two objects gravitationally attract with a force of 36 N if the distance between the two objects centers is decreased by a factor of threee then the new force of attraction is

The interaction energy for two point charges, q₁ and q₂, a distance 'a' apart is q₁q₂/4πε₀a.

In physics, interaction energy is the contribution to the total energy that is caused by an interaction between the objects being evaluated. The interaction energy generally depends on the relative position of the objects.

For example q₁q₂/4πε₀Δr is the electrostatic interaction energy between two objects with charges q₁ and q₂.

[tex]W_{tot}[/tex] = ε₀/2(∫E²dτ)

= ε₀/2{(∫E₁ + E₂)²dτ}

= ε₀/2(∫E₁² + E₂² + 2E₁E₂)dτ

= W₁ + W₂ + ε₀(∫E₁ × E₂)²dτ

E₁ = 1/4πε₀(q₁/r²)r

E₂ = 1/4πε₀(q₂/ᴫ²)ᴫ

[tex]W_{i}[/tex] = ε₀q₁q₂/(4πε₀)²[∫{(1/r²ᴫ²)cosβr²sinθdrdθdφ}]

Where (from the figure)

ᴫ = √(r² + a² - 2ra cosθ), cosβ = (r - a cosθ)/ᴫ

Therefore

[tex]W_{i}[/tex]  = {q₁q₂/(4π)²ε₀} 2π∫{(r - acosθ)/ᴫ³} sinθ drdθ

First do the r integral first, changing variables to ᴫ:

2ᴫdᴫ = (2r - 2a cosθ)

⇒(r - a cosθ)dr = ᴫdᴫ

As r : 0→∞, ᴫ : a→∞, so

[tex]W_{i}[/tex] = {q₁q₂/8πε₀a} [tex]\int\limits^\pi _0[/tex](∫limit 0 to ∞ 1/ᴫ² dᴫ) sinθ dθ

The ᴫ integral is 1/a, so

[tex]W_{i}[/tex] = {q₁q₂/8πε₀a} [tex]\int\limits^\pi _0[/tex] sinθ dθ

[tex]W_{i}[/tex] = q₁q₂/4πε₀a

This is the exact interaction energy of two-point charges.

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molecule possesses neutrons and a total electric charge of one Coulomb. e is the electronic value, 1.60 x 10-19 Coulombs, and the proton has a cost of +e while the electron has a fee of -e.

The quantity of charge carried by a present of one amp for one second is measured in coulombs, which is the unit of measurement used in the SI for electric charge. It may also be a quality of a substance that causes magnetic and electric effects to occur. The symbol for it is C. According to math, 1 Coulomb equals 1 Ampere x 1/sec.

A coulomb is an unit of power charge that represents the charge that is transmitted over one ampere of current in one second. Colomb's rule. depending on the charged items, electric force.

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The four factors that makeup latency are processing delay caused by processor speed, node queueing delays caused by node load, and transmission delay caused by the bit rate of transmission.

The term "latency" refers to the amount of time that passes between the sender and the recipient of data, or between a particular user action and the resulting answer. A user's internet experience will be significantly impacted by network latency, a serious problem with internet access that can be brought on by a number of factors.

Depending on the application case, there are two forms of latency: one-way transmission and round trip. The transmission of data packets from a source to a destination is referred to as one-way latency.

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The height formed by this 25-foot ladder that leans against a wall is 24 feet.

To find out how far up a wall a ladder will reach, you can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, the ladder forms one side of the triangle, the wall forms another side, and the distance between the base of the ladder and the wall forms the hypotenuse.

Let's call the height of the wall h. Using the Pythagorean theorem, we can set up the following equation:

(25 ft)^2 = h^2 + (7 ft)^2

625 = h^2 + 49

576 = h^2

h = sqrt(576) = 24 ft

Therefore, a 25 ft ladder that is 7 feet from the wall will reach 24 feet up the wall.

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Answer:

2.58 m/s

Explanation:

To determine the theoretical speed at which the golf ball must have left the floor, you can use the principle of conservation of energy, which states that the total energy in a closed system remains constant. In this case, we can use the fact that the ball's potential energy changes as it rises and falls.

First, we know that the efficiency of the ball is 61.0%, so we can assume that 39% of the energy is lost as heat, sound, etc. We can calculate the initial kinetic energy (Ei) of the ball as:

Ei = Efficiency * (Initial Potential energy - Final Potential energy)

Ei = 0.61 * (0.444 - 0.271) = 0.119J

Now, we can use this value to calculate the velocity (Vi) of the ball as it left the floor, by using the equation of kinetic energy:

Ei = 0.5 * m * Vi^2

Where:

m = mass of the ball = 0.0453 kg

Vi = velocity of the ball when it left the floor

By substituting the values in the equation we get:

0.119 = 0.5 * 0.0453 * Vi^2

Solving for Vi:

Vi = sqrt(0.119 / (0.5 * 0.0453))

Vi ≈ 2.58 m/s

So, the theoretical speed with which the ball must have left the floor is approximately 2.58 m/s

Keep in mind that this is a theoretical speed and there may be a variance with real-world observations.

(A)  in mechanical equilibrium is correct option, as there is no net force acting on it. A non-rotating object that has no acceleration can be said to be in mechanical equilibrium.

Mechanical Balance When all forces acting on an object of interest are equal to zero, mechanical equilibrium has occurred. The balance of all the forces must exist for this to occur.

A reversible reaction is in a stable state called dynamic equilibrium when the rate of the forward reaction equals the rate of the backward reaction. The reaction has come to an end when there is static equilibrium, sometimes referred to as mechanical equilibrium. Or to put it another way, the system is idle.

When an object's acceleration is equal to zero, it is said to be in mechanical equilibrium. The object is either at rest with no change in position over time or it is traveling at a constant pace in this state. The net force acting on the object is equal to zero since the acceleration is zero.

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The graph that best illustrates how the intensity of sound varies as a detector is moved further and further from a stationary source projecting sound in all directions would be an inverse square law graph. This graph would show that the intensity of sound decreases as the distance from the source increases. The intensity of sound is inversely proportional to the square of the distance from the source.

This means that if the distance from the source is doubled, the intensity of sound is decreased by a factor of four. This relationship is commonly observed in physics and engineering and is known as the inverse square law of sound propagation. This law states that the intensity of sound decreases as the distance from the source increases in a manner that is inversely proportional to the square of the distance.

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You and your friend will have the same potential energy at the top of the tower because gravitational potential only depends on height and not on how an object got there.

The power that a substance retains as a result of its position in relation to other things, internal pressures, electric charge, or other substances is known as potential energy in physics. Potential energy is a form of energy that is stored but is dependent on the interactions of different system components.

A steel ball has more potential energy if it is raised above the ground as opposed to dropping to it. The energy that is present in everything that is raised from rest and has the potential to be released at a later time is known as potential energy.

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The speed of the truck is 14.3m/s without the crate sliding.

The resistive friction force (Fr) multiplied by the usual or horizontal pressure (N) pushing the things together yields the frictional coefficient (fr), which is a numerical value. The formula fr = Fr/N serves as a representation of it.

Call the mass of the egg crate m. The forces on it are its weight Fg =mg vertically down, the normal force n of the truck bed vertically up, and static friction (fs) directed to oppose relative sliding motion of the crate on the truck bed. The friction force is directed radially inward. It is the only horizontal force on the crate, so it must provide the centripetal acceleration. When the truck has maximum speed, friction fs will have its maximum value with fs=μn.

Newton’s second law in component form becomes

∑Fy=ma(y) giving  n−mg = 0  or  n = mg

∑F(x)=ma(x) giving f(s)= ma(r)

From these equations

μ(s)n ≤ mv²/r and μ(s)mg ≤ mv²/r

The mass divides out. The maximum speed is then

v≤[tex]\sqrt{}[/tex]μrg =[tex]\sqrt{}[/tex]0.600(35.0m)(9.80 m/s²) = v ≤1 4.3m/s.

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The numerical value of the vertical velocity of the car at time t=0 is 4.91 meters per second.

Given,

t = 0.25 s

y = 0.75 m

α = 0.95 rad/s²

ω = 6.3 rad/s

Wf=6.54 rad/sec

V=wr

6.54*0.75

V=4.91 m/s

The classic example of independent motions along different axes is projectile motion. Projectile motion is the combination of two separate linear motions. The horizontal motion doesn’t affect the vertical motion, and vice versa. Since there is no acceleration in the horizontal direction (ignoring air resistance), the projectile moves with constant velocity in the x direction.

If an object slides down a friction less plane inclined at angle θ, the acceleration down the plane is g sin θ, because the component of g (the downward acceleration due to gravity) that points along the plane is g sin θ. (There is no acceleration perpendicular to the plane because the normal force from the plane cancels the component of the gravitational force perpendicular to the plane.

Another type of 2-D motion is circular motion. If an object is moving in a circle of radius r with speed v at a given instant, then the (inward) radial component of the acceleration vector a equals. This radially inward acceleration is called the centripetal acceleration. If additionally the object is speeding up or slowing down as it moves around the circle.

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(A) The current in the long straight wire produces a magnetic field that is perpendicular to its direction of flow.

What is Counter clockwise ?

Counter clockwise is a direction opposite to the usual clockwise direction. It is often used to describe the direction of rotation or movement, such as the turning of a wheel, the orbits of planets, or the hands of a clock. Counterclockwise motion can also be referred to as "widdershins" or "anticlockwise."

This magnetic field interacts with the loops of wire, inducing a current in them. The direction of the current in loop A is clockwise due to the right hand rule.
(B) No current is induced. Since the flux through loop B is not changing, no induced current is created.
(C) No current is induced. Since loop C is not moving, the changing magnetic field will not induce any current in it.

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Complete Questions:
(a) What is the direction of the induced current, if any, in loop A?

A) clockwise

B) counterclockwise

C) No current is induced.

(b) What is the direction of the induced current, if any, in loop B?

A clockwise

B counterclockwise

C No current is induced.

(c) What is the direction of the induced current, if any, in loop C?

A clockwise

B counterclockwise

C No current is induced.

The angle must be formed if the tension in each cable is equal to 0.75 of the frame weight is 83.6⁰.

By using the parallelogram law of vector addition, it is possible to calculate the angle between the two wires.

a² + b² - 2abcosθ = R²

Where;

R = is the outcome vector = the frame's weight ⇒ W

Angle between the two wires equals 0.75W for the first wire's tension and 0.75W for the second wire's tension.

(0.75W)² + (0.75W)² - 2(0.75W x 0.75W) cosθ = W²

1.125W² - 1.125W² cosθ = W²

= 1.125W²(1 - cosθ)

W²/1.125W² = 1 - cosθ

0.8889 = 1 - cosθ

cosθ = 1 - 0.8889

cos θ = 0.1111

θ = arc cos(0.1111)

θ = 83.6⁰

So, the angle must be formed if the tension in each cable is equal to 0.75 of the frame weight is 83.6⁰

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A = (v-u)/t, where an is acceleration, v is final speed, u is initial speed, and t is time, is the equation for acceleration. When the values are filled in, we obtain a = (60-20)/5 or an is 8 m/s2.

The equation a = v/t denotes acceleration (a), which is the change in velocity (v) over the change in time (t). This enables you to calculate the change in velocity in meters per second squared (m/s2).

+2 m/s2

If there is no change in velocity between 2 and 3 seconds, the acceleration is 0 m/s2. The acceleration is +2 m/s2 over the first 0 to the second interval. The acceleration is zero between seconds two and three. The acceleration is -3 m/s2 throughout the three to six-second period.

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The temperature difference of  1 K on the Kelvin scale is equivalent to the temperature difference of (5/9)°F on the Fahrenheit scale.  Triple-point temperature of water is approximately 491 degrees Rankine.

The unit of scales on the Rankine scale is the same as those on the Fahrenheit scale. Hence, from the freezing point of water (0⁰C) to the boiling point of water(100⁰C) , Rankine scale is divided into 180 scales.

The absolute zero is zero degrees Rankine.  In Celsius scale, absolute zero is −273 °C.

A). A unit scale on the Kelvin scale is the same size as a unit scale in the Celsius scale. Hence,

ΔT 1 K = ΔT 1°C

The ratio of Celsius and Fahrenheit scale is 5/9, therefore:

K/F = C/F = 5/9

Hence,

ΔT 1 K = ΔT (5/9)°F

B) Triple-point temperature of water is approximately 0 °C. Since zero degrees Rankine is equivalent to  −273 °C, hence:

0 °C = 0 - (9/5)(-273) = 491 degrees Rankine.

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Measuring 27ml of liquid using graduated cylinder, it is used to measures the volumes of liquids.

Long, thin vessels called graduated cylinders are used to measure liquid volume. They are not meant to be heated, stirred, or weighed. Graduated cylinders typically come in sizes between 5 and 500 ml. Some of them can even hold volumes greater than one liter.

With your eyes directly level with the liquid, place the graduated cylinder on a flat surface and measure the height of the liquid inside. The liquid will usually slant downward. The term "meniscus" refers to this curve. Read the measurement at the meniscus's bottom at all times.

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The formulas F(A)×R(A) = F(B)×R(B) should be used to determine the distance of item B from the fulcrum such that it balances object A. where F is the object's force and R is the object's distance from the fulcrum.

The push or pull that causes a massed body to change its speed is the definition of force. An agent with the ability to change a body's rest or moving condition is known as an external force. It has a magnitude as well as direction.

Forces are created by the interactions between two (or more) objects. There is a similar but opposing force acting on each individual on the other. External forces are what cause the item to move.

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Answer:

But the safest way to loosen a tight cap may be to run hot water on it so that it expands slightly.

Explanation:

Thermal energy is the internal energy that exists in a system and is connected to the movement of the particles and can be contributed to a substance.

The energy in such a system that regulates its temperature is referred to as thermal energy. The exchange of thermal energy is referred to as "heating." Thermodynamics, a whole field of physics, is the study of how heat is transmitted between various systems and how work is performed in the process.

In physics, motion is a variation in an object's position with respect to its surroundings over a predetermined amount of time. To describe how an object travelling with a specific mass moves, use the terms below: Distance. Displacement. Speed.

So-called thermal energy is the internal energy present in a system that is connected to particle motion that can be given to a substance.

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The cross-sectional area of a conductor is defined as the diameter of the conductor in mils, squared.

What is  conductor?

A conductor is a material or object that allows the flow of electric current. It is a material that has a large number of free electrons which can move freely between atoms, allowing for the current to flow through the material. Conductors can be either solid or liquid, and can be used to create electrical circuits and systems. Common conductors used in electrical systems include copper, aluminum, silver, and gold. These materials have high electrical conductivity, meaning they have low resistance and allow for large amounts of electric current to pass through them. Conductors are essential in many electronics and electrical devices, as they are responsible for carrying the electric current from one component to another.

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The angular velocity of a point on the surface of the earth is [tex]7.3 * 10^{-5} rad/s[/tex]

What is angular velocity?

Angular velocity is a vector quantity and is described as the rate of change of angular displacement which specifies the angular speed or rotational speed of an object and the axis about which the object is rotating.

What is angular velocity and write its formula?

Angular velocity is the rate of change of the position angle of an object with respect to time, so w = theta / t, where w = angular velocity, theta = position angle, and t = time.

Every point on the earth's surface completes one circular orbit (centered at a point on the axis) in 1 day

1 day = 24x60x60

1 day=86400s

Angular velocity is given by :

[tex]w =2\pi /86400\\ w =7.3*10^{-5} rad/s[/tex]

Thus, [tex]7.3 * 10^{-5} rad/s[/tex] is the correct answer.

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3 real life examples of people displaying data are, analyzing train schedule, tracking, favorite player stats, analyzing data of workout machines.  

Analyzing different types of data is included in our daily life routine. We can understand it by the following examples:

First is analyzing the train schedule to find out which train is going to our destination, and how much time it will take to reach there, etc. Second one is analyzing the player stats to look how amazing the records have been of your favorite player in last 5 years, against a particular team, etc. Third one is analyzing the data of workout machines, like, how much weight you gained/loose, how much weight you are lifting in the gym, etc.

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The rate of fuel consumption is 6.69 kg/hr.

Solution:

To determine the rate of fuel consumption, we need to calculate the amount of energy required by the engine and divide that by the thermal efficiency.

From the question:

W = 110 hp

η = 28%.

r = ?

First, we can convert the power output from horsepower to watts:

1hp = 746 W

power output = 110 hp x 746 W/hp

                       = 82016 W

Then, we can calculate the energy required by the engine by multiplying the power output by the time the engine is running:

Energy = Power x time

Without knowing the time the engine runs, we cannot calculate the energy required.

We can calculate the fuel consumption by using the heating value of the fuel and the thermal efficiency.

Fuel consumption =           ( Power )                    

                                    (heating value * thermal efficiency))

So in this case:

Fuel consumption =     (82016)

                               (44200*0.28)

                            = (82016)

                                 12276

Fuel consumption = 6.69 kg/hr

Hence, the rate of fuel consumption is 6.69 kg/hr.

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Caffeine dosage and time to finish a maze are independent variables, meaning that a change in one does not cause a change in the other. It is possible that caffeine dosage may have an effect on the time it takes to finish a maze, but the time it takes to finish a maze would not cause a change in caffeine dosage.

Caffeine is a stimulant that can affect the central nervous system and can have a range of effects on the body, including increased alertness, focus, and energy. When it comes to completing a maze, the time it takes to finish it could be affected by the person's level of alertness, focus, and energy. Therefore, if a person ingests a certain dosage of caffeine, it could affect the time it takes for them to finish the maze because of the effect caffeine has on the body.

On the other hand, the time it takes to finish a maze does not affect the caffeine dosage, in other words, caffeine dosage is an independent variable, it does not depend on other variables, and does not change based on the time it takes to complete a maze. It is determined by the amount of caffeine consumed.

So, in short, caffeine dosage can have an effect on the time it takes to finish a maze, but the time it takes to finish a maze does not have an effect on caffeine dosage.

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Speed is a scalar quantity that is independent of direction. It is equal to the total distance traveled divided by the total time spent. This means that a plane can normally travel 3952 kilometers in three hours.

Step 1: Make a note of each time the direction changes. Step 2: Determine the distance traveled between each change in direction. Step 3: The total distance traveled is the sum of all the distances from step 2.

As a result, its typical speed is Speed = total distance / total time Speed = 3952 / 3 Speed = 1317.33 km/h.

However, under cloudy conditions, it will travel 184 km less in the same amount of time.

Then, we want to determine the speed under cloudy conditions. Since speed is equal to the total distance divided by the total amount of time, we need to know the total distance under cloudy conditions.

Total distance is equal to the normal distance traveled minus the delay caused by cloudy conditions Total distance. = 3952 - 184 Total distance = 3768 km Total time = 3 hours Speed = 3768 / 3 Speed = 1256 km/hr The plane is traveling at a speed of 1256 km/hr in cloudy conditions. Because it covered less ground in the same amount of time, its speed decreases.

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At the peak  it has the same potential and kinetic energy.

Kinetic energy (K.E.) is inversely proportional to the square of an object's velocity and its mass: K.E. = 1/2 m v2. When a mass is measured in kilograms and a speed is measured in meters per second, the kinetic energy is measured in kilogram-meters squared per second squared.

The velocity will be zero and the ball's displacement will be at its maximum at the highest point of the trajectory. We might state that the energy present is equivalent to the sum of the potential energy.

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In the above situation the net torque on wire 2 due to wire 1 is Zero.

Fleming's left-hand rule identifies the force's direction on a current-carrying wire when it is placed in a magnetic field. It always runs counter to how the magnetic field and electric current are moving.

Torque is a vector quantity by definition. The direction is determined as part of the torque computation. The direction is parallel to both the force and the radius from the axis. It is customary to choose it along the rotational axis in the right-hand rule direction.

a force that is applied that results in a positive counterclockwise torque A negative torque rotates an object in a clockwise direction.

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This problem contains several examples of this.Consider an object sliding on a ramp as depicted here.Downward to the right.

What is the sliding ?

Sliding is a type of motion that involves the movement of an object relative to a surface while keeping contact with it. This type of motion is often used in everyday activities such as walking, running, and skiing. Sliding can also refer to the movement of two or more objects in contact with each other, such as a car door sliding open or a sheet of paper sliding across a table. In physics, sliding is considered to be a type of frictional motion, in which the frictional force between the object and the surface it is sliding on causes the object to move.

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Nuclei of the same element can have different values of Z, N, and A, as these values are all related to the number of protons, neutrons, and nucleons in the nucleus, respectively. Therefore, option 2, 3, and 4 are correct.

Nuclei of the same element can have different values of Z, N, and A due to the number of protons, neutrons, and nucleons they contain, respectively. This is because the number of these particles in the nucleus can vary, although they all will still be the same element. Therefore, option 2, 3, and 4 are correct and option 1 is incorrect.

Nuclei of the same element can have different values of Z, N, and A, as these values are all related to the number of protons, neutrons, and nucleons in the nucleus, respectively. Therefore, option 2, 3, and 4 are correct.

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Wave amplitude at a specific distance is charged (r). It can be expressed as energy; however Coulomb's law says that it is frequently described as a force.

Charge, also known as electric charge, electrical charge, or electrostatic charge and denoted by the symbol q, is a property of a unit of matter that indicates how many more or fewer electrons than protons it contains.

Protons and electrons are the most prevalent charge carriers for the positive and negative forms of electric charges, respectively. Subatomic particles or matter particles are examples of the different forms of charges: Positive charge characterizes protons. Negative charge characterizes electrons.

Tcosθ=mg \sTsinθ=Fe\stanθ=

mg \sFe

​∵ Fe= \sr \s2

Kq \s2

Fe= \s(2d) \s2

Kq \s2

Fe=4.l2 sin2 Kq2

"tan" equals "4l 2 sin 2 mg Kq 2"

equals (4l 2 sin 2 mg)4 0

​q \s2​

Q 2 equals (4mgl 2 sin 2 tan).

4πϵ \s0

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Under certain circumstances, the grounded (neutral) conductors of a residential service are permitted to be sized smaller than the phase conductors.

What is conductors?

A material that easily permits the flow of electricity is referred to as an electrical conductor. Conductivity is the quality of conductors that enables them to conduct electricity.

Electric current is the name given to the movement of electrons through a conductor. Voltage is the amount of power necessary to cause that current to flow through the conductor.

What is phase ?

Phases are parts of a system that are mechanically separable from other parts of the system and are physically distinct from other parts of the system. types of substance. Solid, liquid, or gaseous phases can exist in a system. Strong atomic bonding and high viscosity, which produce a hard form in solids, are their distinguishing characteristics.

Therefore, Under certain circumstances, the grounded (neutral) conductors of a residential service are permitted to be sized smaller than the phase conductors.

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