and other colors are absorbed.

a) F₂₁ = 0.02 N, attracting.

b) F₁₂ = 0.02 N, attracting.

Power or force applied or brought to bear: Power active is the source of motion or change. the elements of nature

A) According to Coulomb's Law, the amount of force that q1 exerts on q2 (F21) is as follows:

\(F_{21} = K * q1 * q2 / r^2 = 9e9N.m^2 / C2* (25-9) *(75-9) / 0.03^2 = 0.02N\)

b)

Using Newton's Third Law or (1), one can determine the force on q1 caused by q2, and since all the parameters are equal, F12 (in magnitude) = F21 = 0.02 N.

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Answer:

b.

Explanation:

b) Heat the solution, dissolve the solute, and let the solution cool verifying nothing settled out.

Answer:

La fuerza resultante sobre q₃ es  -1.2245 × 10⁻¹⁵ i  + -0.24 × 10⁻¹⁵ j

La magnitud de la fuerza resultante sobre q₃ es aproximadamente 1.25 × 10⁻¹⁵ N

Explanation:

q₁ = -45 μC = -45 × 10⁻⁶ C

r₁₂ = 30 mm = 30 × 10⁻³ m

q₂ = 25 μC = 25 × 10⁻⁶ C

r₂₃ = 50 mm = 50 × 10⁻³ m

q₃ = 20 μC = 20 × 10⁻⁶ C

k = 9×10⁻⁹ N·m²/C²

Por lo tanto;

r₁₃ = √(50² + 30²) = 10·√(34)

F₁₂ = 9×10⁻⁹ × (-45 × 10⁻⁶)×(25 × 10⁻⁶)/(30 × 10⁻³)² = -1.125 × 10⁻¹⁴

F₁₂ = -1.125 × 10⁻¹⁴ N

F₂₃ = 9×10⁻⁹ × (20 × 10⁻⁶)×(25 × 10⁻⁶)/(50 × 10⁻³)² = 1.8 × 10⁻¹⁵ j

F₁₃ = 9×10⁻⁹ × (-45 × 10⁻⁶)×(20 × 10⁻⁶)/(10·√34 × 10⁻³)² = -2.38× 10⁻¹⁵

Los componentes de F₁₃ son;

-2,38 × 10⁻¹⁵ × cos (arctan (30/50)) = -2,04 × 10⁻¹⁵ j

-2,38 × 10⁻¹⁵ × sin (arctan (30/50)) = -1,2245 × 10⁻¹⁵ i

La fuerza resultante sobre la carga q₃, \(\left | \underset {F_3} \rightarrow \right |\) = \(\underset{F_{13}}{\rightarrow}\) + \(\underset{F_{23}}{\rightarrow}\)

∴ \(\left | \underset {F_3} \rightarrow \right |\) = 1.8 × 10⁻¹⁵ j + -1.2245 × 10⁻¹⁵ i + -2.04 × 10⁻¹⁵ j

La fuerza resultante sobre q₃ es \(\left | \underset {F_3} \rightarrow \right |\)  = -1.2245 × 10⁻¹⁵ i  + -0.24 × 10⁻¹⁵ j

La magnitud de la fuerza resultante sobre q₃,

\(\left | F_3 \right |\) = √((-1.2245 × 10⁻¹⁵)² + (-0.24 × 10⁻¹⁵)²) ≈ 1.25 × 10⁻¹⁵

La magnitud de la fuerza resultante sobre q₃, \(\left | F_3 \right |\) ≈ 1.25 × 10⁻¹⁵ N.

Cystic fibrosis is a recessive genetic disorder caused by a mutation in the CFTR gene. It affects the lungs, pancreas, and other organs, causing difficulties in breathing and digestive problems.

Hemophilia is an X-linked recessive genetic disorder that affects blood clotting due to mutations in clotting factor genes. Hemophilia A is caused by a mutation in the F8 gene while hemophilia B is caused by a mutation in the F9 gene.

Duchenne muscular dystrophy is an X-linked recessive genetic disorder caused by mutations in the DMD gene, which codes for a protein called dystrophin. It affects muscle function and leads to muscle weakness and wasting.

Huntington's disease is an autosomal dominant genetic disorder caused by a mutation in the HTT gene. It affects brain function, leading to psychiatric symptoms and movement problems.

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Cystic fibrosis -  autosomal recessive pattern, Hemophilia -  X-linked recessive pattern, Duchenne muscular dystrophy -  X-linked recessive pattern and Huntington's disease - autosomal dominant pattern.

Gene alterations that are essentially present in every cell in the body cause many hereditary diseases. These illnesses thus frequently impact many bodily systems, and the majority cannot be treated. To treat or manage some of the accompanying symptoms, there might be methods available.

Genetic disorders connected to mutations in genes on the X chromosome are referred to as having X-linked recessive inheritance. Because he contains just one X chromosome, a male who carries this mutation will be affected. A female who carries a gene mutation in one X chromosome but has a normal gene on the other X chromosome usually has no symptoms.

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Explanation:

28kgm/s

that is the answer

momentum is conserved

The work required to bring a seventh particle of charge q from very far away and place it at the center of the circle is \(W =  \frac{6k(q^2)}{r}\).

1. Since there are six particles equally spaced around the circle, the distance between the center of the circle and each particle is r.
2. The work required to bring a particle of charge q close to another particle of charge q is given by Coulomb's Law:

\(W =  \frac{k(q1 * q2)}{d}\),

where k is the electrostatic constant, q1 and q2 are the charges of the particles, and d is the distance between them.
3. In this case,

q1 = q2 = q and d = r.

So the work required to bring the seventh particle close to one of the six particles is \(W =  \frac{6k(q^2)}{r}\).
4. Since there are six particles, the total work required to bring the seventh particle to the center of the circle is the sum of the work done to bring it close to each of the six particles. Therefore, the total work is \(W =  \frac{6k(q^2)}{r}\).
The work required to bring a seventh particle of charge q from very far away and place it at the center of the circle with six equally spaced particles of charge q is \(W =  \frac{6k(q^2)}{r}\).

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Answer:

A. It pulls objects towards the center of Earth.

Explanation:

Think about dropping something, where does it go? If you are on earth, this goes down towards the ground due to the attractive force of gravity on every object (to pull everything to center of earth). Like Newton's apple.

The cyclist's speed is 3.33 m/s, distance bob travelled is 13.5m in 7.44s, the acceleration of car is -7.0 m/s² and the characteristics are zero initial velocity and gravitational acceleration.

1. The cyclist's speed is calculated by dividing the distance by the time:
Speed = Distance ÷ Time = 24,000 m ÷ 7200 s = 3.33 m/s
2. Bob will travel a distance of 2.68 m/s × 7.44 s = 19.9632 meters in 7.44 seconds.
3. We can use the formula:
Distance = (Final Velocity - Initial Velocity) ÷ Acceleration × Time + Initial Velocity × Time
Distance = (6 m/s - 3 m/s) ÷ 3 m/s² × 4.5 s + 3 m/s × 4.5 s
Distance = 13.5 m
4. The acceleration of the car can be found using the formula:
Acceleration = (Final Velocity - Initial Velocity) ÷ Time
Acceleration = (-9.0 m/s - (-2.0 m/s)) ÷ 2.0 s
Acceleration = -7.0 m/s² (note that the negative sign indicates acceleration in the opposite direction to forward velocity)
5. The two important motion characteristics of free-falling objects are:
- They experience constant acceleration due to gravity, which is approximately 9.8 m/s² near the Earth's surface.
- They have an initial velocity of 0 m/s when dropped from rest.

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When a metal car is struck by lightning, the resulting electric field inside the car is zero.

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The rate at which work is completed is indicated by the power word, hence option b is correct. Power, which can be defined as the amount of work done W.

Is the time rate at which the job is completed or energy is given. Energy transferred, expressed as W/t or energy transferred against the time interval t. Work (or energy) per unit time, foot-pounds per minute, joules per second (or watts), and ergs per second are all ways to express power. Work is defined as involving both force applied to the body and displacement of the body. Consider a block that is resting on a horizontal, frictionless floor. A consistent force is acting on this block.

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Answer:  B.) power

Explanation: Get dem hearts up:)

Answer:i think they do i dont understand your question it does not make sence

Explanation:

The potential energy of the sled at its maximum height is: P.E. = mgh = 210 kg x 9.8 m/s^2 x h = 2058 h J

To calculate the gravitational potential energy of the sled at its maximum height, we first need to know the height it reaches. We can use the conservation of energy principle which states that the total energy of a system remains constant if no external forces act on it. At point A, the sled has only potential energy due to its position with respect to the ground. As it travels up the track, this potential energy gets converted into kinetic energy as the sled gains speed. At the maximum height, the sled has no kinetic energy since it has come to a stop and all the energy is potential. The potential energy of an object can be calculated using the formula P.E. = mgh, where m is the mass of the sled, g is the acceleration due to gravity (9.8 m/s^2), and h is the maximum height reached by the sled. Given that the mass of the sled is 210kg and assuming that the track is vertical, we can calculate the maximum height using the conservation of energy principle. The total energy of the sled at the bottom of the track is zero, and at the maximum height, it is equal to the potential energy. Therefore, the potential energy of the sled at its maximum height is: P.E. = mgh = 210 kg x 9.8 m/s^2 x h = 2058 h J Since we do not know the height reached by the sled, we cannot calculate the potential energy in joules. However, we can calculate it once we know the height reached by the sled.

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If A diffraction grating has 45,000 slits/cm then The distance between adjacent slits on this diffraction grating is approximately 2.22 micrometers.

To determine the distance between adjacent slits on a diffraction grating, we need to use the formula:
d = 1/n * dλ/a
where d is the distance between adjacent slits, n is the number of slits per unit length (in this case, 45,000 slits/cm), dλ is the wavelength of the incident light, and a is the angle between the incident light and the diffracted light.
Assuming we are working with visible light (with a wavelength of approximately 500 nm) and a diffraction angle of 30 degrees, we can calculate the distance between adjacent slits as follows:
d = 1/(45,000/cm) * (500 nm)/(sin(30 degrees))

d = 1/(4.5 x 10^5 /m) * (500 x 10^-9 m)/(0.5)
d = 2.22 x 10^-6 m
Therefore, the distance between adjacent slits on this diffraction grating is approximately 2.22 micrometers.

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The formula for the spacing of a diffraction grating: d = 1/N * λ/sin(θ)

To answer this question, we need to use the formula for the spacing of a diffraction grating: d = 1/N * λ/sin(θ)

Where d is the distance between adjacent slits,

N is the number of slits per unit length (in this case, 45,000 slits/cm),

λ is the wavelength of the incident light, and θ is the angle between the incident light and the diffracted light.

Assuming we are using visible light with a wavelength of 500 nm (0.0005 cm), and that the diffraction angle is 30 degrees, we can calculate the spacing as follows:

d = 1/45000 * 0.0005 / sin(30) = 1.155 x 10^-6 cm

So the distance between adjacent slits in this diffraction grating is approximately 1.155 micrometers (or 1155 nanometers).

In conclusion, the distance between adjacent slits in a diffraction grating with 45,000 slits/cm is 1.155 x 10^-6 cm, or approximately 1.155 micrometers. This calculation is based on the formula for diffraction grating spacing, which takes into account the number of slits per unit length, the wavelength of the incident light, and the diffraction angle.

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It would take 1.556 seconds for the barrier to crumple and safely slow down the person with a force of 1180 N.

To calculate the time required to crumple the barrier and safely slow down the person, we can use the concept of impulse.

The impulse, denoted by J, is defined as the product of force and time, and it represents the change in momentum of an object. In this case, the impulse required to safely slow down the person can be calculated using the maximum force and the person's initial momentum.

The momentum of a person is given by the product of their mass and velocity:

Momentum = mass × velocity

Given that the person's mass is 68 kg and their velocity is 27 m/s, the initial momentum is:

Initial momentum = 68 kg × 27 m/s

To safely slow down the person, the impulse provided by the barrier should be equal to the change in momentum.

Therefore, we have:

Impulse provided by barrier = Final momentum - Initial momentum

Since the person is brought to rest, the final momentum is zero. Thus, we have:

Impulse provided by barrier = -Initial momentum

Now we can express the impulse in terms of force and time:

Impulse provided by barrier = Force × Time

Plugging in the known values, we can solve for time:

-Initial momentum = Force × Time

68 kg × 27 m/s = 1180 N × Time

Simplifying the equation, we find:

Time = (68 kg × 27 m/s) / 1180 N

Evaluating the expression:

Time = 1836 kg·m/s / 1180 N

Finally, converting kg·m/s to seconds, we get:

Time ≈ 1.5559 seconds

Therefore, it would take approximately 1.556 seconds for the barrier to crumple and safely slow down the person with a force of 1180 N.

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A graph is called weighted if a numerical weight or cost is assigned to each edge of the graph. When a weighted graph has more than one edge between any two vertices, it is known as a multigraph. The minimum spanning tree (MST) problem is the problem of finding the spanning tree of minimum weight in a connected, undirected graph.

The minimum spanning tree of a graph is the tree with the smallest possible sum of edge weights. MSTs are frequently used in network design and optimization, particularly in computer networks. Compare Prim's and Kruskal's algorithms. Prim's algorithm and Kruskal's algorithm are two well-known algorithms for finding the minimum spanning tree in a graph.

The following are the differences between them: Prim's algorithm finds the minimum spanning tree starting from a single vertex, whereas Kruskal's algorithm starts with the smallest weight edge and then chooses the smallest weight edge that does not form a cycle. Prim's algorithm runs in O(ElogV), while Kruskal's algorithm runs in O(ElogE).

Prim's algorithm is better suited to dense graphs, whereas Kruskal's algorithm is better suited to sparse graphs. If not, give an example of a graph that has more than one minimum spanning tree. In some cases, a weighted graph can have multiple minimum-spanning trees.

Consider the following graph as an example: No, a minimum spanning tree cannot contain a cycle because it is a tree. A tree is a graph that does not contain any cycles, and a minimum-spanning tree is a tree that spans all of the vertices in the graph with the smallest possible weight.

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The four tires of an automobile are inflated to an absolute pressure of 2.0 x 10⁵ Pa. A total of 0.024 m2 of each tire is in touch with the ground. Then the weight (Fg) of the automobile is 19.2 × 10³ N.

The definition of pressure is "force per unit area." P = F/A, for example, yields the force on a unit area. Its Pascal (Pa) SI unit is equivalent to N/m2. is a scalar quantity. its dimensions are [M¹ L⁻¹ T⁻²].  Mass times the gravitational acceleration equals weight.

Pressure is P = F/A

Force on each tire,

F' = PA = 2.0 x 10⁵ Pa × 0.024 m²

F' = 4.8 × 10³ N

For on for tires,

F = F'×4

F =  4.8 × 10³ N × 4

F =  4.8 × 10³ N × 4

F = 19.2 × 10³ N

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The vertical component of jeff's velocity is  4.79m/s.

Since gravity's acceleration in the vertical direction constantly affects vertical velocity, it is a unique type of velocity.

We are given that,

Jeff horizontal velocity = V = 7.0m/s

Vector velocity = v₁ = 5.1 m/s

Therefore , the vertical component of Jeff's velocity(V₂) can be calculated by formula,

V = √V²₁ + V²₂

V₂ = √V - V²₂

V₂ = √(7m/s)² -(5m/s)²

V₂ = 4.79 m/s

Since , the vertical component of jeff's velocity would be 4.79m/s.

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the vertical component of jeff's velocity is 4.794 m/s

The rate at which an object's location changes as seen from a certain point of view and as measured by a particular unit of time is defined as its velocity, which is the direction it is travelling in. Velocity is a fundamental concept in kinematics, the branch of classical mechanics that deals with the motion of bodies.

The motion of celestial objects like satellites, planets, stars, and galaxies is described by a physical theory known as classical mechanics, as well as that of macroscopic objects like projectiles and machine parts. Understanding the current state of a classically governed object makes it possible to predict both its future motion (determinism) and its past motion (reversibility).

Given velocity v = 7.0 m/s, velocity in x direction is vx = 5.1m/s

then \((V^{2}) =(Vx_{} )^2 +(Vy_{} )^2\)

\((7^{2}) =(5.1_{} )^2 +(Vy_{} )^2\)

\((Vy_{} )^2\)=22.99

\((Vy_{} )^2\)=4.79 m/s

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