The thermal expansion of a steel archbridge between
temperature
extremes −15°C and 35°C can be found out by using the formula;ΔL = LαΔTWher
e;L = Length of steel arch bridg
eα = Coefficient of linear expansion of steelΔ
T = Change in temperature of steel arch bridgeHere, the
length
of the New River Gorge bridge in West Virginia is L
= 518 m.
The
coefficient
of linear
expansion
of steel, α = 1.20 × 10⁻⁵ /°C.Δ
T = (35°C) - (-15°C)
= 50°C
Substituting the given values in the above equation,ΔL = LαΔ
T= (518 m) (1.20 × 10⁻⁵ /°C) (50°C)≈ 0.311 mTherefore, the length of the steel arch bridge would change by approximately 0.311 m between temperature extremes −15°C and 35°C.
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A woman stands on a bathrooct scale in a Part A motioniess elevator. When the elevator begins to move; the sceie briefly reads only \( 0.71 \) of har regsilar weight Calculate the magnitude of the doc
The magnitude of the acceleration of the elevator is 0.71 times the acceleration due to gravity (g), based on the observed decrease in the woman's apparent weight on the bathroom scale.
To calculate the magnitude of the acceleration of the elevator, we can use the equation that relates the apparent weight of the woman to the acceleration.
Apparent weight in the elevator (W_apparent) = 0.71 times her regular weight
Regular weight of the woman (W_regular) = her actual weight
The apparent weight of the woman in the elevator is the force exerted by the scale on her. It is equal to the difference between the force of gravity (W_regular) and the upward force provided by the scale (N), which is the normal force.
Mathematically, we have:
W_apparent = N = W_regular - mg,
where m is the mass of the woman and g is the acceleration due to gravity.
Since the elevator is initially motionless, the net force on the woman is zero. Thus, the force of gravity is balanced by the upward force provided by the scale.
When the elevator starts to move, the net force on the woman is no longer zero. The normal force from the scale is reduced, resulting in a decrease in the apparent weight.
We can write the equation for the apparent weight in terms of acceleration (a) as follows:
W_apparent = N = W_regular - mg = ma,
where a is the acceleration of the elevator.
Given that W_apparent is 0.71 times W_regular, we can rewrite the equation as:
0.71W_regular = ma.
Dividing both sides by the regular weight (W_regular), we have:
0.71 = a/g.
Solving for the acceleration (a), we get:
a = 0.71g.
Therefore, the magnitude of the acceleration of the elevator is 0.71 times the acceleration due to gravity (g).
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Complete Question :A woman stands on a bathroom scale in a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.71of her regular weight. Calculate the magnitude of the acceleration of the elevator.
Design series inverter :- supplies a maximum load current (1 A) passing through load resistance (150 ohm) with frequency 400 HZ, if Tyristor turn off, time is 25 u sec.
Design series inverter: supplies a maximum load current of 1 A, which flows through a load resistance of 150 ohm at a frequency of 400 Hz. When the Thyristor is turned off, the time is 25 microseconds (us).
An inverter is a circuit that converts a direct current (DC) source to an alternating current (AC) source. An inverter converts direct current (DC) to alternating current (AC). An inverter is used to power appliances, machinery, and other electrical equipment in remote areas or places where electricity is inaccessible.
In a series inverter, the load is connected in series with the thyristor. A voltage is applied to the load through a capacitor and an inductor when the thyristor is switched on. The capacitor is used to store energy, while the inductor is used to create a magnetic field. The inductor and capacitor combination creates a resonant circuit that allows for a current to flow through the circuit, which is then fed into the load.
The thyristor is then turned off, and the current is allowed to flow through the inductor and the load. The inductor's stored energy is released in the form of a current pulse, which is used to power the load. When the current is no longer needed, the circuit is broken by turning the thyristor back on. This is how a series inverter works.
The maximum load current is 1 A in this particular circuit, and it flows through a load resistance of 150 ohm at a frequency of 400 Hz. When the Thyristor is turned off, the time is 25 microseconds (us).
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Determine the values of \( h(n) \) for linear phase low-pass FIR filter with 11 taps and a cut-off frequency of \( 0.22 \) pi radians using the frequency sampling method. \[ H_{k} \text { at } \Omega_
A linear phase low-pass FIR filter with 11 taps and a cut-off frequency of \(0.22 \pi\) radians can be created using the frequency sampling method. This can be accomplished by using the following steps:1. Determine the ideal frequency response of the filter[tex]\(H_{d}(e^{j \Omega})\)2.[/tex]
Determine the impulse response of the filter\(h(n)\)3. Determine the frequency response of the filter using the impulse response\(H(e^{j \Omega})\)4. Determine the desired frequency response of the filter\(H_{k}\)5. Determine the values of the impulse response of the filter\(h(n)\) using the inverse Fourier transform of \(H_{k}\)The ideal frequency response of the filter is determined by the equation\[tex](H_{d}(e^{j \Omega}) = \begin{cases}1, &0 \leq \Omega \leq \Omega_{c}\\0, &\Omega_{c} \leq \Omega \leq \pi\end{cases}\)where \(\Omega_{c} = 0.22 \pi\) radians.[/tex]
The desired frequency response of the filter can be determined by sampling the ideal frequency response at equally spaced frequencies:\(H_{k} = H_{d}(e^{j \frac{2 \pi}{N} k})\)The values of the impulse response of the filter can be found by taking the inverse Fourier transform of the desired frequency response:\(h(n) = \frac{1}{N} \sum_{k=0}^{N-1} H_{k} e^{j \frac{2 \pi}{N} kn}\)where \(N\) is the number of taps.In summary, to determine the values of \(h(n)\) for a linear phase low-pass FIR filter with 11 taps and a cut-off frequency of \(0.22 \pi\) radians using the frequency sampling method, the following steps should be taken:1.
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An object is dropped from the top of a cliff 625 meters high. Its height above the ground t seconds after it is dropped is 625−4.9t². Determine its speed 7 seconds after it is dropped.
The speed of the object 7 seconds after it is dropped is ___m/sec.
(Simplify your answer.)
The speed of the object 7 seconds after it is dropped is -68.6 m/s (negative sign indicates downward direction).
The height of the object above the ground at time t is given by the equation h(t) = 625 - 4.9t².
To find the speed of the object at 7 seconds, we need to calculate the derivative of the height function with respect to time. The derivative gives us the rate of change of the height, which corresponds to the velocity or speed.
Taking the derivative of h(t) with respect to t:
h'(t) = d(h(t))/dt = d(625 - 4.9t²)/dt = -9.8t.
Now we can substitute t = 7 seconds into the derivative to find the speed at that time:
h'(7) = -9.8 * 7 = -68.6 m/s.
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the gold foil experiment performed in rutherford's lab ________.
The gold foil experiment, conducted by Ernest Rutherford in 1911, provided evidence for the existence of a compact, positively charged nucleus within the atom.
The gold foil experiment, also known as the Rutherford scattering experiment, was conducted by Ernest Rutherford in 1911. Rutherford aimed to investigate the structure of the atom and the distribution of positive charge within it.
In the experiment, Rutherford used a beam of alpha particles, which are positively charged particles, and directed them towards a thin sheet of gold foil. The prevailing model at the time suggested that atoms were composed of a diffuse positive charge with electrons scattered throughout, so Rutherford expected the alpha particles to pass through the gold foil with minimal deflection.
However, the results of the experiment were surprising. Rutherford observed that some of the alpha particles were deflected at large angles, and a few even bounced back. This indicated that the positive charge of the atom was concentrated in a small, dense region called the nucleus, while the majority of the atom was empty space.
The gold foil experiment provided evidence for the existence of a compact, positively charged nucleus within the atom. It revolutionized the understanding of atomic structure and led to the development of the modern model of the atom, with electrons orbiting the nucleus.
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Laplace Transform problem (20 points) 1) Transform the circuit to the Laplace domain 2) Find the expression for current \( I_{S}(s) \) in the Laplace domain (no need to do the inverse Laplace transfor
1) Transform the circuit to the Laplace domain In the circuit given, I is the current flowing through the inductor and R1 and R2 are the resistance of the resistors. V is the voltage across the inductor.
The given circuit can be transformed into the Laplace domain by applying the basic formulae.
Using Ohm's Law, V = IRi.e., I
= V/R
Substituting R1 + R2 as R, we get I
= V/R ...(1)The voltage V across the inductor L is given by:
L(di/dt) + Ri = V => L(di/dt) = V - Ri
Now, taking Laplace transform on both sides, we get:
L(sI(s) - i(0)) + R(I(s))
= V(s)
=> I(s)
= [V(s) + Li(0)]/[sL + R]
Thus, the transformed circuit in Laplace domain is as follows:
2) Find the expression for current \(I_{S}(s)\) in the Laplace domain (no need to do the inverse Laplace transform)
By Kirchoff's Current Law, I1 + I2 = I
where I1 is the current passing through the resistor R1 and I2 is the current passing through the resistor R2 and I is the current passing through the inductor L.
We can use Ohm's Law to represent I1 and I2 in terms of voltage V across the inductor and R1 and R2 respectively.
Substituting the values of I1 and I2 in the above equation, we get V/R1 + V/R2 = I(s)Now, substituting the value of V from above, we get:
I(s) = V/R
= L(di/dt + I(s))/R1 + L(di/dt + I(s))/R2
=> I(s)
= [sL + (R1 + R2)]/[s^2L + s(R1 + R2)]
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Please solve the problem showing clear steps
not just the answer. Thank you.
The observed orbital synodic periods of Venus and Mars are 583.9 days and 779.9 days respectively. Calculate their sidereal periods.
For a monoatomic gas, the formula to calculate the average square speed (v^2) is v^2 = (3 * k * T) / m, where k is the Boltzmann constant, T is the temperature in Kelvin, and m is the molar mass of the gas. For a diatomic gas, the formula is v^2 = (5 * k * T) / (3 * m).
In a monoatomic gas, each molecule has three degrees of freedom, while in a diatomic gas, each molecule has five degrees of freedom. The formula to calculate v^2 for a monoatomic gas takes into account the average kinetic energy per degree of freedom, which is (1/2) * k * T, multiplied by the number of degrees of freedom (3 in this case). For a diatomic gas, there are additional degrees of freedom due to molecular rotation, resulting in a different formula for v^2.
The molar mass (m) of the gas is also considered in both formulas. These formulas provide the average square speed of the gas molecules.
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Assuming a nuclear meltdown unfortunately occurs in Daya Bay nuclear power plant on 1 Jan 2050 and due to this accident the total amount of radioactive cesium-137 released into the air in 30 days is 5.5 × 1018 Bq.
Hong Kong is about 50 km from Daya Bay nuclear power plant. If this accident occurs during a windy season, the cesium-137 could spread out further in a shape of a much bigger cylinder with a height of 12 km. It is assumed that the spreading just reaches Hong Kong on the 30th day after the accident. Find Hong Kong’s average radioactivity in Bq/m3 of the released cesium-137 due to this nuclear disaster.
The average radioactivity in Hong Kong due to the nuclear disaster in Daya Bay nuclear power plant is approximately 4.79 × [tex]10^8[/tex] Bq/m³ of cesium-137.
In order to calculate the average radioactivity in Hong Kong, we need to consider the volume of the cylinder-shaped area where the cesium-137 has spread. The volume of a cylinder is calculated by multiplying its base area by its height. Assuming the spread of cesium-137 forms a cylinder with a height of 12 km, we need to determine the base area.
Given that Hong Kong is approximately 50 km away from the nuclear power plant, we can consider the area of a circle with a radius of 50 km as the base area of the cylinder. The formula to calculate the area of a circle is A = πr², where A is the area and r is the radius.
Substituting the values, we get A = 3.14 × (50 km)² = 7850 km².
Now, we multiply the base area by the height of the cylinder to obtain the volume: V = 7850 km² × 12 km = 94,200 km³.
To find the average radioactivity in Hong Kong, we divide the total amount of cesium-137 released ([tex]5.5 × 10^18 Bq[/tex]) by the volume of the cylinder (94,200 km³) and convert the units to Bq/m³: ([tex]5.5 × 10^18 Bq[/tex]) / (94,200 km³ × 1,000,000,000 m³/km³) = [tex]4.79 × 10^8 Bq/m³[/tex].
Therefore, the average radioactivity in Hong Kong due to the nuclear disaster is approximately [tex]4.79 × 10^8 Bq/m³[/tex] of cesium-137.
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QUESTION 10 A force of 60 N has a x-component of 28 N. What is the y-component? OA. 2800 N OB. 53 N OC.57N OD. 66 N OE. 94 N QUESTION 11 Two reindeer-in-training pull on a sleigh. Connie pulls with a force of 200 N at an angle of 20° above the (positive) x-axis, while Randolph pulls with a force of 500 N at an angle of 30° below the (positive) x-axis. What is their resultant force on the sleigh? OA. 620 N B. 180 N C. 650 N D. 590 N E. 21 N 2 points Save Answer 2 points
The magnitude of the y-component of the force is 53 N. The magnitude of the resultant force on the sleigh is 187.4 N.
Question 10
Given data, force
F = 60 N, x-component of force = 28 N
We need to find the y-component of the force F.
We know that force has two components, the x-component, and the y-component.
Using Pythagoras theorem we have,
F² = x² + y² where F is the magnitude of the force F, x is the magnitude of the x-component of the force F, and y is the magnitude of the y-component of the force F.
By squaring both sides we get, (F² - x²) = y²
Put the given values in the above equation,
y² = (60 N)² - (28 N)²
= 3600 N² - 784 N²y²
= 2816 N²y
= √2816 N²
= 53 N
Therefore, the magnitude of the y-component of the force is 53 N.
Hence, the correct option is OB.
Question 11.
Connie pulls with a force of 200 N at an angle of 20° above the (positive) x-axis, while Randolph pulls with a force of 500 N at an angle of 30° below the (positive) x-axis.
We need to find the resultant force on the sleigh by these two forces.
Let the force on the sleigh by Connie and Randolph are F1 and F2 respectively. Let F be the resultant force and α be the angle that F makes with the positive x-axis.
Resolving the forces in the x and y directions, we get:
Net x-component,
Fcosα = F1 cosθ1 + F2 cosθ2
where θ1 and θ2 are the angles made by F1 and F2 with the positive x-axis.
Net y-component, Fsinα = F1 sinθ1 - F2 sinθ2
Substitute the given values in the above equations.
F1 = 200 N, θ1 = 20°, F2 = 500 N, θ2 = -30°, α =?
Then we have,
Fcosα = F1 cosθ1 + F2 cosθ2
= (200 N) cos20° + (500 N) cos(-30°)
= 187.37 N
Net y-component,
Fsinα = F1 sinθ1 - F2 sinθ2
= (200 N) sin20° - (500 N) sin(-30°)
= - 34.95 N∴ F = √(Fcosα)² + (Fsinα)²
= √(187.37 N)² + (-34.95 N)²= √(35123.75) N²
= 187.4 N
Therefore, the magnitude of the resultant force on the sleigh is 187.4 N. Hence, the correct option is B.
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Two independent single phase semiconverters are supplying the armature and field circuits of a separately excited dc motor for controlling its speed. The firing angle of the converter supplying the field adjusted such that maximum field current flows. The machine parameters are armature resistance = 0.25 2, field circuit resistance 147 , motor voltage constant K = 0.7032 V/A *rad/s. The load torque is T = 45 Nm at 1000 rpm. The converters are fed from a 208 V, 50 Hz ac supply, and the friction and windage losses are neglected. The = m. 1032V/4 e ind inductance of the field and armature circuits is sufficient to make the armature and field current continuous and ripple free. Determine (a) The field current (b) The delay angle of the armature converters (c) The input power factor of armature circuit converters.
(a) Field current is calculated as;If = V/ff Rfwhere, V
= 208 V (supply voltage)ff
= 50 Hz (supply frequency)Rf
= 147 Ω (field circuit resistance)Therefore,If
= 208/50*147
= 0.282 A(b) The motor voltage equation is given by,Ea
= KφNwhere,Ea
= V - Ia Raφ is fluxN is the speedK
= 0.7032 V/A rad/sIa
= V1 / Rawhere V1 is the converter output voltage.Rearranging these equations,φ
= (Ea - V1) / KIa
= V1 / RaEa
= KφN + Ia RaV - V1
= KφN + V1 / Ra Ra∴ V1
= (V - KφN Ra ) / (1 + Ra ).
Where,V = 208 VK = 0.7032 V/A rad/sRa
= 0.25 ΩN = 1000 rpm
= 2πN / 60 rad/s≈ 104.67 rad/s Substituting all these values,V1
= (208 - 0.7032 * φ * 104.67 * 0.25) / (1 + 0.25)
= 31.79φHence, Ia
= V1 / Ra
= 31.79/0.25
= 127.16 A The power input to the armature circuit,P
= V1 Ia cos (α)
= 31.79 * 127.16 cos(α)
The load torque TL = 45 Nm
So, α = cos⁻¹ (TL / KIaN)
α = cos⁻¹ (45 / 0.7032 * 127.16 * 104.67)
α = 47.23°(c) The input power factor of armature circuit converters is given as:
PF = cos (α) = cos (47.23°)
= 0.68.
Therefore, the power factor of the armature circuit converters is 0.68.
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Explain the quantum nanostructures with schematic diagram?
Quantum nanostructures are materials or devices that exhibit quantum mechanical properties at the nanoscale level.
Quantum nanostructures are structures that are engineered at the nanoscale to take advantage of quantum mechanical effects. These effects arise due to the wave-particle duality of particles at the atomic and subatomic levels. Quantum nanostructures can be categorized into various types, including quantum dots, quantum wells, and quantum wires.
Quantum Dots: Quantum dots are tiny semiconductor particles with dimensions on the order of nanometers. They confine electrons in all three dimensions, resulting in discrete energy levels. The size of the quantum dot determines the energy levels and properties of the confined electrons.Quantum Wells: Quantum wells are thin layers of a semiconductor material sandwiched between two different materials. They confine electrons in one dimension, forming quantized energy levels. The width of the well determines the energy levels and characteristics of the confined electrons.Quantum Wires: Quantum wires are elongated nanostructures that confine electrons in two dimensions. They are typically created by growing semiconductor materials in specific directions, resulting in a thin wire-like structure. Quantum wires exhibit quantized energy levels and unique electrical properties.Learn more about Quantum nanostructures: https://brainly.com/question/28823573
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(Maccoby) Narcissistic leaders: The incredible pros, the inevitable cons
narcissistic leaders possess qualities such as confidence and charisma that can be advantageous in leadership roles. However, their excessive focus on their own needs and lack of empathy can lead to negative consequences, including a toxic work environment and poor collaboration.
pros and cons of narcissistic leadersNarcissistic leaders are individuals who exhibit excessive self-importance, a sense of entitlement, and a lack of empathy towards others. While they may possess certain qualities that can be advantageous in leadership roles, such as confidence and charisma, their narcissistic tendencies can also lead to negative consequences.
Pros of Narcissistic LeadersInspiration and Motivation: Narcissistic leaders have the ability to inspire and motivate others. Their self-assured nature and grandiose vision can attract followers and create a sense of excitement and ambition within a team or organization.Confidence and Assertiveness: Their confidence and assertiveness can help them make tough decisions and take risks that others may shy away from. This can lead to innovation and progress.Cons of Narcissistic LeadersLack of Empathy: Narcissistic leaders often lack empathy towards others, leading to a toxic work environment. Employees may feel undervalued and unheard, which can negatively impact morale and productivity.Poor collaboration and Teamwork: Narcissistic leaders prioritize their own success over the collective goals of the group, making collaboration and teamwork challenging. This can hinder the overall effectiveness of the team or organization.It is important to note that not all leaders with narcissistic traits are inherently bad or ineffective. Some individuals may be able to balance their narcissistic tendencies with empathy and a genuine concern for others. However, it is crucial to be aware of the potential negative consequences that can arise from narcissistic leadership and to foster a healthy and inclusive work environment.
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The open circuit and short circuit test data of a 6kVA, 200/400volt and 50Hz single phase transformer are
⦁ O.C test …….. Primary voltage = 200 volts, No load current = 0.75A, W = 75w
⦁ S.C test ……… Primary voltage = 18 volts, Secondary current = 12.5A, W=60w.
Find the parameters of the equivalent circuit.
the parameters of the equivalent circuit of the given transformer are;
R_1 = 533.33 Ω, R_0 = 93.33 Ω, R_2 = 1.44 Ω, X_1 = 226.67 Ω, X_0 = 40 Ω, X_2 = 16.2 Ω.
Transformer rating, kVA = 6 Voltage ratio, V1 / V2 = 200 / 400
Primary voltage, V1 = 200V
Frequency, f = 50Hz
For Open Circuit test:
Primary voltage, V1 = 200V
No-load current, Io = 0.75A
Power, W = 75W
For Short Circuit test:
Primary voltage, V1 = 18V
Secondary current, I2 = 12.5A
Power, W = 60W
As the voltage ratio is 2:1, the turns ratio (
a) is 1:√2. Number of turns in the primary, N1 = kV1/√2
Number of turns in the secondary, N2 = kV2/√2
=6 × 400/√2
=1697.1 turns
Equivalent circuit parameters can be found as follows:
Calculation of R_1,R_0,R_2,X_1,X_0 and X_2 is as follows;
Calculation of R_1:I_1 =(W_0/V_1)
= 75/200
= 0.375AR_1
= (V_1/I_1)
= (200/0.375) Ω
= 533.33 Ω
Calculation of R_0:
R_0 = ((V_1/I_0)-R_1)
= ((200/0.75) - 533.33) Ω
= 93.33 Ω
Calculation of R_2:
R_2 = (V_2/I_sc)
= (18/12.5) Ω
= 1.44 Ω
Calculation of X_1:
X_1 = [(V_1/I_m) - R_1]
= [(200/0.667) - 533.33] Ω
= 226.67 Ω
Calculation of X_0:
X_0 = [(V_1/I_0) - R_0]
= [(200/0.75) - 93.33] Ω
= 40 Ω
Calculation of X_2:
X_2 = [(V_2/I_m) - R_2]
= [(18/0.888) - 1.44] Ω
= 16.2 Ω
Let us write the equivalent circuit diagram:
Total resistance on the primary side of transformer:
Total resistance on the secondary side of transformer
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What are cond to the largest potential enero Nond Help? 17. 1-/1 Points DETAILS SERPSE 10 28.A.OP.027.MI. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER A partide with positive charge -1.75*10cmoves with a velocity v1.-) / through a region where born a uniform magnetic field and a uniform electne nederst Chote che total force on the moving ortice, takong 8 -44.5+ Tand --- Vm Give your answers in for each component) - what ng does the force vector more with the positive X-7 (ve your answer in degree counterdockwise from the #xaxis.) Interdeckwise from the to what in for what vector electric field would the total force on the partice be wrow your answers in Wim for each component.) W W/m Need Help 1 in 2 DET
The force vector makes an angle of θ = 135° with the positive x-axis in the counterclockwise direction. The electric field vector that would result in the total force on the particle is given by E = Ex i + Ey j = [25.4 × 10-6 + v1.-) / 1.75] i.
A particle with positive charge -1.75 x 10C moves with a velocity v1.-) / through a region where born a uniform magnetic field and a uniform electric field.
The total force on the moving particle is 8 -44.5+ T and --- Vm and need to find the force vector on the positive x-7 and electric field that would result in the total force on the particle.
Solution: The total force on the moving particle, F = 8 - 44.5 + T, q = 1.75 x 10C, v = v1.-).
The force on a moving charged particle due to magnetic field is given by Fm = q v × B.
The force is perpendicular to both the velocity and the magnetic field vectors.
Thus, the force vector makes an angle of θ = 135° with the positive x-axis in the counterclockwise direction.
The magnetic field vector B is perpendicular to the force vector and to the velocity vector.
The total force on the particle is given by F = Fm + Fe, where Fm is the force due to the magnetic field and Fe is the force due to the electric field.
Therefore, Fe = F - Fm = 8 - 44.5 + T - q v × B.
The force on a moving charged particle due to electric field is given by Fe = qE, where E is the electric field vector.
The electric field vector E that would result in the total force on the particle is therefore given by E = Fe / q = (8 - 44.5 + T - q v × B) / q.
The electric field vector E has two components along the x-axis and y-axis.
The x-component is given by Ex = E cosθ and the y-component is given by Ey = E sinθ.
Therefore, Ex = [8 - 44.5 + T - q v B cosθ] / q = [8 - 44.5 + (- 1.75 × 10 C) × v1.-) × ( - 44.5 × 10-6 T) cos135°] / (1.75 × 10-6 C) = (44.5 × 10-6 + 1.75 × 10-6 × v1.-) / 1.75 = 25.4 × 10-6 + v1.-) / 1.75
The y-component is given by Ey = E sinθ = [8 - 44.5 + T - q v B sinθ] / q = [8 - 44.5 + (- 1.75 × 10 C) × v1.-) × ( - 44.5 × 10-6 T) sin135°] / (1.75 × 10-6 C) = 0 N/C.
Thus, the electric field vector that would result in the total force on the particle is given by E = Ex i + Ey j = [25.4 × 10-6 + v1.-) / 1.75] i.
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In a 3 phase transformer connected in wye-delta with rating 200V:2200V
For the wye side, is the 220V voltage the phase or line voltage?
Example 3 phase 20KVA transformer 220V:2200V with impedence 4+5i reffered to low voltage side supplies a load of 12KVA at PF of 8 lagging. The feeder has 1+1i impedence. Find the sending end voltage.
WYE-delta
In a wye-delta connection, the 220V refers to the line voltage on the wye side. The sending end voltage is approximately 277.2V + 57.2V * i.
In a wye-delta connection of a three-phase transformer, the 220V voltage refers to the line voltage on the wye side. In this configuration, the line voltage is higher than the phase voltage by a factor of [tex]\sqrt{3}[/tex](approximately 1.732). The phase voltage is obtained by dividing the line voltage by [tex]\sqrt{3}[/tex].
Now, let's calculate the sending end voltage for the given scenario. We have a 3-phase, 20KVA transformer with a rating of 220V:2200V. The impedance of the transformer is given as 4+5i, referred to the low voltage (wye) side. The load connected to the transformer is 12KVA at a power factor (PF) of 8 lagging, and the feeder has an impedance of 1+1i.
To find the sending end voltage, we need to consider the voltage drop across the feeder and the transformer's impedance. The power factor allows us to calculate the real and reactive power components of the load.
1. Calculate the load current:
Load (S) = 12KVA
Power Factor (PF) = 8 lagging
Load (P) = S * PF = 12KVA * 0.8 = 9.6kW
Load (Q) = [tex]\sqrt{(S^2 - P^2) = √(12KVA^2 - 9.6kW^2) }[/tex]= [tex]\sqrt{(144KVA^2 - 9.6kVA^2) }[/tex]= [tex]\sqrt{(136.8kVA^2}[/tex]) = 11.7kVA
Load Current (I) = Load (S) / ([tex]\sqrt{3}[/tex] * Line Voltage) = 11.7kVA / (1.732 * 220V) ≈ 28.6A
2. Calculate the voltage drop across the feeder:
Feeder Impedance (Zf) = 1+1i
Feeder Voltage Drop (Vf) = Load Current (I) * Feeder Impedance (Zf) = 28.6A * (1+1i) ≈ 57.2V * (1+1i)
3. Calculate the voltage at the transformer's primary side:
Primary Voltage (Vp) = Line Voltage + Voltage Drop (Vf) = 220V + 57.2V * (1+1i) = 220V + 57.2V + 57.2V * i ≈ 277.2V + 57.2V * i
Therefore, the sending end voltage is approximately 277.2V + 57.2V * i.
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Take a vector with magnitude A=3.4 and angle from the x-axis θ=23.0 degrees. What are the components of this vector and their proper unit vector assignation? Answer to 3 sig figs without units. Use vector component order of x-axis then y-axis values. A=
The components of this vector and their proper unit vector(PUV) assignation are (-2.86, 1.46), with unit vectors (-0.919, 0.395) along x and y-axis values respectively.
The components of this vector and their PUV assignation are (-2.86, 1.46), with unit vectors(UV) (-0.919, 0.395) along x and y-axis values respectively. Given, A = 3.4and angle θ = 23°Using the given magnitude and angle, we can calculate the horizontal and vertical components as: x = A cosθy = A sinθ. On substituting the given values, we get; x = 3.4 cos 23°y = 3.4 sin 23° Evaluating the above expression gives the components of the vector as follows; x = 3.4 cos 23° = 2.86y = 3.4 sin 23° = 1.46. We need to find the UVs for the above components.
Unit vector means dividing each component by its magnitude(m) to get a vector of magnitude 1.x-axis unit vector = (x / |x|) = -2.86/3.4 = -0.919 y-axis unit vector = (y / |y|) = 1.46/3.4 = 0.395.
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Determine the maximum normal stress (in MPa, using 2 decimal places) for a beam with the following data: 1. Beam is 5 m in length (simply supported) 2. Has an applied uniform distributed load of 22 kN/m 3. Rectangular cross section rectangular with a base of 166 mm and a height of 552 mm
the maximum normal stress of the beam is 1.43 MPa (approx.).
The formula to calculate the moment of inertia of a rectangular cross-section of a beam is:I = (b × h³)/12
where,b = baseh = height
Substituting the given values in the above formula:
I = (166 × 552³)/12I = 13236681536 mm⁴
Maximum bending moment of the beam:
The formula to calculate the maximum bending moment of the beam is:
M = (wL²)/8
where,w = load per unit area
w = (22 × 10⁶)/1000
w = 22 kN/mL = Length of the beam = 5 mM
= (22 × 5²)/8M = 68.75 kN.m
Converting kN.m into N.mM = 68.75 × 10⁶ N.mm
Maximum normal stress of the beam:
The formula to calculate the distance from the neutral axis to the outermost fiber of the beam is
c = h/2c = 552/2c = 276 mm
Substituting the given values in the formula:
σ = (Mc)/Iσ = (68.75 × 10⁶ × 276)/13236681536σ = 1.43 MPa
Hence, the maximum normal stress of the beam is 1.43 MPa (approx).
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A coil with a resistance of 100 Q and an inductance of 2 mH is placed in series with a capacitance of 20 nF. The circuit has an A.C. supply of 60 volts at 10 kHz connected to it. Determine the following, expressing all answers to 3 places after decimal point.
i) The inductive reactance, XL.
ii) The capacitive reactance, Xc.
iii) The impedance of the circuit, Z.
v) The resonant frequency, fr
A coil with a resistance of 100 Q and an inductance of 2 mH is placed in series with a capacitance of 20 nF. The circuit has an A.C. supply of 60 volts at 10 kHz connected to it. Determine the following, expressing all answers to 3 places after decimal point.
i) The inductive reactance, XL.
ii) The capacitive reactance, Xc.
iii) The impedance of the circuit, Z.
v) The resonant frequency, fr
Therefore, the values are:
i) Inductive reactance (XL) ≈ 125.663 Ω
ii) Capacitive reactance (Xc) ≈ 795.775 Ω
iii) Impedance (Z) ≈ 795.897 Ω
v) Resonant frequency (fr) ≈ 79577.768 Hz
i) Inductive reactance (XL) can be calculated using the formula:
XL = 2πfL
ii) Capacitive reactance (Xc) can be calculated using the formula:
Xc = 1 / (2πfC)
iii) Impedance (Z) can be calculated using the formula:
Z = √((R^2) + ((XL - Xc)^2))
v) Resonant frequency (fr) can be calculated using the formula:
fr = 1 / (2π√(LC))
Given values:
Resistance (R) = 100 Ω
Inductance (L) = 2 mH = 0.002 H
Capacitance (C) = 20 nF = 20 * 10^-9 F
AC supply voltage (V) = 60 V
Frequency (f) = 10 kHz = 10 * 10^3 Hz
Let's calculate the values one by one:
i) Inductive reactance (XL):
XL = 2πfL
= 2 * π * 10^4 * 0.002
≈ 125.663 Ω
ii) Capacitive reactance (Xc):
Xc = 1 / (2πfC)
= 1 / (2 * π * 10^4 * 20 * 10^-9)
≈ 795.775 Ω
iii) Impedance (Z):
Z = √((R^2) + ((XL - Xc)^2))
= √((100^2) + ((125.663 - 795.775)^2))
≈ 795.897 Ω
v) Resonant frequency (fr):
fr = 1 / (2π√(LC))
= 1 / (2 * π * √(0.002 * 20 * 10^-9))
≈ 79577.768 Hz
Therefore, the values are:
i) Inductive reactance (XL) ≈ 125.663 Ω
ii) Capacitive reactance (Xc) ≈ 795.775 Ω
iii) Impedance (Z) ≈ 795.897 Ω
v) Resonant frequency (fr) ≈ 79577.768 Hz
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_________________is a electromechanical device that performs
the same function as a fuse and in addition acts as a switch.
_______________is a device that changes or transforms
alternating current (AC
An electromechanical device that performs the same function as a fuse and acts as a switch is known as a circuit breaker. A transformer is a device that changes or transforms alternating current (AC) to direct current (DC) or vice versa.
A circuit breaker is a type of electrical switch that automatically interrupts the electrical circuit in the event of a short circuit, overload, or a fault. In addition, the circuit breaker can be manually tripped to switch off the electrical circuit.
Circuit breakers are commonly found in residential, commercial, and industrial electrical systems. They are more convenient than fuses since they can be reset rather than having to replace them when they fail. A circuit breaker has two main components: a current sensor and a contact system. When an abnormal current flows through the circuit breaker, the current sensor senses the current, and the contact system interrupts the flow of current.In electrical engineering, a device that changes or transforms alternating current (AC) to direct current (DC) or vice versa is known as a transformer. It works on the principle of electromagnetic induction. It has two windings, primary and secondary, that are wrapped around a magnetic core.
When AC current flows through the primary winding, it produces a varying magnetic field that induces a voltage in the secondary winding. The transformer can increase or decrease the voltage level in the secondary winding based on the number of turns in the primary and secondary windings. The transformer is an essential component of electrical power transmission and distribution systems.
A circuit breaker is an electromechanical device that performs the same function as a fuse and in addition acts as a switch.
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tIs it correct that the larger the gate length the lower the
leakage?
Yes, it is correct that the larger the gate length, the lower the leakage because in MOSFET, the leakage current through the gate oxide increases as the gate length decreases, increasing the gate length decreases the leakage current.
For MOSFET (Metal-Oxide-Semiconductor Field-Effect Transistor), when the gate oxide is thin, the gate leakage current increases and the MOSFET has less threshold voltage (VT). So, when the MOSFET's gate length reduces, the gate oxide thickness is less, and that leads to an increase in gate oxide leakage. Gate leakage can have a significant impact on power dissipation and performance in VLSI (Very Large-Scale Integration) circuits.
Therefore, minimizing gate leakage is crucial. By increasing the gate length of MOSFETs, gate oxide leakage can be reduced. Thus, the larger the gate length, the lower the leakage, making it possible to minimize power dissipation and boost performance in VLSI circuits. In conclusion, it is correct that the larger the gate length, the lower the leakage.
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3 marks Question 7 One of the most important concepts in particle physies is conservation laws'. These describe certain properties of a system that do not change when a physical process or interuction (like beta - decay or beta + decay) takes place A radionuclide decays by a beta positive decay when a proton transmutates into a neutron and a positron and a neutrino. p^n + B +v a) What is the baryon number and electronic lepton number (L) of the neutron? Lepton number (1) A B С D Mule Baryon number B 1 1/3 0 1 0 1 0 1 mark
The baryon number and electronic lepton number (L) of the neutron are 1 and 0, respectively. The baryon number and electronic lepton number (L) of the neutron are 1 and 0, respectively.
What is the baryon number and electronic lepton number (L) of the neutron?
The baryon number (B) is a quantity that is preserved in all strong interactions and is given by: B = 1/3 (Nq − N¯q) where Nq and N¯q are the number of quarks and antiquarks, respectively. The neutron is a baryon, which means it consists of three quarks. Since there are no antiquarks in the neutron, Nq = 3 and N¯q = 0. Therefore, the baryon number of the neutron is B = 1/3 (Nq − N¯q) = 1.Electronic lepton number (L) is defined as the difference between the number of leptons (electrons, muons, and tau particles) and the number of antileptons in a system. Since the neutron does not contain any leptons or antileptons, its electronic lepton number is zero (L = 0).
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To check the radius of a railroad curve, the effect of 20 lb weight is observed to be 20.7 lbs on a spring scale suspended from the rood of an experimental car rounding the curve at 40 mph. What is the radius of the curve in ft.
The radius of the railroad curve is approximately 2551 ft.
The radius of the railroad curve is approximately 2551 ft.
The effect of 20 lb weight is observed to be 20.7 lbs on a spring scale suspended from the road of an experimental car rounding the curve at 40 mph.
To determine the radius of the railroad curve in ft. The force exerted on the object can be defined as, F = mature, the force exerted on the object is given by, F = 20.7 - 20 = 0.7lbs.
The object is undergoing circular motion, so its acceleration can be defined as,
a = v² / rWhere,v = velocity of the object = radius
the velocity of the object is 40 mph,
40 * 1.47 = 58.8 ft/substituting the values of F, a, and v
the above equation,0.7 = (58.8)² / rr = (58.8)² / 0.7r ≈ 2551 ft.
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the operating speed of a fluid power system is adjusted by the ____.
The operating speed of a fluid power system is adjusted by the flow control valve. Flow control valves are used in fluid power systems to adjust the speed of actuator operations. They function by limiting the flow of fluid in the system.
They also act as a pressure regulator, ensuring that the actuator receives only the fluid it requires to execute its task. The fluid flow in a hydraulic system can be adjusted or regulated using a flow control valve. The flow control valve, or metering valve, is a device that regulates the speed of fluid flow to the actuator. It is used in a variety of hydraulic systems, from braking systems to production line machinery.
The flow control valve is a critical component in a hydraulic system. It is a simple device that regulates fluid flow. It regulates the speed of fluid flow through the system to maintain the desired speed of actuator movement. This guarantees that the actuator does not move too quickly or too slowly and that the system is efficient and reliable.
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Can someone explain why the voltage drop is going to be the
same? and What would be the difference if the bulbs are connected
in series instead? A 120-V, 60-W incandescent light bulb; a 120-V, 120-W incandescent light bulb; and a 120-V, 240-W incandescent light bulb are connected in parallel as shown. The voltage between points a and b is 120 V. Through which bulb is there the greatest voltage drop? A. the 120-V, 60-W light bulb B. the 120-V, 120-W light bulb C. the 120-V, 240-W light bulb D. The voltage drop across all three light bulbs is the same. a 120 V 60 W 120 V 120 W 120 V 240 W b
Given, three light bulbs are connected in parallel as shown below where the voltage between points a and b is 120V.120V, 60W120V, 120W120V, 240WThe power of each bulb can be given by P = V²/R, where R is the resistance of the bulb. For this problem, resistance of each bulb is not given.
So, we can find the current flowing through each bulb using P = VI. We can use I = P/V to calculate the current through each bulb.I₁ = 60/120 = 0.5 AI₂ = 120/120 = 1 AI₃ = 240/120 = 2 A So, the bulb with the greatest voltage drop is the one with the highest current flowing through it. In this case, the 240-W bulb has the greatest current flowing through it and so, it will have the greatest voltage drop.
However, we can say that the total voltage drop across all three bulbs would be equal to the voltage between points a and b, which is 120V. This is because the sum of the voltage drops across each element in a series circuit is equal to the total voltage of the circuit.In conclusion, the voltage drop is going to be the same for the given circuit and if the bulbs are connected in series, the total voltage drop across all three bulbs would be the same.
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3. A sky wave is incident on the ionosphere at an angle of 60°. The electron density of this ionosphere layer is
N = 24.536 x 10^11electrons/m^3
a. For the point of reflection, determine the refractive index of the ionospheric layer. (3 Marks)
b. Identify the critical frequency for the communication link. (2 Marks)
c. Determine the maximum usable frequency (2 Marks)
d. Give reasons why the transmissions would fail the following frequencies if the frequencies were 10 MHz and 30 MHz respectively. (4 Marks)
if the MUF is lower than the transmission frequencies of 10 MHz and 30 MHz, the transmissions would fail.The refractive index (n) of a medium can be calculated using the formula:n = √(1 - (f_p/f)^2). where f_p is the plasma frequency and f is the frequency of the incident wave. Given that the incident angle is 60°, the point of reflection corresponds to the vertical incidence where the wave travels straight up and down.
For vertical incidence, the critical frequency (f_c) is related to the plasma frequency by: f_c = f_p / 2π.Using the relationship between critical frequency and plasma frequency, we can calculate the refractive index for the ionospheric layer. b. The critical frequency (f_c) for the communication link can be calculated by rearranging the equation mentioned above: f_c = f_p / 2π.Substituting the given electron density value (N), we can calculate the critical frequency.c. The maximum usable frequency (MUF) corresponds to the highest frequency that can be refracted and returned to Earth by the ionosphere. It is given by:MUF = f_c / sin(θ). where θ is the incident angle. By substituting the critical frequency (f_c) and incident angle (θ), we can determine the MUF.d. The transmissions would fail at frequencies of 10 MHz and 30 MHz if they exceed the maximum usable frequency (MUF) determined in part c. If the frequencies are higher than the MUF, the ionosphere will not be able to refract and return the waves to Earth, resulting in a loss of communication. Therefore, if the MUF is lower than the transmission frequencies of 10 MHz and 30 MHz, the transmissions would fail.
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One arm of a U-shaped tube (open at both ends) contains water, and the other alcohol. If the two flulds meet at exactly the bottom of the U, and the alcohol is at a height of 16.0 cm, at what height will the water be? Assume pulrikil =0.790 ×10 3kg/m 3
Express your answer with the appropriate units. X Incorrect; Try Again; 5 attempts remaining
The height of the water is found using the principle of communicating vessels. The principle of communicating vessels is a concept of fluid mechanics that states that any fluid in a container will attempt to find its level, and the pressure is the same at all points that are at the same height from the liquid's surface.
When the two fluids are joined together in a U-shaped tube, they will form a single column with the same height in both arms. Therefore, the height of the water can be determined using the following steps:Let the height of the water column be 10 meters.
Let the density of water be w and the density of alcohol be a. The pressure at the bottom of the U-shaped tube is the same on both sides. wgh = agh + Patm Where Patm is the atmospheric pressure, g is the acceleration due to gravity (9.8 m/s2), and h is the height of the water column.
ρw = 1000 kg/m³ and
a = 790 kg/m3.
Substituting these values into the above equation, we get:h = (ρa / ρw) * 16.0 cm
= (790 kg/m³ / 1000 kg/m³) * 0.16 m
= 0.1264 m
Therefore, the height of the water column is 0.1264 meters, or 12.64 centimeters. Answer: 12.64 cm.
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determine the magnitude of the forces P for which the deflection is
zero at end A of the beam. Use E 5 29 3 106 psi.
A beam is subjected to forces that cause deflection. This question requires the determination of the magnitude of forces P for which the deflection is zero at end A of the beam.The beam is considered as an engineering structure that is designed to support loads.
Its capacity to support loads is dependent on its structure, including its materials, cross-sectional area, and length. In the context of mechanical engineering, the maximum stress that a material can withstand before it yields is known as yield stress. It's a significant design consideration for beams.The problem statement indicates that the deflection is zero at end A of the beam.
Therefore, a point load is considered at point B on the beam to obtain the magnitude of the forces P. The beam's dimensions and other essential parameters have been supplied in the image below. The problem-solving approach entails applying the formula for the deflection of a beam due to a point load and utilizing the result to determine the value of P. The equation to use here isδ = PL^3/3EI
Whereδ = deflection
P = Force
L = Length
E = Modulus of Elasticity
I = Moment of Inertia
The Moment of Inertia for a rectangular beam is given by:
I = (bh^3)/12Whereb is the width h is the height
Substituting the given values of length, modulus of elasticity, width, height, and the moment of inertia into the deflection equation provides a value of P that can be solved. Here's the calculation for P:P = (3 x EI x 0)/L^3The formula for the moment of inertia for a rectangular beam is:I = (bh^3)/12
The height of the beam (h) is equal to 3 in and the width (b) is equal to 4 in.
I = (4 x 3^3)/12
I = 27/4
Substituting the values for the moment of inertia, length, and modulus of elasticity results in:
P = 0 P is the magnitude of the forces required to produce zero deflection at point A of the beam. This indicates that the beam can withstand any load up to and including this force without deflecting. The engineering structure's maximum capacity is equal to this force. Therefore, the maximum load the beam can support is P.
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substitute known quantities and solve for the unknown quantity. (cont.) solving ohm's law for the instantaneous current gives (175 v)sin(55лt) r and substituting known values gives i = ¡ = = av r = av (175 v)sin(55лt) r = r -3 (175 v)sin 55(4.30 × 10 s)] = 0.423 a. 280 ω -3 the unknown quantity to be determined in part (e) is the instantaneous power
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Question: Substitute Known Quantities And Solve For The Unknown Quantity. (Cont.) Solving Ohm's Law For The Instantaneous Current Gives (175 V)Sin(55лt) R And Substituting Known Values Gives I = ¡ = = Av R = Av (175 V)Sin(55лt) R = R -3 (175 V)Sin 55(4.30 × 10 S)] = 0.423 A. 280 Ω -3 The Unknown Quantity To Be Determined In Part (E) Is The Instantaneous Power

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Substitute known quantities and solve for the unknown quantity. (cont.) Solving Ohm's law for the instantaneous current gives (175 V)sin(55лt) R and substituting known values gives i = ¡ = = Av R = Av (175 V)sin(55лt) R = R -3 (175 V)sin 55(4.30 × 10 S)] = 0.423 A. 280 Ω -3 The unknown quantity to be determined in part (e) is the instantaneous power dissipated by the resistor when t = 4.30 x 10 s. The instantaneous power dissipated by the resistor is given by P = i²R. What instantaneous power is dissipated by the resistor at t = 4.30 × 10¯ s? -3 X Incorrect. Substitute the instantaneous current and resistance into the power equation. W Submit Skip (you cannot come back)
Answer: The instantaneous power dissipated(P) by the resistor when t = 4.30 x 10 s is 0.05 W.
The instantaneous power dissipated by the resistor(r) when t = 4.30 x 10 s is P = i²R. Current(i) Therefore, substituting the given values will give: P = (0.423 A)² × 280 ΩP = 0.05 W.
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Question 1 For a light emitting diode made from a material with a bandgap of 2.040 (eV). Accounting for the peak in the distribution of energies for electrons in the conduction band, what is the spectral linewidth, Dl, for this material at 380 (K)? Give your answer in (nm) to 4 significant digits.
The spectral linewidth for this material at 380 K is 42.7 nm.
From the given information, the bandgap of a material is given as 2.040 eV and temperature is given as 380 K. Now, we can use the following formula to calculate the spectral linewidth:
∆E ≈ 2.198 kBT where, ∆E = spectral linewidth, k = Boltzmann’s constant = 1.3807 × 10^−23J/K, T = temperature
To find the spectral linewidth in nm, we will use the relation,
∆E = hν = hc/λ where h = Planck’s constant = 6.626 × 10−34J.s, ν = frequency, c = speed of light in vacuum = 2.998 × 10^8m/s, λ = wavelength
Solving the formula, we get the spectral linewidth as 0.0209 eV
Substituting the values in the above relation, we get the spectral linewidth in nm as 42.7 nm.
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If equal amounts of heat are added to two containers of water and the resultant temperature change of the water in one container is five times that of the water in the other container, then what can you say about the quantities of water in the containers? O The container with five times the temperature change contains one-fifth as much water. O The container with five times the temperature change contains twenty-five times as much water. O The container with five times the temperature change contains five times as much water. O The quantities of water in the two containers are equal.
The container with five times the temperature change contains one-fifth as much water.
It is to be determined what can be said about the quantities of water in the containers if equal amounts of heat are added to two containers of water and the resultant temperature change of the water in one container is five times that of the water in the other container. So, the answer is "The container with five times the temperature change contains one-fifth as much water."
Let the amount of water in one container be W1, and that in the other be W2 and let the temperature increase be T1 and T2 respectively.
The specific heat capacity of water is the same for both containers.
Let the amount of heat added be Q1 and Q2.
Q1 = Q2, T1 = 5T2.
So, W1 × T1 = Q1 = Q2 = W2 × T2W1 × 5T2 = W2 × T2W1/W2 = 1/5
Therefore, the container with five times the temperature change contains one-fifth as much water.
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