A long, thin solenoid has 450 turns per meter and a radius of 1.17 cm. The current in the solenoid is increasing at a uniform rate did. The magnitude of the induced electric field at a point which is near the center of the solenoid and a distance of 3.45 cm from its axis is 8.20×10−6 V/m.
Calculate di/dt
di/dt = _________.

Answers

Answer 1

Answer:

[tex]\frac{di}{dt} = 7.31 \ A/s[/tex]

Explanation:

From the question we are told that  

     The  number of turns is  [tex]N = 450 \ turns[/tex]

      The  radius is  [tex]r = 1.17 \ cm = 0.0117 \ m[/tex]

       The  position from the center consider is  x =  3.45 cm  =  0.0345 m

       The  induced emf is  [tex]e = 8.20 *10^{-6} \ V/m[/tex]

Generally according to Gauss law

        [tex]\int\limits { e } \, dl = \mu_o * N * \frac{di}{dt } * A[/tex]

=>    [tex]e * 2\pi x = \mu_o * N * \frac{d i }{dt } * A[/tex]

Where A is the  cross-sectional area of the solenoid which is mathematically represented as

                [tex]A = \pi r ^2[/tex]

=>      [tex]e * 2\pi x = \mu_o * N * \frac{d i }{dt } * \pi r^2[/tex]

=>       [tex]\frac{di}{dt} = \frac{2e * x }{\mu_o * N * r^2}[/tex]ggl;

Here  [tex]\mu_o[/tex] is the permeability of free space with value

          [tex]\mu_o = 4\pi * 10^{-7} \ N/A^2[/tex]

=>     [tex]\frac{di}{dt} = \frac{2 * 8.20*10^{-6} * 0.0345 }{ 4\pi * 10^{-7} * 450 * (0.0117)^2}[/tex]

=>      [tex]\frac{di}{dt} = 7.31 \ A/s[/tex]

Answer 2

The value of di/dt from the given values of the solenoid electric field is;

di/dt = 7.415 A/s

We are given;

Number of turns; N = 450 per m

Radius; r = 1.17 cm = 0.0117 m

Electric Field; E = 8.2 × 10⁻⁶ V/m

Position of electric field; r' = 3.45 cm = 0.0345 m

According to Gauss's law of electric field;

∫| E*dl | = |-d∅/dt |

Now, ∅ = BA = μ₀niA

where;

n is number of turns

i is current

A is Area

μ₀ = 4π × 10⁻⁷ H/m

Thus;

E(2πr') = (d/dt)(μ₀niA)  (negative sign is gone from the right hand side because we are dealing with magnitude)

Since we are looking for di/dt, then we have;

E(2πr') = (di/dt)(μ₀nA)

Making di/dt the subject of the formula gives;

di/dt = E(2πr')/(μ₀nA)

Plugging in the relevant values gives us;

di/dt = (8.2 × 10⁻⁶ × 2 × π × 0.0345)/(4π × 10⁻⁷ × 450 × π × 0.0117²)

di/dt = 7.415 A/s

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Related Questions

Show that the entire Paschen series is in the infrared part of the spectrum. To do this, you only need to calculate the shortest wavelength in the series.

Answers

Answer and Explanation:

The computation of the shortest wavelength in the series is shown below:-

[tex]\frac{1}{\lambda} = R(\frac{1}{n_f^2} - \frac{1}{n_i^2} )[/tex]

Where

[tex]\lambda[/tex] represents wavelength

R represents Rydberg's constant

[tex]n_f[/tex] represents Final energy states

and [tex]n_i[/tex] represents initial energy states

Now Substitute is

[tex]1.097\times 10^7\ m^{-1}\ for\ R, \infty for\ n_i,\ 3 for\ n_i,\\\\\ \frac{1}{\lambda} = R(\frac{1}{n_f^2} - \frac{1}{n_i^2} )[/tex]

now we will put the values into the above formula

[tex]= 1.097\times 10^7 m^{-1}(\frac{1}{3^2} - \frac{1}{\infty^2} )\\\\ = 1.097\times10^7\ m^{-1} (\frac{1}{9} )[/tex]

[tex]= 1218888.889 m^{-1}[/tex]

Now we will rewrite the answer in the term of [tex]\lambda[/tex]

[tex]\lambda = \frac{1}{1218888.889} m\\\\ = 0.82\times 10^{-6} m[/tex]

So, the whole Paschen series is in the part of the spectrum.

From a hot air balloon 2 km​ high, a person looks east and sees one town with angle of depression of 16 degrees. He then looks west to see another town with angle of depression of 84 degrees. What is the distance between the two towns?

Answers

Answer:

7km

Explanation:

The angle of depression is congruent to the angle of elevation and can be explained as angle below horizontal in which the person observing an object must view for him/her to view object's that are lower than him/her.

In angle of depression, there is assumption that object is closer to the person observing it, so there is parallel horizontal for both observing and object been observed.

hot air balloon 2 km​ high,

there exist two triangles

From trigonometry

Tanx= opposite/adjacent

Opp= 2km

Adj= X1

first triangle have base length of

Tan(16)=2/X1

X1=2/ tan(16)

X1=6.97

For Second triangle

Tanx= opposite/adjacent

Opp= 2km

Adj= X2

the other with a base length of

X2=2/tan(84)

X2=0.21

Therefore,, the total distance between the two towns is

x1+x2=6.97+0.21=7.18km

g As observed on earth, a certain type of bacteria is known to double in number every 24 hours. Two cultures of these bacteria are prepared, each consisting initially of one bacterium. One culture is left on earth and the other placed on a rocket that travels at a speed of 0.893c relative to the earth. At a time when the earthbound culture has grown to 256 bacteria, how many bacteria are in the culture on the rocket, according to an earth-based observer

Answers

Answer:

86.4 hrs

Explanation:

The amount of bacteria is initially 1

It doubles every 24 hrs.

After first 24 hrs, the amount = 2

After next 24 hrs = 4

After next 24 hrs = 8

After next 24 hrs = 16

After next 24 hrs = 32

After next 24 hrs = 64

After next 24 hrs = 128

After next 24 hrs = 256

Total time taken to reach 256 = 24 x 8 = 192 hrs

For the bacteria culture on the rocket that travels at a speed of 0.893c relative to the earth, this time is contracted by the relationship

t = t'(1 - ¥^2)^0.5

Where t is the contracted time =?

t' is the time on earth

¥ = v/c

Where v is the speed of the rocket

c is the speed of light

since v = 0.893c

¥ = 0.893

Substituting, we have

t = 192 x (1 - 0.893^2)^0.5

t = 192 x 0.2025^0.5

t = 192 x 0.45 = 86.4 hrs

A bar magnet is dropped from above and falls through the loop of wire. The north pole of the bar magnet points downward towards the page as it falls. Which statement is correct?a. The current in the loop always flows in a clockwise direction. b·The current in the loop always flows in a counterclockwise direction. c. The current in the loop flows first in a clockwise, then in a counterclockwise direction. d. The current in the loop flows first in a counterclockwise, then in a clockwise direction. e. No current flows in the loop because both ends of the magnet move through the loop.

Answers

Answer:

b. The current in the loop always flows in a counterclockwise direction.

Explanation:

When a magnet falls through a loop of wire, it induces an induced current on the loop of wire. This induced current is due to the motion of the magnet through the loop, which cause a change in the flux linkage of the magnet. According to Lenz law, the induced current acts in such a way as to repel the force or action that produces it. For this magnet, the only opposition possible is to stop its fall by inducing a like pole on the wire loop to repel its motion down. An induced current that flows counterclockwise in the wire loop has a polarity that is equivalent to a north pole on a magnet, and this will try to repel the motion of the magnet through the coil. Also, when the magnet goes pass the wire loop, this induced north pole will try to attract the south end of the magnet, all in a bid to stop its motion downwards.

The current in the loop always flows in a counterclockwise direction. Hence, option (b) is correct.

The given problem is based on the concept and fundamentals of magnetic bars. When a magnet falls through a loop of wire, it induces an induced current on the loop of wire. There is some magnitude of current induced in the wire.

This induced current is due to the motion of the magnet through the loop, which cause a change in the flux linkage of the magnet. According to Lenz law, the induced current acts in such a way as to repel the force or action that produces it. For this magnet, the only opposition possible is to stop its fall by inducing a like pole on the wire loop to repel its motion down. An induced current that flows counterclockwise in the wire loop has a polarity that is equivalent to a north pole on a magnet, and this will try to repel the motion of the magnet through the coil. Also, when the magnet goes pass the wire loop, this induced north pole will try to attract the south end of the magnet, all in a bid to stop its motion downwards.

Thus, we can say that the current in the loop always flows in a counterclockwise direction. Hence, option (b) is correct.

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NASA is giving serious consideration to the concept of solar sailing. A solar sailcraft uses a large, low- mass sail and the energy and momentum of sunlight for propulsion.
Should the sail be absorbing or reflective? Why?
a. The sail should be reflective because in this case the momentum transferred to the sail per unit area per unit time is smaller than for absorbing sail, therefore the radiation pressure is larger for the reflective sail
b. The sail should be absorbing because in this case the momentum transferred to the sail per unit area per unit time is larger than for reflective sail, therefore the radiation pressure is larger for the absorbing sail
c. The sail should be absorbing because in this case the momentum transferred to the sail per unit area per unit time is smaller than for reflective sail, therefore the radiation pressure is larger for the absorbing sail.
d. The sail should be reflective because in this case the momentum transferred to the sail per unit area per unit time is larger than for absorbing sail, therefore the radiation pressure is larger for the reflective sail

Answers

Answer:

d. The sail should be reflective because in this case the momentum transferred to the sail per unit area per unit time is larger than for absorbing sail, therefore the radiation pressure is larger for the reflective sail.

Explanation:

Let us take the momentum of a photon unit as u

we know that the rate of change of momentum is proportional to the force exerted.

For a absorbing surface, the photon is absorbed, therefore the final momentum is zero. From this we can say that

F = (u - 0)/t = u/t

for a unit time, the force is proportional to the momentum of the wave due to its energy density. Therefore,

F = u

For a reflecting surface, the momentum of the wave strikes the sail and changes direction. Since we know that the speed of light does not change, then the force is proportional to

F = (u - (-u))/t = 2u/t

just as the we did above, it becomes

F = 2u.

From this we can see that the force for a reflective sail is twice of that for an absorbing sail, and we know that the pressure is proportional to the force for a given area. From these, we conclude that the sail should be reflective because in this case the momentum transferred to the sail per unit area per unit time is larger than for absorbing sail, therefore the radiation pressure is larger for the reflective sail.

A vertical spring stretches 3.8 cm when a 13-g object is hung from it. The object is replaced with a block of mass 20 g that oscillates in simple harmonic motion. Calculate the period of motion.

Answers

Answer:

The period of motion is 0.5 second.

Explanation:

Given;

extension of the spring, x = 3.8 cm = 0.038 m

mass of the object, m = 13 g = 0.013 kg

Determine the force constant of the spring, k;

F = kx

k = F / x

k = mg / x

k = (0.013 x 9.8) / 0.038

k = 3.353 N/m

When the object is replaced with a block of mass 20 g, the period of motion is calculated as;

[tex]T = 2\pi\sqrt{\frac{m}{k} } \\\\T = 2\pi\sqrt{\frac{0.02}{3.353} } \\\\T = 0.5 \ second[/tex]

Therefore, the period of motion is 0.5 second.

Question 5 of 25
Which of the following means that a mirror is convex?
A. +d;
B. -d;
O C. +f
O D. -f


Answers

The sign that represents a convex mirror is +f (option C). Details about convex mirror can be found below.

What is a convex mirror?

A convex mirror is that which is curved or bowed outward like the outside of a bowl or sphere or circle.

The focal length is the distance at which a lens or mirror is in focus. The focal length (f) is usually positive (+) for a convex mirror.

Therefore, the sign that represents a convex mirror is +f.

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"When red light in vacuum is incident at the Brewster angle on a certain glass slab, the angle of refraction is"

Answers

Complete Question

When red light in vacuum is incident at the Brewster angle on a certain glass slab,  the angle of refraction is [tex]36.0 ^o[/tex] . What are

(a) the index of refraction of the glass and

(b) the Brewster angle?

Answer:

a

   [tex]n_r = 1.376[/tex]

b

  [tex]i = 54^o[/tex]

Explanation:

From the question we are told that

     The angle of refraction is  [tex]r = 36.0 ^o[/tex]

   

Generally according Brewster law

              [tex]i + r = 90[/tex]

Here [tex]i[/tex] is the angle of incidence which is also the Brewster angle

So

              [tex]i + 36.0 = 90[/tex]

              [tex]i = 54^o[/tex]

Now the refractive index is mathematically represented as

           [tex]n_r = tan (i)[/tex]

substituting values

           [tex]n_r = tan (54)[/tex]

           [tex]n_r = 1.376[/tex]

On the way to school, the bus speeds up from 20 m/s to 36 m/s in 4 seconds. What distance does the bus cover in this time frame

Answers

Answer:

Explanation:

initial velocity u = 20 m /s

final velocity v = 36 m /s

time taken t = 4 s .

acceleration = (v - u) / t

= (36 - 20) / 4

a = 4 m / s ²

from the formula

v² - u² = 2 a s  , s is distance covered .

putting the values

36² - 20² = 2 x 4 x s

1296 - 400 = 8 x s

s = 112 m .

Answer:112

Explanation:

you check the weather and find that the winds are coming from the west at 15 milers per hour. this information describes the winds

Answers

Answer:

Velocity

Explanation:

We finds that the winds are coming from the west at 15 miles per hour. This information shows the velocity of the wind. Since, velocity is a vector quantity. It has both magnitude and direction. 15 miles per hour shows the speed of wind and west shows the direction of wind motion.

Hence, the given information describes wind velocity.

Consider a bus traveling to the west (negative x direction) that begins to slow down as it approaches a traffic light. Which statement concerning its acceleration in the x direction is correct

Answers

Complete question is;

Consider a bus traveling to the west (-x direction) begins to slow down as it approaches a traffic light. Which statement concerning its acceleration in the x direction is correct

a) The bus is decelerating and its acceleration is positive.

b) The bus is decelerating, and its acceleration is negative.

c) The acceleration is zero.

d) A statement cannot be made using the information given.

Answer:

Option A - bus is decelerating and acceleration is positive.

Explanation:

We are told that the bus is travelling in (negative x direction) and begins to slow down. Since the bus is slowing down, it means that the bus is undergoing a negative acceleration which is called deceleration.

Thus, the bus is decelerating.

Since it is moving in the negative x-axis, it means acceleration is now; -(-a) which gives +a.

Thus, bus is decelerating and acceleration is positive.

A concrete slab shown in Figure 5 is being lifted by using three cables connected to the slab at points A, B and C. The slab is in the xy plane. The vertical force required to lift this slab is 60 kN (F 60 kN). Find the tensions in cables DA, DB and DC (show all your workings that you do to find these)

Answers

Answer:

Fad = 28.8 kN

Fbd = 16.4 kN

Fcd = 28.1 kN

Explanation:

First, find the length of each cable.

AD = √((2 m)² + (0.5 m)² + (2.5 m)²)

AD = √10.5 m

AD ≈ 3.24 m

BD = √((1.5 m)² + (1 m)² + (2.5 m)²)

BD = √9.5 m

BD ≈ 3.08 m

CD = √((1 m)² + (1 m)² + (2.5 m)²)

CD = √8.25 m

CD ≈ 2.87 m

Next, use similar triangles to find the x, y, and z components of each tension force.

Fadx = 2/3.24 Fad = 0.617 Fad

Fady = 0.5/3.24 Fad = 0.154 Fad

Fadz = 2.5/3.24 Fad = 0.772 Fad

Fbdx = 1.5/3.08 Fbd = 0.487 Fbd

Fbdy = 1/3.08 Fbd = 0.324 Fbd

Fbdz = 2.5 / 3.08 Fbd = 0.811 Fbd

Fcdx = 1/2.87 Fcd = 0.348 Fcd

Fcdy = 1/2.87 Fcd = 0.348 Fcd

Fcdz = 2.5/2.87 Fcd = 0.870 Fcd

Now sum the forces in the x, y, and z directions:

∑Fx = ma

-0.617 Fad + 0.487 Fbd + 0.348 Fcd = 0

∑Fy = ma

-0.154 Fad − 0.324 Fbd + 0.348 Fcd = 0

∑Fz = ma

60 kN − 0.772 Fad − 0.811 Fbd − 0.870 Fcd = 0

To solve this system of equations algebraically, start by subtracting the first two equations, eliminating Fcd.

-0.463 Fad + 0.811 Fbd = 0

0.811 Fbd = 0.463 Fad

Fbd = 0.571 Fad

Substitute into either of the first two equations:

-0.617 Fad + 0.487 (0.571 Fad) + 0.348 Fcd = 0

-0.617 Fad + 0.278 Fad + 0.348 Fcd = 0

-0.339 Fad + 0.348 Fcd = 0

0.348 Fcd = 0.339 Fad

Fcd = 0.975 Fad

Now substituting into the third equation:

60 kN − 0.772 Fad − 0.811 Fbd − 0.870 Fcd = 0

60 kN − 0.772 Fad − 0.811 (0.571 Fad) − 0.870 (0.975 Fad) = 0

60 kN − 0.772 Fad − 0.463 Fad − 0.849 Fad = 0

60 kN − 2.083 Fad = 0

Fad = 28.8 kN

Solving for the other two tension forces:

Fbd = 0.571 Fad = 16.4 kN

Fcd = 0.975 Fad = 28.1 kN

Answer:

Tensions of:

DA = 28.81 KN

DB = 16.45 KN

DC = 28.07 KN

Explanation:

see attached

Electromagnetic radiation is more common than you think. Radio and TV stations emit radio waves when they broadcast their programs; microwaves cook your food in a microwave oven; dentists use X rays to check your teeth. Even though they have different names and different applications, these types of radiation are really all the same thing: electromagnetic (EM) waves, that is, energy that travels in the form of oscillating electric and magnetic fields. Which of the following statements correctly describe the various applications listed above?
a) All these technologies use radio waves, including low-frequency microwaves.
b) All these technologies use radio waves, including high-frequency microwaves.
c) All these technologies use a combination of infrared waves and high-frequency microwaves.
d) Microwave ovens emit in the same frequency band as some wireless Internet devices.
e) The radiation emitted by wireless Internet devices has the shortest wavelength of all the technologies listed above.
f) All these technologies emit waves with a wavelength in the range 0.10 to 10.0 m.
g) All the technologies emit waves with a wavelength in the range 0.01 to 10.0 km.

Answers

Answer:

d) Microwave ovens emit in the same frequency band as some wireless Internet devices.

Explanation:

Microwave are radio waves of short wavelength, from about 10 centimetres to one millimetre, in the Super High Frequency and the Extremely High Frequency bands. Microwaves can penetrate into materials and deposit their energy below the surface which is why is is used in microwave heating found in microwave oven. Transmission of data sometimes involves the use of microwaves to send and receive information over a long distance. Microwaves are the mainly used in radar, used for satellite communication, and wireless networking technologies such as Wi-Fi.

PLEASE HELP ANSWER FAST As the vibration of molecules decreases, the _____ of the substance decreases. 1.temperature 2.internal energy 3.kinetic energy 4.all of the above

Answers

I think 1 and 3 is absolutely right but im not sure about number 2.
I think the answer is 4 all of the above because as the vibration decrease automatically the kinetic energy decrease and the temperature is decrease because when the vibration of molecules decrease thats mean the substances is slightly become a solid and you can get a solid cube of liquid if you freeze them

2. The glass core of an optical fiber has an index of refraction 1.60. The index of refraction of the cladding is 1.48. What is the maximum angle a light ray can make with the wall of the core if it is to remain inside the fiber?

Answers

Answer:

We know that the maximum angle that a light ray can wake with the wall of the core is equipment to the minimum angle with the normal of the core that will give rise in total internal reflection. so using Snell's law the angle is subtracted from 90° to get the maximum angle a light ray can make with the wall of the core if it is to remain inside the fiber.

So using

n1sinစ1. = n2sinစ2

1.6sin(x1) = 1.48sin(90),

But sin(90)=1

1.6sin(စ1) = 1.48,

sin(စ1) = 1.48/1.6

စ = 68°

Explanation:

Answer:

i = 67.66⁰

Explanation:

Using the Snell's law formula to solve this question which states that the ratio of the sine of angle of incidence to the sine of angle of refraction is a constant for a given pair of media. This constant is known as the refractive index for the given pair of media. Mathematically,

n = sin(i)/sin(r) where;

i is the angle of incidence

r is the angle of refraction.

n is the refractive index.

Given the refractive index of the optical fibre n₁ = 1.60 and that of cladding n₂ = 1.48

n₂/n₁ = sin(i)/sin(r)

The light ray can make with the wall of the core when its angle of refraction is 90⁰. The angle of incidence at this maximum point is known as the critical angle.

On substitution:

1.48/1.60 = sin(i)/sin90

1.48/1.60  = sin(i)/1

sin(i) = 1.48/1.60

sin(i) = 0.925

i = sin⁻¹0.925

i = 67.66⁰

Hence the maximum angle a light ray can make with the wall of the core if it is to remain inside the fiber is 67.66⁰.

What is the radiation pressure 1.5 m away from a 700 W lightbulb? Assume that the surface on which the pressure is exerted faces the bulb and is perfectly absorbing and that the bulb radiates uniformly in all directions.

Answers

Answer:

3.30 x 10^-7 Pascal

Explanation:

distance r = 1.5 m

power P = 700 W

the radiation pressure is given as

Pr = P/A*c

where

area of the surface A = 4πr^2

calculate for A

speed of light is c = 3×10^8  m/s

plugging above values in equation above gives

Pr = 3.30 x 10^-7 Pascal

A ferry boat sails east across a lake at 10 km/h. A woman is walking east on
the boat at 1.5 km/h. What is her speed relative to the boat?
A. 8.5 km/h west
B. 8.5 km/h east
C. 1.5 km/h east
O D. 1.5 km/h west

Answers

Answer:

B

8.5 km/h east

Explanation:

Relative velocity= Va -Vb

=10-1.5

=8.5 km/h east

The concept relative speed is used when two or more bodies moving with some speed are considered. The relative speed of woman to the boat is 8.5 km/h east. The correct option is B.

What is relative speed?

The relative speed of two bodies is defined as the sum of their speeds if they are moving in the opposite direction and it is the difference of their speeds if they are moving in the same direction.

The speed of the moving body with respect to the stationary body is known as the relative speed. The term relative means in comparison to. The relative speed is a scalar quantity.

Here both the boat and women are travelling in the same direction. So the relative speed is given as:

Relative speed = 10 - 1.5 = 8.5 km / h

Therefore the relative speed is 8.5 km/h east.

Thus the correct option is B.

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6. If you wanted to develop a telescope, what kind of lenses would you use for the objective lens (the lens that collects the light) and the eyepiece? Explain your reasoning. Draw a picture with ray tracing of your setup.

Answers

Answer:

objetive: a converging lens for large diameter lenses

eyepiece you must select a lens with a small focal length and the diameter is not important

The selected lenses should decrease chromatic aberration.

Explanation:

A telescope is an instrument that collects light from very distant objects, therefore very weak.

Therefore you should select a converging lens for large diameter lenses, to collect magnanimous light and with a large focal length.

For the eyepiece you must select a lens with a small focal length and the diameter is not important

the telescope magnification is

                 m = f_objective / F_ocular

The selected lenses should decrease chromatic aberration.

In general, these lenses are heavy, so refractory telescopes were imposed, so it uses a concave mirror instead of an objective lens.

Answer: this the real answer try it objetive: a converging lens for large diameter lenseseyepiece you must select a lens with a small focal length and the diameter is not importantThe selected lenses should decrease chromatic aberration.Explanation:A telescope is an instrument that collects light from very distant objects, therefore very weak.Therefore you should select a converging lens for large diameter lenses, to collect magnanimous light and with a large focal length.For the eyepiece you must select a lens with a small focal length and the diameter is not importantthe telescope magnification is                 m = f_objective / F_ocularThe selected lenses should decrease chromatic aberration.In general, these lenses are heavy, so refractory telescopes were imposed, so it uses a concave mirror instead of an objective lens.

Explanation:

You measure the power delivered by a battery to be 4.26 W when it is connected in series with two equal resistors. How much power will the same battery deliver if the resistors are now connected in parallel across it

Answers

Answer:

The power delivered by the battery is 17.04 W

Explanation:

Power through a circuit is given as

P = IV    ....1

where P is the power

I is the current through the circuit

V is the voltage through the circuit

The voltage in a circuit is given as

V = IR    ....2

Let us take the value of each resistor as equal to R

when connected in series, the total resistance will be

[tex]R_{t}[/tex] = R + R = 2R

If we assume constant voltage through the circuit, then from equation 2, the current in this case is

I = V/2R

If the resistors are connected in parallel, then the total resistance will be

[tex]\frac{1}{R_{t} }[/tex] = [tex]\frac{1}{R}[/tex] +

[tex]R_{t}[/tex] = R/2

The current in this case will be increased since the resistance is reduced

I = 2V/R

comparing the two situations, we can see that the current increased when connected in parallel to a ratio of

[tex]\frac{2V}{R}[/tex] ÷  [tex]\frac{V}{2R}[/tex] =  

This means that the current increased 4 times

From equation 1, we can see that electrical power is proportional to the current at a constant voltage, therefore, the power will also increase by four times to

P = 4 x 4.26 = 17.04 W

A metal sample of mass M requires a power input P to just remain molten. When the heater is turned off, the metal solidifies in a time T. The heat of fusion of this metal is

Answers

Answer:

L = Pt/M

Explanation:

Power, P= Q/t = mL/t

we know that, (Q=m×l)

Now ⇒l= Pt/M

Thus l= Pt/M

A spherical balloon has a radius of 6.95m and is filled with helium. The density of helium is 0.179 kg/m3, and the density of air is 1.29 kg/m3. The skin and structure of the balloon has a mass of 960kg . Neglect the buoyant force on the cargo volume itself. Determine the largest mass of cargo the balloon can lift.

Answers

Answer:

602.27 kg

Explanation:

The computation of the largest mass of cargo the balloon can lift is shown below:-

Volume of helium inside the ballon= (4 ÷ 3) × π × r^3

= (4 ÷ 3) × 3.14 × 6.953

= 1406.19 m3

Mass the balloon can carry = volume × (density of air-density of helium)

= 1406.19 × (1.29-0.179)

= 1562.27 kg

Mass of cargo it can carry = Mass it can carry - Mass of structure

= 1562.27 - 960

= 602.27 kg

A city of Punjab has a 15 percent chance of wet weather on any given day. What is the probability that it will take a week for it three wet weather on 3 separate days?

Answers

Answer: 0.0617

Explanation:

Given: The probability of wet weather on any given day in a city of Punjab : p=15%=0.15

Let X be a binomial variable that represents the number of days having wet weather.

Binomial probability formula : [tex]P(X=x)=^nC_xp^x(1-p)^x[/tex], where n= total outcomes, p = probability of success in each outcomes.

Here, n= 7 ( 1 week = 7 days)

The probability that it will take a week for it three wet weather on 3 separate days:

[tex]P(X=3)^=\ ^7C_3(0.15)^3(1-0.15)^{7-3}\\\\=\dfrac{7!}{3!(7-3)!}(0.15)^3(0.85)^4\\\\=\dfrac{7\times6\times5}{3\times2}\times 0.003375\times0.52200625\approx0.0617[/tex]

Hence, the required probability =0.0617

PLEASE HELP Which of the following describes the efficiency of real machines? 1.Efficiency is 100% 2.IMA is always larger than the AMA 3.IMA is always smaller than the AMA 4.IMA is equal to the AMA

Answers

Answer:

IMA is always larger than the AMA

Explanation:

IMA is Ideal Mechanical Advantage and it equals the length of effort that is divided by the length of resistance which is given by the formula

IMA= Fr/Fe

Where Fr is the resistance force

Fe is the effort force.

IM= de/dr

Where de is the distance of the applied effort  

dr is the distance traveled by the load.

In any real machine, the effort is needed to overcome friction and because of this, the ideal mechanical advantage(IMA) is always larger than the actual mechanical advantage (AMA)

a trombone can be modeled like an open closed air tube. the trombone plays a fifth harmonic of 159 hz. the speed of sound is 343 m/s. what is the wavelength of this sound

Answers

Answer:

The wavelength is 2.16 m.

Explanation:

Given the speed of the sound = 343 m/s

Trombone generate the frequency = 159 Hz

Now we have to find the wavelength of the sound. Here, we can find the wavelength by dividing the speed of the sound with frequency.

The wavelength of the sound = Speed of sound/frequency

Wavelength of the sound = 343 / 159 = 2.16 m

16. If one body is positively charged and another body is negatively charged, free electrons tend to
O A. move from the negatively charged body to the positively charged body
O B. remain in the positively charged body
OC. move from the positively charged body to the negatively charged body
O D. remain in the negatively charged body

Answers

Answer:

Hey there!

The correct answer would be option A. If one body is positively charged and another body is negatively charged, free electrons tend to move from the negatively charged body to the positively charged body

Let me know if this helps :)

The mass (M) of a piece of metal is directly proportional to its volume (V), where the proportionality constant is the density (D) of the metal. (1) Write an equation that represents this direct proportion, in which D is the proportionality constant. The density of lead metal is 11.3 g/cm3. (2) What is the mass of a piece of lead metal that has a volume of 17.3 cm3

Answers

Answer:

1) M = 11.3V2) 195.49 grams

Explanation:

1) If the mass (M) of a piece of metal is directly proportional to its volume (V), where the proportionality constant is the density (D) of the metal, this is expressed mathematically as shown;

M ∝ V

M = kV

For every proportionality sign, there will always be a proportionality constant 'k'

Since the proportionality constant is the density (D) of the metal, the equation will become;

M = DV

Given the density to be 11.3 g/cm3, the equation will become;

M = 11.3V

Hence, the equation that represents this direct proportion, in which D is the proportionality constant with metal density of 11.3g/cm³ is M = 11.3V

2) If the volume of the metal is 17.3cm³, on substituting this values into the equation in (1) to get the mass of the metal, we will have;

M = 11.3V

M = 11.3 * 17.3

M = 195.49 grams

Hence, the mass of a piece of lead metal that has a volume of 17.3 cm³ is 195.49 grams.

Suppose, we have a parallel plate capacitor and we know the following about it: Area of each plate = $0.0012m^2$ Distance between the two plates = $0.002m$ Charge on each plate after fully charging the capacitor = $2\times10^{-6}C$ Potential difference between the plates after fully charging the capacitor = $4\times 10^{-3}V$ My solution: We know that the electric field intensity at a point between two equally and oppositely charged plates is $\LARGE\frac{\sigma}{\epsilon_0}$. So, for the above case, $$\large E = \frac{\sigma}{\epsilon_0}$$ $$\large\implies E = \frac{\frac{2\times10^{-6}}{0.0012}}{8.85\times10^{-12}}{NC^{-1}}$$ $$\large\implies E =188323917.1NC^{-1}$$ My book's solution: $$E = \frac{V}{d}$$ $$\implies E=\frac{4\times 10^{-3}V}{0.002m}NC^{-1}$$ $$\implies E = 2NC^{-1}$$ If the books solution is correct, could you please explain why my answer is wrong and the book's is correct? Thanks in advance!

Answers

Answer:

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Design a voltage divider to provide the following approximate voltages with respect to ground using a 30 V source: 8.18 V, 14.7 V, and 24.6 V. The current drain on the source must be limited to no more than 1 mA. The number of resistors, their values, and their wattage ratings must be specified. A schematic showing the circuit arrangement and resistor placement must be provided

Answers

Answer:

R₁ = 14.7 10³ Ω , R₂ = 8.18 10³ Ω ,  R₃ = 1.72 10³ Ω ,  R₄ = 5.4 10³ Ω    1/8 W resistor

Explanation:

For this exercise we must use a series circuit since the sum of the voltage on each resin is equal to the source voltage (V = 30 V)

Therefore we build a circuit with 4 resistors in series, in such a way that

   V = i R

let the voltage

1st resistance

         V = i R

         R₁ = V / i

         R₁ = 14.7 / 1 10⁻³

         R₁ = 14.7 10³ Ω

power is

        P = V i

        P = 14.7 1 10⁻³

        P = 14.7 10⁻³ W = 0.0147 W

a resistance of ⅛ W is indicated

2nd resistance

          R₂ = 8.18 / 1 10⁻³

          R₂ = 8.18 10³ Ω

Power

          P = 8.18 1 10⁻³

          P = 0.00818W

a 1/8 W resistor

3rd resistance

this resistance is calculated in such a way that

          V₁ + V₂ + V₃ = 24.6

          V₃ = 24.6 - V₁ -V₂

          V₃ = 24.6 - 14.7 - 8.18

          V₃ = 1.72 V

          R₃ = 1.72 / 1 10⁻³

          R₃ = 1.72 10³ Ω

           

power

          P = Vi

          P = 1.72 10⁻³

          P = 0.00172 W

a resistance of ⅛ W

To obtain the voltage of 24.6 we use this three resistors together

4th resistance

The value of this resistance is calculated so that the sum of all the voltages reaches the source voltage

           30 = V₁ + V₂ + V₃ + V₄

           V₄ = 30 - V₁ -V₂ -V₃

           V₄ = 30 -14.7 - 8.18 - 1.72

           V₄ = 5.4 V

          R₄ = 5.4 / 1 10⁻³

          R₄ = 5.4 10³ Ω

Power

         P = V i

         P = 5.4 10⁻³

         P = 0.0054 W

⅛ W resistance

The values ​​of these resistance are commercially

Let's check the consumption of the circuit

  R_total = R₁ + R₂ + R₃ + R₄

  R_total = (14.7 + 8.18 + 1.72 + 5.4) 10³

   R_total = 30 10³

the current circulating in the circuit is

     i = V / R_total

     i = 30/30 10³

     i = 1 10⁻³ A

therefore it is within the order requirement.

for connections see attached diagram

A cyclist moves effortlessly at a constant speed of 12 m / s, but enters a muddy area where the coefficient of kinetic friction is 0.60. Will the rider leave the muddy area without having to pedal if the mud extends 11m? If so, how fast will it emerge?

Answers

Answer:

3.5 m/s

Explanation:

There are 3 forces on the cyclist:

Weight force mg pulling down,

Normal force N pushing up,

and friction force Nμ pushing left.

Sum of forces in the y direction:

∑F = ma

N − mg = 0

N = mg

∑F = ma

-Nμ = ma

-mgμ = ma

a = -gμ

a = -(10 m/s²)(0.60)

a = -6 m/s²

Velocity reached at end of 11 m:

v² = v₀² + 2aΔx

v² = (12 m/s)² + 2 (-6 m/s²) (11 m)

v = √12 m/s

v ≈ 3.5 m/s

Define the following, and give the letter which we will abbreviate them by:
Center of curvature:
Vertex:
Focal Point:
Radius of curvature:
Focal length:

Answers

Answer:

As in explanation.

Explanation:

A) Centre of Curvature: This is defined as the point in the center of the sphere from which the mirror was sliced. It is represented by the letter "C"

B) Vertex: It is defined as the point on the mirror's surface where the principal axis meets the mirror. It is represented by the letter A.

C) Focal Point: This is defined as the Midway point between the vertex and the center of curvature. It is represented by the letter "F"

D) Radius of Curvature: This is defined as the distance from the vertex to the center of curvature. It is represented by the letter "R"

E) Focal Length: This is defined as the distance from the mirror to the focal point. It's represented by the letter "f"

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