Use nodal analysis to find V1 and V2 in the circuit shown in Fig. 6.

Answer:  240 inch-lbs.

Explanation:

The spring constant, k, is given by:

k = (F/x)

where F is the force, x is the displacement, and k is the spring constant.

Using the given information, we can calculate the spring constant as:

k = (80 lbs / 2 in) = 40 lbs/in

To find the work done in stretching the spring from its relaxed state to a total of 4 inches, we need to integrate the force over the displacement:

W = ∫F dx

Since the force required to stretch the spring varies with displacement, we need to break up the integration into two parts: one from 0 to 2 inches, and another from 2 to 4 inches.

W = ∫0^2 F dx + ∫2^4 F dx

The first integral is:

∫0^2 F dx = ∫0^2 (kx) dx = (1/2)kx^2 = (1/2)(40 lbs/in)(2 in)^2 = 80 inch-lbs

The second integral is:

∫2^4 F dx = ∫2^4 (2k) dx = 2kx = 2(40 lbs/in)(4 in - 2 in) = 160 inch-lbs

Therefore, the total work done in stretching the spring from its relaxed state to a total of 4 inches is:

W = ∫0^2 F dx + ∫2^4 F dx = 80 inch-lbs + 160 inch-lbs = 240 inch-lbs

So, the work done in stretching the spring from its relaxed state a total of 4 inches is 240 inch-lbs.

Answer:

A) The maximum height above the roof reached by the rock can be found using the formula:

h = (v₀²sin²θ)/(2g)

where v₀ is the initial velocity (32.0 m/s), θ is the angle of the initial velocity (29.0°), and g is the acceleration due to gravity (9.81 m/s²).

Plugging in the values, we get:

h = (32.0²sin²29.0)/(2(9.81)) = 31.1 m

Therefore, the maximum height above the roof reached by the rock is 31.1 meters.

B) The vertical component of the velocity just before the rock strikes the ground is:

vᵥ = v₀sinθ - gt

where t is the time it takes for the rock to reach the ground.

We can find t by using the formula:

h = v₀sinθt - (1/2)gt²

where h is the height of the building (14.0 m). Rearranging this formula and solving for t, we get:

t = (v₀sinθ + sqrt((v₀sinθ)² + 2gh))/g

Plugging in the values, we get:

t = (32.0sin29.0 + sqrt((32.0sin29.0)² + 2(9.81)(14.0)))/9.81 = 4.01 s

Therefore, the vertical component of the velocity just before the rock strikes the ground is:

vᵥ = 32.0sin29.0 - 9.81(4.01) = -14.3 m/s

Note that the negative sign indicates that the velocity is directed downwards.

C) The horizontal distance from the base of the building to the point where the rock strikes the ground can be found using the formula:

d = v₀cosθt

Plugging in the values, we get:

d = 32.0cos29.0(4.01) = 96.4 m

Therefore, the horizontal distance from the base of the building to the point where the rock strikes the ground is 96.4 meters.

Hence, the radio waves from KROQ have a wavelength of roughly 2.81 metres.

A radio wave's frequency is determined by dividing its velocity (c = 299 792 458 m/s, or the speed of light) by its wavelength. Wavelength is the length in metres of a single complete wave. In maths, frequency is defined as f = c/.

The frequency of radio waves is 106,700,000 Hz, while the speed of light  is roughly 300,000,000 m/s. The formula is as follows: c = fλ

where the wavelength is used.

When we rearrange this formula to account for, we obtain: λ = c / f

Inputting the values provided yields:

λ = 300,000,000 m/s / 106,700,000 Hz

λ ≈ 2.81 meters

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Answer:

First, we need to find the equivalent resistance of the parallel combination of 5.0 and 9.0 resistors:

1/R = 1/5.0 + 1/9.0

1/R = 0.4 + 0.1111

1/R = 0.5111

R = 1/0.5111

R ≈ 1.955 ohms

The equivalent resistance of the parallel combination is approximately 1.955 ohms.

Next, we need to find the total resistance of the circuit:

R_total = 4.0 + 1.955

R_total = 5.955 ohms

The total resistance of the circuit is approximately 5.955 ohms.

Using Ohm's Law, we can find the current through the circuit:

I = V/R_total

I = 6.0/5.955

I ≈ 1.006 A

The current through the circuit is approximately 1.006 A.

Finally, we can use the current divider rule to find the current through the 5.0-ohm resistor:

I_5 = (R_parallel / (R_parallel + R_series)) * I_total

I_5 = (1.955 / (1.955 + 4.0)) * 1.006

I_5 ≈ 0.383 A

The current through the 5.0-ohm resistor is approximately 0.383 A.

Hence, R = 28.97 m, 24.5 degrees is the vector sum of T and U.

A vector's direction is frequently stated as a rotation of the vector's "tail" anticlockwise with respect to due East. In accordance with this practise, a vector having a direction of 30 degrees is a vector that has been anticlockwise rotated 30 degrees with respect to due east.

Let's begin by separating the components of the vector T:

T~ = 40 m, 30 degrees

T_x = 40 cos(30) = 34.64 m

T_y = 40 sin(30) = 20 m

Let's now decompose the vector U into its constituent parts:

U~ = 12 m, 225 degrees

U_x = 12 cos(225) = -8.49 m

U_y = 12 sin(225) = -8.49 m

It is possible to combine elements of the same type (x and y):

R_x = T_x + U_x = 34.64 m - 8.49 m = 26.15 m

R_y = T_y + U_y = 20 m - 8.49 m = 11.51 m

The Pythagorean theorem can be used to determine the size of the resulting vector R:

|R~| = sqrt(R_x² + R_y²) = sqrt((26.15 m)² + (11.51 m)²) = 28.97 m

The inverse tangent function can be used to determine the direction of the resulting vector R:

theta = tan⁻¹(R_y/R_x) = tan⁻¹(11.51 m/26.15 m) = 24.5 degree.

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The moment of inertia of the wheel if the block rises to a height of h is 7.5 cm before momentarily coming to rest is 0.068 kg m².

We can use the conservation of mechanical energy to solve for the moment of inertia of the wheel. Initially, the system has kinetic energy, which is converted to potential energy at the highest point of the block's trajectory. Therefore, we can write:

Initial kinetic energy = Final potential energy

At the start, the wheel and block have kinetic energy due to the motion of the block:

KE i = 0.5 * m * v²

At the highest point of the block's trajectory, all of the kinetic energy is converted to potential energy due to the block's height above the ground:

PE_f = m * g * h

where g is the acceleration due to gravity.

Since the string is wrapped around the circumference of the wheel, the distance that the block moves upwards is equal to the distance that the string moves around the wheel, which is equal to the circumference of the wheel:

h = 2 * pi * R

Substituting this into the expression for potential energy:

PE_f = m * g * 2 * π * R

Equating initial kinetic energy with final potential energy:

0.5 * m * v² = m * g * 2 * π * R

Simplifying and solving for the moment of inertia of the wheel, I:

I = (m * v²) / (2 * g * π * R)

Substituting the given values:

I = (1.9 kg * 0.43 m/s)² / (2 * 9.81 m/s² * π * 0.081 m)

I = 0.068 kg m²

Therefore, the moment of inertia of the wheel is 0.068 kg m².

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Ball A will have the greater density because it has twice as much mass as ball B for the same volume. Ball C will have the greater density because it has 3 times the volume of ball D and only 1/3 the mass.

Volume is the quantity of three-dimensional space occupied by an object or a substance. It is measured in cubic units, such as liters or gallons. Volume is an important concept in mathematics, physics, chemistry, and engineering, and is often used to calculate the amount of material needed for a certain project. For example, in architecture, engineers may use volume to determine the amount of concrete needed to build a bridge. In cooking, cooks use volume to measure the amount of ingredients needed for a recipe. In physics, volume is used to measure the amount of space an object occupies, or the amount of space within an object, such as a liquid or gas.

Ball P will have the greater density because it is twice as large as ball Q for the same mass. Ball X will have the greater density because it is twice as big as ball Y but weighs only half as much.

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Answer: (0.17 * 6) + ( 0.16 * 0 ) = (0.17 * 0) + ( 0.16 *  v2)

v2 = 6.375 m/s

Explanation:

The answer is v2 = 6.375 m/s

(I did the equation and everything but just in case, check with someone else so you don't get the wrong answer)

To solve this problem, we can use the principle of conservation of momentum, which states that the total momentum of a system remains constant if there are no external forces acting on it. We can set the momentum of the asteroid before the collision equal to the momentum of the asteroid-Silly Putty system after the collision.

The momentum of the asteroid before the collision is:

P_before = m_ast * v_ast

where m_ast is the mass of the asteroid and v_ast is its velocity.

The momentum of the asteroid-Silly Putty system after the collision is:

P_after = (m_ast + m_sp) * v_final

where m_sp is the mass of the Silly Putty, v_final is the velocity of the asteroid-Silly Putty system after the collision, which we assume to be zero.

We can equate these two expressions for momentum and solve for the mass of the Silly Putty:

m_sp = (m_ast * v_ast) / (-v_final)

Substituting the given values:

m_ast = 25,000 kg

v_ast = 1500.0 m/s

v_final = -100.0 m/s

m_sp = (25,000 kg * 1500.0 m/s) / (-(-100.0 m/s))

m_sp = 375,000 kg m/s / 100.0 m/s

m_sp = 3750 kg

Therefore, we would need 3750 kg of Silly Putty to stop the asteroid if we launched it at a velocity of -100.0 m/s.

The relationship of the wavelength of a particle and its mass is they are inversely related.

Option D is correct.

The link between a particle's mass and wavelength is provided by the de Broglie wavelength equation: = h/p,

where is the wavelength, h is the Planck constant, and p is the particle's momentum.

This condition shows that a molecule's energy is contrarily relative to its frequency. Because momentum (p = mv) is defined as the product of mass and velocity, we can also say that a particle's wavelength is inversely proportional to its mass.

A wavelength is the distance between two identical points (adjacent crests) in consecutive cycles of a waveform signal that travels in space or down a wire. In wireless systems, its length is typically measured in meters (m), centimeters (cm), or millimeters (mm).

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This is the pressure at the top of the container due to the height of the water. The pressure at the bottom of the container due to the height of the water is 0 Pa since the datum was set at the bottom.

Pressure is a physical quantity used to measure the force applied by an object to another object or by an object to a surface. It can be expressed as the force per unit area and is typically measured in units such as pounds per square inch (psi) or pascals (Pa). Pressure can be applied to gases, liquids, and solids, and is generated by the weight of the atmosphere, the force of gravity, and by the movement of air or liquids. Pressure can also be created by mechanical devices such as pumps and compressors, as well as by chemical reactions.

ρ = density of water = 1000 kg/m3

g = acceleration due to gravity = 9.81 m/s2

h = height of the container = 7.7 in = 0.198 m

Using the equation ρgh = density x gravity x height, we can calculate the pressure at the top of the container to be:

ρgh = (1000 kg/m3)(9.81 m/s2)(0.198 m) = 1960.38 Pa

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Answer:

D. Thermoelectric thermometer

Explanation:

It preferred for rapidly changing temperature

Answer:d. 109N/C

Explanation: The atomic electric field, the field between the atomic nucleus and the surrounding electron cloud, should possess information about the atomic species, local chemical bonding, and charge redistributions between bonded atoms.

Answer:

Start:

Higher energy of reactants -> Transition state

Finish:

Lower energy of reactants -> Higher energy of products

Explanation:

Answer:

if the temperature of the sink is lowered by 6.7%, the efficiency of the Carnot engine will increase by 10%.

Explanation:

The efficiency of a Carnot engine is given by the equation:

η = 1 - T_sink / T_source

where η is the efficiency, T_sink is the temperature of the sink, and T_source is the temperature of the source.

In this case, we are given that the efficiency of the engine is 40%. Therefore, we can write:

0.4 = 1 - T_sink / T_source

Rearranging this equation, we get:

T_sink / T_source = 1 - 0.4

T_sink / T_source = 0.6

Next, we are asked to find the temperature of the sink needed to increase the efficiency of the engine by 10%. Let's call this new efficiency η_new. Since the efficiency of a Carnot engine is given by the same equation as before, we can write:

η_new = 1 - T_sink_new / T_source

where η_new is the new efficiency, and T_sink_new is the new temperature of the sink.

We know that the new efficiency is 10% higher than the original efficiency, so we can write:

η_new = η + 0.1η = 0.4 + 0.1(0.4) = 0.44

Substituting this into the equation above, we get:

0.44 = 1 - T_sink_new / T_source

Rearranging this equation, we get:

T_sink_new / T_source = 1 - 0.44

T_sink_new / T_source = 0.56

Now we can set up an equation to find the new temperature of the sink:

0.56 = T_sink_new / T_source

T_sink_new = 0.56T_source

To find the temperature difference between the old and new sink temperatures, we can subtract the two equations we have derived:

T_sink_new - T_sink = 0.6T_source - 0.56T_source

T_sink_new - T_sink = 0.04T_source

Finally, we can substitute the given efficiency of 40% to find the source temperature:

0.4 = 1 - T_sink / T_source

T_source = T_sink / (1 - 0.4)

T_source = T_sink / 0.6

Substituting this expression for T_source into the equation for the temperature difference, we get:

T_sink_new - T_sink = 0.04(T_sink / 0.6)

Simplifying, we get:

T_sink_new - T_sink = 0.067T_sink

Multiplying both sides by 100, we get:

(T_sink_new - T_sink) * 100 = 6.7T_sink

Therefore, if the temperature of the sink is lowered by 6.7%, the efficiency of the Carnot engine will increase by 10%.

The intensity of the force F is calculated to be approximately 2.83 N.

Coefficient of sliding friction is a value that measures force of sliding friction for particular surface type.

Weight = mg = 1 kg x 10 m/s² = 10 N (acting downwards)

F_vertical - Weight = 0

F_vertical = 10 N

As Frictional force = coefficient of friction x normal force

Frictional force = 0.2 x 10 N = 2 N (acting to the left)

F_horizontal = F x cos(45) = F / √2

F_horizontal - frictional force = 0

F_horizontal = frictional force = 2 N

F / √2 = 2 N

F = 2 N x √2

F ≈ 2.83 N

Therefore, the intensity of the force F is approximately 2.83 N.

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To derive the equation for the buoyant force, we can start with the equation for the pressure from a fluid at a certain depth:

P = ρgh + Patm

where P is the pressure at a depth h, ρ is the density of the fluid, g is the acceleration due to gravity, and Patm is the atmospheric pressure at the surface of the fluid.

Now, let's consider a simple submerged object, such as a perfect cube with sides of length s, as the hint suggests. The object is fully submerged in the fluid, so it experiences a pressure difference between the top and bottom surfaces. The pressure at the top surface of the object is Ptop = ρghtop + Patm, where htop is the depth of the top surface below the surface of the fluid. The pressure at the bottom surface of the object is Pbottom = ρghbottom + Patm, where hbottom is the depth of the bottom surface below the surface of the fluid. Since the object is at rest in the fluid, the net force acting on the object must be zero. Therefore, the buoyant force must be equal and opposite to the weight of the object:

Buoyant force = Weight of object

The weight of the object is given by its mass multiplied by the acceleration due to gravity:

Weight of object = mg

where m is the mass of the object and g is the acceleration due to gravity.

To find the buoyant force, we need to find the difference between the pressure at the top and bottom surfaces of the object, and then multiply that difference by the surface area of the object:

Buoyant force = Pressure difference × Surface area

The pressure difference is given by:

Pressure difference = Pbottom - Ptop

= (ρghbottom + Patm) - (ρghtop + Patm)

= ρg(hbottom - htop)

Therefore, the buoyant force is:

Buoyant force = ρg(hbottom - htop) × Surface area

For a perfect cube with sides of length s, the surface area is given by A = 6s^2. Therefore, the buoyant force on the cube is:

Buoyant force = ρg(hbottom - htop) × 6s^2

This is the equation for the buoyant force on a submerged object, derived from the equation for the pressure from a fluid at a certain depth and the concept of the buoyant force being due to the pressure difference between the top and bottom of an object.

Maria is taking the Rorschach inkblot test.

The test is designed to assess an individual's personality traits and psychological functioning based on their responses to the images.

The Rorschach inkblot test, which  uses a set of inkblot images and asks participants to describe what they see. The Rorschach test is a projective test that is often used to assess an individual's personality, emotional functioning, and thought processes.

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Answer:

The energy produced by the sun when it converts 2 kg of mass into energy is given by Einstein's famous equation E = mc², where E is the energy produced, m is the mass converted, and c is the speed of light.

Substituting the values, we have:

E = (2 kg) x (299,792,458 m/s)²

E = 2 x 89,875,517,873,681,764 J

E ≈ 1.7975 x 10²⁰ J

Therefore, the sun produces approximately 1.7975 x 10²⁰ joules of energy when it converts 2 kg of mass into energy.

Answer: Applying a weight limit to a road is often done in an attempt to protect a roadway's appearance in particular. It also aims to protect the character and environment of rural areas, villages, and residential estates. Restricting overweight freights may just prevent damages like pot holes and cracks in the road.

Explanation:

I HOPE THIS HELPED GOOD LUCK AND I AM OPEN FOR FREE ANSWERS!

The magnitude of the normal force of the car is given by Fn = Fg cotθ.

The normal force is the force exerted by the racetrack perpendicular to the car's motion. Let's now derive the expression for the magnitude of the normal force of the car:

The perpendicular component of the normal force is given by:

Fn⊥ = Fg cosθ

The parallel component of the normal force provides the centripetal force required for circular motion.

The centripetal force (Fc) is given by:

Fc = mv²/r

where;

The centripetal force can also be expressed in terms of the parallel component of the normal force:

Fc = Fn∥ = Fn sinθ

Equating the two expressions for Fc, we get:

Fn sinθ = mv²/r

Solving for Fn, we get:

Fn = mv²/(r sinθ)

Substituting the expression for Fg cosθ, we get:

Fn = Fg cosθ / sinθ

or

Fn = Fg cotθ

where;

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The complete question is below:

Circular turns of radius r in a racetrack are often banked at an angle θ to allow the cars to achieve higher speeds around the turns. Assume friction is not present.

Now write the magnitude of the normal force of the car, in terms of the gravitational force Fg, g, θ, the radius of the track r, and the velocity that the car is traveling v.

To solve this problem, we can use the kinematic equation for vertical motion under constant acceleration, which is given by:

[tex]y = vi*t + (1/2)at^2[/tex]

What is displacement?

Displacement is a vector quantity that refers to the overall change in position of an object from its initial position to its final position.

It is a straight line distance between the initial and final position, in a specific direction.

where y is the displacement (in this case, the vertical distance the ball falls), vi is the initial velοcity (0 in this case since the ball is thrοwn hοrizοntally), a is the acceleratiοn due tο gravity[tex](-32.2 ft/s^2)[/tex], and t is the time it takes fοr the ball tο reach hοme plate. We can find t by dividing the distance tο hοme plate by the hοrizοntal velοcity:

[tex]t = 60.5 ft / (102.5 mi/h * 5280 ft/mi * 1 h/3600 s) = 0.400 s[/tex]

Now we can use the kinematic equation to find y:

[tex]y = 0 + (1/2)(-32.2 ft/s^2)(0.400 s)^2 = -2.57 ft[/tex]

Note that the negative sign indicates that the displacement is downward. Therefore, the ball falls about 2.57 feet vertically by the time it reaches home plate.

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Answer: 0.1

Explanation:

To find the tension on the stone, we can use the centripetal force formula, which is given by F = (mv^2)/r, where m is the mass of the object, v is its velocity, and r is the radius of the circular path.

In this case, the stone is tied to a string and is moving in a circle of radius 50 cm (or 0.5 m), so we have:

F = (0.05 kg) x (1 m/s)^2 / 0.5 m

F = 0.1 N

Therefore, the tension on the string is 0.1 N.

So, the correct answer is 0.1.

The gravitational potential energy of the two climbers would be 26,460 J.

The gravitational potential energy (PE) of an object is given by the formula:

PE = mgh

where m is the mass of the object, g is the acceleration due to gravity, and h is the height of the object above some reference point.

In this case, the combined mass of the two climbers is 150 kg, and they are 18 m above the ground. Using g = 9.8 m/s², we can calculate their gravitational potential energy as:

PE = (150 kg) x (9.8 m/s²) x (18 m) = 26,460 J

Rounded to the nearest thousand, the gravitational potential energy of the two climbers is 26,000 J.

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The frequency of vibration of the block supported by two identical parallel vertical springs with spring stiffness constant k and mass m is [tex](1 / 2\pi) * \sqrt(2k / m).[/tex]

In physics, frequency is the number of waves that pass a fixed point in a unit of time as well as the number of cycles or vibrations that a body in periodic motion experiences in a unit of time.

The frequency of vibration of a mass-spring system is given by the formua:

[tex]f = (1 / 2\pi) * \sqrt(k / m)[/tex]

where f is the frequency of vibration, k is the spring constant, and m is the mass of the object.

In this case, the block is supported by two identical parallel vertical springs, each with spring stiffness constant k. So, the effective spring constant is the sum of the individual spring constants:

k_eff = 2k

The mass of the block is given as m.

So, the frequency of vibration of the block supported by two identical parallel vertical springs can be calculated as:

[tex]f = (1 / 2\pi) * \sqrt(k_eff / m) = (1 / 2\pi) * \sqrt((2k) / m)\\f = (1 / 2\pi) * \sqrt(2k / m)[/tex]

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The metaphor "sawing himself in two" highlights the basketball player's agility as his legs and upper body move in opposing directions before coming together at the rim to hit a shot.

Essentially, employing figurative language involves distorting the meaning of words to convey a point, sound clever, or create a joke. Figurative language is a common technique used in narrative writing when the author wants to make the reader feel strongly about something.

Literature forms like poetry, drama, prose, and even speeches use figurative language. Figurative language is a literary element that is employed throughout

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Answer:

Explanation:

The rate of heat transfer from the transistor to the heat sink through the mica sheet can be calculated using Fourier’s Law of heat conduction. The formula for this law is Q = kA(T1 - T2)/d where Q is the rate of heat transfer, k is the thermal conductivity of the material, A is the cross-sectional area through which heat is transferred, T1 and T2 are the temperatures at either end of the material and d is its thickness.

In this case, we know that Q = 1.00 W (the rate at which energy enters the device), k = 0.0753 W/m·°C (the thermal conductivity of mica), A = 8.25 mm * 6.25 mm = 5.15625e-5 m² (the cross-sectional area of the mica sheet), T2 = 35°C (the temperature of the heat sink) and d = 0.0852 mm = 8.52e-5 m (the thickness of the mica sheet).

Substituting these values into Fourier’s Law gives us:

1.00 W = (0.0753 W/m·°C)(5.15625e-5 m²)(T1 - 35°C)/(8.52e-5 m)

Solving for T1 gives us:

T1 ≈ 35 + (1 / ((0.0753 * 5.15625e-5) / 8.52e-5)) ≈ 35 + 22 ≈ 57°C

So under steady-state conditions with an energy input rate of 1 W and a heat sink temperature of 35°C, we can expect that the operating temperature of this power transistor would be approximately 57°C.

Answer:

35J

Explanation:

The mass of the ball=2.5kg

The initial speed=10m/s

we have to calculate the height= h

s=ut+1/2at^2

h=10*0.2 -1/2*10*0.04

h=2-0.2

h= 1.8m

the potential energy= mgh

                                 = 2.5kg*10*1.8

                                = 25*1.8

                                 = 35J

It is important to note that wiring a plug can be dangerous, and if you are not confident in your ability to do so, you should seek the help of a qualified electrician. Incorrectly wiring a plug can result in electrical shock.

What are the step for plug wired ?

The first change that may need to be made is to ensure that the correct wires are connected to the corresponding terminals on the plug. Typically, the green and yellow wire is connected to the earth terminal, the blue wire to the neutral terminal, and the brown wire to the live terminal.

Voltage can be measured with a multimeter. A probe should be inserted into each slot to measure the line voltage. A fully functioning outlet registers between 110 and 120 volts. Check the outlet and the wiring if there is no reading.

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