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
Related Questions
A box is sliding down an incline tilted at a 12° angle above horizontal. The box is initially sliding down the incline at a speed of 1.5 m/s. The coefficient of kinetic friction between the box and the incline is 0.34. How far does the box slide down the incline before coming to rest?
Answers
Answer:
The box will cover a distance of 0.9199m before coming to rest
Explanation:
We are given;
Angle of tilt; θ = 12°
Speed of sliding down; u = 1.5 m/s
Coefficient of kinetic friction; μ = 0.34
We are told that the box is sliding down an incline tilted at a 12° angle above horizontal.
Thus,
The components of the weight of the block would be;
Fx = mg sinθ = mg sin 12
Fy = mg cosθ = mg cos 12
For, the normal force on the block, it will be counter balanced by the Y component of weight of block and so we have;
Normal force; Fn = mg cos 12
Now formula for the frictional force would be given by;
Ff = μmg cos 12
So, Ff = 0.34mg cos 12
So, the net force along the inclined plane is;
Fnet = Fx - Ff
Fnet = mg sin 12 - 0.34mg cos 12
Where Fnet = mass x acceleration.
Thus;
ma = mg sin 12 - 0.34mg cos 12
m will cancel out to give;
a = g sin 12 - 0.34g cos 12
a = 9.81(0.2079) - 0.34(9.81 × 0.9781)
a = -1.223 m/s²
According to Newton's equation of motion, we have;
(v² - u²) = 2as
s = (v² - u²)/2a
Final velocity is zero. Thus;
s = (0² - 1.5²)/(2 × -1.223)
s = -2.25/-2.446
s = 0.9199 m
Thus, the box will cover 0.9199m before coming to rest
In a certain process a gas ends in its original thermodynamic state. Of the following, which is possible as the net result of the process?
A. It is adiabatic and the gas does 50 J of work.
B. The gas does no work but absorbs so J of energy as heat.
C. The gas does no work but rejects 50 J of energy as heat.
D. The gas rejects 50 J of energy as heat and does 501 of work.
E. The gas absorbs 50 of energy as heat and does 50」ot work.
Answers
Answer:
E. The gas absorbs 50 of energy as heat and does 50」ot work
Explanation:
This is following the law of thermodynamics that energy is neither created nor destroyed
A car moving east at 45 km/h turns and travels west at 30 km/h. What is the
magnitude and direction of the change in velocity?
mahalle 1.11
Answers
Explanation:
Change in Velocity = final velocity - initial velocity
Change in velocity = 30km/h - (- 45km/h )
= 75 km/h due west
Why would someone choose a for-profit fitness center over a nonprofit center?
For-profits have important social missions that deserve support. For-profits have important social missions that deserve support. , ,
For-profits are more likely to be located in low-income communities.For-profits are more likely to be located in low-income communities. , ,
For-profits have services like homework support and job training. , For-profits have services like homework support and job training. , ,
For-profits usually have nicer equipment than nonprofit centers.For-profits usually have nicer equipment than nonprofit centers. , ,
Answers
Someone would choose a for-profit fitness center over a nonprofit center because for-profits usually have nicer equipment than nonprofit centers.
A for-profit institution is an institution that provides a service to society to obtain an economic profit from this service. On the other hand, non-profit institutions are those that provide a service to society and do not intend to make a profit, they are generally institutions that are part of the government, foundations, or non-governmental organizations.
Non-profit institutions can function thanks to donations, volunteers, public resources, and do not charge for providing the service they provide, while for-profit institutions charge for their service and a percentage of that charge is profit for the owner of the institution and another is reinvested in equipment, human resources or others to improve the service.
According to this, for-profits are likely to have better equipment, while non-profit are characterized by supporting missions and offering services to low-income communities.
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You are walking around your neighborhood and you see a child on top of a roof of a building kick a soccer ball. The soccer ball is kicked at 31° from the edge of the building with an initial velocity of 15 m/s and lands 63 meters away from the wall. How tall, in meters, is the building that the child is standing on?
Answers
Answer:
69.58 m tall
Explanation:
Pls see attached file
Someone help me with these questions please!
Answers
Answer:
a 25 and b 25
2. 26
60n
Cho hai mặt cầu đồng tâm O tích điện đều. Bán kính của hai mặt cầu lần lượt là R1 và R2 (R2>R1). Điện tích mặt trong là q và mặt ngoài là Q
Tính cường độ điện trường tại một điểm cách tâm O một đoạn r (biết R1 < r < R2)
Tính hiệu điện thế giữa hai mặt cầu
Answers
Answer:
you will stc ohxoyxct txxtx xigigjjgjvvixiffjz,iffzikzfjvixii. hi h ohigiogooigoh
Explanation:
k jjvhvojvovvojivivivihvi hj
A bucket filled with water has a mass of 23 Kg and is attached to a rope, which in turn is wound around a 0.050 m radius cylinder at the top of a well. What torque does the weight of water and bucket produce on the cylinder if the cylinder is ont permitted to rotate? (g= 9.8 m/s2)
Answers
Answer:
The torque is 11.27 N m
Explanation:
Recall that torque is the vector product of the force times the distance to the pivoting point. So in our case, the distance to the pivoting point is the radius of the cylinder (0.05 m), and the force is given by the weight of the bucket full of water (W = 9.8 * 23 N = 225.4 N)
Then the torque is: 0.05 * 225.4 N m = 11.27 N m
Scouts at a camp shake the rope bridge they have just crossed and observe the wave crests to be 9.70 m apart. If they shake the bridge twice per second, what is the propagation speed of the waves (in m/s)?
Answers
Answer:
The speed of the wave is 19.4 m/s
Explanation:
The wave's crest to crest distance (the wavelength of this rope's wave) λ= 9.70 m
The bridge is shaken twice, meaning that two wavelengths passed a given point on the rope per sec. The frequency of a wave is the amount of that wave that passes a given point in a second.
this means that the frequency f = 2 Hz
The speed of a wave = fλ = 9.70 x 2 = 19.4 m/s
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
Currents in DC transmission lines can be 100 A or higher. Some people are concerned that the electromagnetic fields from such lines near their homes could pose health dangers.
A. For a line that has current 150 A and a height of 8.0 m above the ground, what magnetic field does the line produce at ground level? Express your answer in teslas.
B. What magnetic field does the line produce at ground level as a percent of earth's magnetic field which is 0.50 G?
C. Is this value of magnetic field cause for worry? Choose your answer below.
i. Yes. Since this field does not differ a lot from the earth's magnetic field, it would be expected to have almost the same effect as the earth's field.
ii. No. Since this field is much lesser than the earth's magnetic field, it would be expected to have less effect than the earth's field.
iii. Yes. Since this field is much greater than the earth's magnetic field, it would be expected to have more effect than the earth's field.
iv. No. Since this field does not differ a lot from the earth's magnetic field, it would be expected to have almost the same effect as the earth's field.
Answers
Answer:
Explanation:
magnetic field due to an infinite current carrying conductor
B = k x 2I / r where k = 10⁻⁷ , I is current in conductor and r is distance from wire
putting the given data
B = 10⁻⁷ x 2 x 100 / 8
= 25 x 10⁻⁷ T .
B )
earth's magnetic field = .5 gauss
= .5 x 10⁻⁴ T
= 5 x 10⁻⁵ T
percent required = (25 x 10⁻⁷ / 5 x 10⁻⁵) x 100
= 5 %
C )
ii. No. Since this field is much lesser than the earth's magnetic field, it would be expected to have less effect than the earth's field.
A capacitor consists of two parallel conducting plates, each of area 0.4 m2 and separated by a distance of 2.0 cm. Assume there is air between the plates. While connected to a battery the electric field within the plates is 500 N/C. The potential difference between the plates is: ________
a) 5.0 V
b) 10 V
c) 30 V
d) 20 V
Answers
Answer:
check photo
Explanation:
Which best identifies the requirements for work to be performed? an object that has a force acting on it an object that is moving and has no net force a force acting on a motionless object a force that moves an object
Answers
Answer:
a force that moves an object
Explanation:
the formula for work is force * distance
This question involves the concepts of work, force, and displacement.
The statement that best identifies the requirements for work to be performed is "a force that moves an object".
Work is defined as the product of force applied on an object and the distance moved by the object. Mathematically,
Work = (Force)(Displacement)
Hence, both the applied force and the displacement of the object as a result of the application of the force is necessary for the work to be done. If any one of these values becomes zero, the work automatically becomes zero, which means no work is performed.
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two thin lenses with the focal length of magnitude 15.0 cm . the first is diverging and second is converging lens are located 11.3 cm apart. an object 1.60 mm tall is placed 25 cm to the left of the first diverging lens. how far the first lens is the final image is formed?
is the final image is real or virtual?
what is the height of image?
Answers
Answer:
grandson annual Iranian Jamal Jamal Hannah travel
A scuba diver fills her lungs to capacity (6.0 L) when 10.0 m below the surface of the water and begins to ascend to the surface. Assume the density of the water in which she is swimming is 1000 kg/m3 and use g = 10 m/s2A. Assuming the temperature of the air in her lungs is constant, to what volume must her lungs expand when she reaches the surface of the water?B. What effect would the warming of the air in her lungs have on the volume needed when she surfaces?C. Assuming the temperature of the air in her lungs is constant, what effect does her ascent have on the vrms of the air molecules in her lungs?
Answers
Answer:
Explanation:
As temperature is constant , we shall apply Boyle's law
P₁V₁ = P₂V₂
P₁ = pressure at depth of 10 m
= P + hdg , h = 10 , d = 10³ , g = 10
P is atmospheric pressure which is 10⁵ Pa
P₁ = 10⁵ + 10 x 10³ x 10
= 2 x 10⁵
applying the formula
2 x 10⁵ x 6 = 10⁵ x v
v = 2 x 6 = 12 L
volume will be doubled at the surface .
B )
warming of air at the surface will increase the volume of air in her lungs so so she will need more lung capacity .
C )
The rms value of a gas depends upon the temperature of the gas . As temperature of the gas is constant , the rms value of the gas particles will remain constant when she goes to the surface .
The lungs will expand 12 L when she reaches the surface of the water, and the warming of the air results in more lung capacity, and [tex]\rm V_{rms}[/tex] the value remains the same.
What is Boyle's law?According to the law, the pressure of the gas is inversely proportional to the volume of the gas. In other words when the pressure of the gas increases the volume of the gas decreases.
We know the pressure at the 10 meters depth:
[tex]\rm P_1 = P+h\times \rho\times g[/tex]
Where P = Atmospheric pressure
h = Depth
ρ =Density of the water
We have: [tex]\rm P = 10^5 \ Pa[/tex], h = 10 meters, and [tex]\rm \rho = 1000 \ kg/m^3[/tex], and [tex]\rm g = 10 \ m/s^2[/tex]
Putting the values in the above equation, we get:
[tex]\rm P_1 = 10^5+ 10\times 1000\times 10[/tex]
[tex]\rm P_1 = 2\times 10^5[/tex]
From the Boyle's law:
[tex]\rm P_1\times V_1 = P_2\times V_2[/tex]
[tex]\rm 2\times10^5\times 6 = 10^5\times V_2[/tex]
[tex]\rm V_2 = 12 \ L[/tex]
We know that as the air at the surface warms, the volume of air in her lungs expands, requiring more lung capacity.
The temperature of the gas is constant and [tex]\rm V_{rms}[/tex] values for gas depend on the temperature of the gas, but here the temperature of the gas is constant thus, the [tex]\rm V_{rms}[/tex] will remains constant.
Thus, the lungs will expand 12 L when she reaches the surface of the water, and the warming of the air results in more lung capacity, and [tex]\rm V_{rms}[/tex] the value remains the same.
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The temperature difference between the inside and the outside of a house on a cold winter day is 33°F. (a) Express this difference on the Celsius scale. 0.55 Incorrect: Your answer is incorrect. °C (b) Express this difference on the Kelvin scale. 273.7 Incorrect: Your answer is incorrect. K
Answers
Answer:
a) 0.56°C
b) 273.56 K
Explanation:
If we want to convert from Fahrenheit scale to Celcius scale we use the formula;
T(°C) = (T(°F) - 32) × 5/9
Where T(°F) = 33°F
Hence;
T(°C) = (33°F - 32) × 5/9
T°C = 0.56°C
b)
T(K) = T°C + 273
T(K) = 0.56 + 273
T(K) = 273.56 K
What is the minimum thickness of coating which should be placed on a lens in order to minimize reflection of 566 nm light? The index of refraction of the coating material is 1.46 and the index of the glass is 1.71.
Answers
Answer:
The thickness is [tex]t = 1.415 *10^{-7 } \ m[/tex]
Explanation:
From the question we are told that
The wavelength is [tex]\lambda = 566 \ nm = 566 *10^{-9} \ m[/tex]
The index of refraction of glass is [tex]n_g = 1.71[/tex]
The index of refraction of the coating is [tex]n= 1.46[/tex]
Generally the condition for destructive interference is
[tex]2 t = (m + \frac{1}{2} ) * \frac{\lambda }{n }[/tex]
Here m is the order of the interference pattern and given from the question that we are considering minimizing reflection m = 0
t = thickness of the coating
substituting values
[tex]2 t = (0 + \frac{1}{2} ) * \frac{ 566 *10^{-9}}{ 1.46 }[/tex]
=> [tex]t = 1.415 *10^{-7 } \ m[/tex]
Describe at least two unique characteristics of the new space telescope.
Answers
Answer: Astro 1 will have a 10x larger field of view than the Hubble.
Explanation: The hubble will also be extremely light weight that way it can go further into space and the mission will be able to last a longer amount of time.
Which object forms when a supergiant explodes? a red giant a black hole a white dwarf a neutron star
Answers
Answer:
a neutron star
Explanation:
Answer:
d
Explanation:
"In a Young's double-slit experiment, the slit separation is doubled. To maintain the same fringe spacing on the screen, the screen-to-slit distance D must be changed to"
Answers
Answer:
To maintain the same fringe spacing on the screen, the screen-to-slit distance D must be changed to a value 2D that is twotimes D
In an inertia balance, a body supported against gravity executes simple harmonic oscillations in a horizontal plane under the action of a set of springs. If a 1.00-kg body vibrates at 1.00 Hz, a 2.00-kg body will vibrate at Group of answer choices
Answers
Answer;
a 2.00-kg body will vibrate at 0.707Hz
Answer:-7.9
Explanation:
Monochromatic light falls on two very narrow slits 0.047 mm apart. Successive fringes on a screen 6.60 m away are 8.9 cm apart near the center of the pattern.
Determine the wavelength and frequency of the light.
Answers
Answer::
[tex]\lambda = 634 nm[/tex]
[tex]f = 4.73 *10^{14} \ Hz[/tex]
Explanation:
From the question we are told that
The distance of separation is [tex]d = 0.047 \ mm = 0.047 *10^{-3} \ m[/tex]
The distance of the screen is [tex]D = 6.60 \ m[/tex]
The width of the fringe is [tex]y = 8.9 \ cm = 0.089 \ m[/tex]
Generally the width of the width of the fringes is mathematically represented as
[tex]y = \frac{\lambda * D }{d }[/tex]
=> [tex]\lambda = \frac{y * d }{D }[/tex]
=> [tex]\lambda = \frac{ 0.089 * (0.047 *10^{-3}) }{6.60 }[/tex]
=> [tex]\lambda = 634 *10^{-9}[/tex]
=> [tex]\lambda = 634 nm[/tex]
Generally the speed of light is mathematically represented as
[tex]c = f * \lambda[/tex]
=> [tex]f= \frac{ c}{\lambda }[/tex]
=> [tex]f= \frac{ 3.0 *10^{8}}{634 *10^{-9}}[/tex]
=> [tex]f = 4.73 *10^{14} \ Hz[/tex]
A motorist traveling with a constant speed of 15 m/s (about 34 mi/h) passes a school-crossing corner, where the speed limit is 0 m/s (about 22 mi/h). Just as the motorist passes, a police officer on a motorcycle stopped at the comer starts off in pursuit with constant acceleration of 3.0 m/S2. (a) How much time elapses before the officer catches up with the motorist? (b) What is the officer's speed at that point? (c) What is the total distance each vehicle has traveled at that point? Please help me
Answers
Answer:
(a) 10 s
(b) 30 m/s
(c) 150 m
Explanation:
The motorist's position at time t is:
x = 15t
The officer's position at time t is:
x = ½ (3) t² = 1.5 t²
(a) When they have the same position, the time is:
15t = 1.5 t²
t = 0 or 10 s
(b) The officer's speed is:
v = 3t
v = 30 m/s
(c) The position is:
x = 15t = 150 m
Coherent light that contains two wavelengths, 660 nm (red) and 470 nm (blue), passes through two narrow slits that are separated by 0.310 mm. Their interference pattern is observed on a screen 4.40 m from the slits. What is the disatnce on the screen between the first order bright fringe for each wavelength?
Answers
Answer:
0.002699 m or 2.699 mm
Explanation:
y = Fringe distance
d= Distance between slits = 0.310mm
L = Screen distance = 4.40m
λ= Wavelength
Given from question
λ₁= 660 nm = 6.6 x 10^-9 m
λ₂= 470 nm = 4.7 x 10^-9 m
d = 0.340 mm = 3.4 x 10^-3 m
L = 4.40 m
In the case of constructive interference, we use below formula
y/L = mλ/d
For first order wavelength
(y₁/4.40) =(1×660x10⁻⁹)/(0.310*10⁻³)
y₁= (0.310*10⁻³)×(4.40)/(0.310*10⁻³)
y₁=0.00937m
(y2/4.40) =(1×470x10⁻⁹)/(0.310*10⁻³)
y2= =(1×470x10⁻⁹)×(4.40)/(0.310*10⁻³)
y2=0.00667m
distance between the fringes is given by (y₁ -y2)
=0.00937-0.00667=0.002699m
Therefore, distance on the screen between the first-order bright fringes for the two wavelengths is 0.002699 m or 2.699 mm
¿Cómo podrías utilizar el sistema de posicionamiento global para proponer recorridos alternativos para llegar a un lugar específico (centro educativo, supermercado, el hogar, el parque, entre otros)?
Answers
Answer:
El sistema de posicionamiento global (conocido mundialmente como GPS) podría utilizarse para proponer recorridos alternativos para llegar a un lugar específico, como un parque, a través de la creación de un recorrido guiado por una aplicación móvil con diferentes rutas de acceso al lugar.
Así, por ejemplo, se crearían diferentes rutas de acceso desde un punto A hasta un punto B, teniendo en cuenta factores como: rapidez, congestión vehicular, pago o no de peajes, posibilidad de acceso a pie y determinados factores extra que influyan en la forma de llegar al lugar. Todo ello plasmado en un mapa interactivo en el cual se señalen las rutas disponibles mediante el marcado del mapa en cuestión.
What did the results of photoelectric-effect experiments establish?
Answers
Answer:
Option A
Electrons are emitted if low intensity, high-frequency light hits a metal surface.
Explanation:
From the experiments conducted to study the photoelectric effect, conclusions were made that the key factor that contributes to the emission of electrons from the surface of the metal is the frequency of the beam of light. This frequency has to be beyond a minimum threshold, if not, there will be no emission of electrons from the metal surface no matter the intensity of the beam of light or the length of time it is incident upon the metal surface.
This makes option A correct because it highlights the contributions made by the threshold frequency to the photoelectric effect.
Test Bank, Question 18.83 Inside a room at a uniform comfortable temperature, metallic objects generally feel cooler to the touch than wooden objects do. This is because: a given mass of wood contains more heat than the same mass of metal the human body, being organic, resembles wood more closely than it resembles metal metal conducts heat better than wood heat tends to flow from metal to wood
Answers
Answer:
metal conducts heat better than wood.
Explanation:
Metals are generally good conductors of heat, and they usually conduct heat at a relatively rapid rate. Inside the room with a uniform temperature, a metal when touched will rapidly conduct the heat from your hand, leaving your hand with a cooler feeling. Wood on the other hand is a poor heat conductor, so the heat is not conducted from your hand fast enough to cool it up to the point that your hand feels cool.
Photons of wavelength 65.0 pm are Compton-scattered from a free electron which picks up a kinetic energy of 0.75 keV from the collision. What is the wavelength of the scattered photon?
Answers
0.6764*10^-10m
Explanation:
Using E= hc/wavelength
(4.14x10^-15)x(3.0x10^8)/(65x10^-12)=0.1911x10^5 eV=19.1 keV
So subtract the calculated energy from the given energy of scattered photons
9.11-0.75=18.36 keV
To find wavelength
Wavelength= hc/ E
[(4.14x 10^-15)x (3.0x10^8)]/(18.36*10^3) =0.6764^-10 m
A non-ideal battery has a 6.0-V emf and an internal resistance of 0.6 l. Determine the terminal voltage (in volts) when the current drawn from the battery is 1.0 A
Answers
=6,0 --0.6 =5.4 volts terminal volts 5.4 volts
In a physics laboratory experiment, a coil with 250 turns enclosing an area of 14 cm2 is rotated in a time interval of 0.030 s from a position where its plane is perpendicular to the earth's magnetic field to a position where its plane is parallel to the field. The earth's magnetic field at the lab location is 5.0×10^−5 T.Required:a. What is the total magnetic flux through the coil before it is rotated? After it is rotated? b. What is the average emf induced in the coil?
Answers
Explanation:
Consider a loop of wire, which has an area of [tex]A=14 \mathrm{cm}^{2}[/tex] and [tex]N=250[/tex] turns, it is initially placed perpendicularly in the earth magnetic field. Then it is rotated from this position to a position where its plane is parallel to the field as shown in the following figure in [tex]\Delta t=0.030[/tex] s. Given that the earth's magnetic field at the position of the loop is [tex]B=5.0 \times 10^{-5} \mathrm{T}[/tex], the flux through the loop before it is rotated is,
[tex]\Phi_{B, i} &=B A \cos \left(\phi_{i}\right)=B A \cos \left(0^{\circ}\right[/tex]
[tex]=\left(5.0 \times 10^{-5} \mathrm{T}\right)\left(14 \times 10^{-4} \mathrm{m}^{2}\right)(1)[/tex]
[tex]=7.0 \times 10^{-8} \mathrm{Wb}[/tex]
[tex]\quad\left[\Phi_{B, i}=7.0 \times 10^{-8} \mathrm{Wb}\right[/tex]
after it is rotated, the angle between the area and the magnetic field is [tex]\phi=90^{\circ}[/tex] thus,
[tex]\Phi_{B, f}=B A \cos \left(\phi_{f}\right)=B A \cos \left(90^{\circ}\right)=0[/tex]
[tex]\qquad \Phi_{B, f}=0[/tex]
(b) The average magnitude of the emf induced in the coil equals the change in the flux divided by the time of this change, and multiplied by the number of turns, that is,
[tex]{\left|\mathcal{E}_{\mathrm{av}}\right|=N\left|\frac{\Phi_{B, f}-\Phi_{B, i}}{\Delta t}\right|}{=} & \frac{1.40 \times 10^{-5} \mathrm{Wb}}{0.030 \mathrm{s}}[/tex]
[tex]& 3.6 \times 10^{-4} \mathrm{V}=0.36 \mathrm{mV}[/tex]
[tex]\mathbb{E}=0.36 \mathrm{mV}[/tex]
(a) The initial and final flux through the coil is 1.75 × 10⁻⁵ Wb and 0 Wb
(b) The induced EMF in the coil is 0.583 mV
Flux and induced EMF:Given that the coil has N = 250 turns
and an area of A = 14cm² = 1.4×10⁻³m².
It is rotated for a time period of Δt = 0.030s such that it is parallel with the earth's magnetic field that is B = 5×10⁻⁵T
(a) The flux passing through the coil is given by:
Ф = NBAcosθ
where θ is the angle between area vector and the magnetic field
The area vector is perpendicular to the plane of the coil.
So, initially, θ = 0°, as area vector and earth's magnetic field both are perpendicular to the plane of the coil
So the initial flux is:
Φ = NABcos0° = NAB
Ф = 250×1.4×10⁻³×5×10⁻⁵ Wb
Ф = 1.75 × 10⁻⁵ Wb
Finally, θ = 90°, and since cos90°, the final flux through the coil is 0
(b) The EMF induced is given by:
E = -ΔФ/Δt
E = -(0 - 1.75 × 10⁻⁵)/0.030
E = 0.583 × 10⁻³ V
E = 0.583 mV
Learn more about magnetic flux:
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