The correct answer to the question is option d. The power supply(P) is warm. The computer power supply used in your computer is not 100% efficient.
The power supply is an important component of a computer system(CS). The computer power supply is responsible for converting the alternating current from the outlet to direct current to power the computer components like the Central processing unit (CPU), motherboard, hard disk drives(HDD), and graphics card. It is not 100% efficient due to the following reasons: The power supply produces a lot of heat which is due to the inefficiency of the power supply and the conversion process. This heat is usually dissipated through the power supply unit using a fan that is mounted inside the computer. As a result, the power supply unit is always warm to the touch.The power supply unit has a cooling fan inside it that helps to regulate the temperature inside the computer. When the computer is turned on, the fan begins to spin and the power supply unit starts to get warm. This is evidence that the power supply is not 100% efficient since it is producing heat that needs to be dissipated. So, the option d. The power supply is warm. is the correct answer.
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Q12. A step-down transformer used in the national grid has an input power of 28,000 W and an output power of 23,000 W. a. Calculate the efficiency of the transformer. (2) b. (i) How much power is dissipated due to the heating effect? (ii) If the transformer is used for 3.5 hours, how much energy is wasted during that time? (4)
Energy wasted = power dissipated × time used Energy wasted = 5,000 W × 3.5 hours Energy wasted = 17,500 Wh or 17.5 kWh (4 significant figures)Therefore, the energy wasted by the transformer during 3.5 hours is 17.5 kWh.
A step-down transformer used in the national grid has an input power of 28,000 W and an output power of 23,000 W. a. Calculate the efficiency of the transformer. (2) b. (i) How much power is dissipated due to the heating effect? (ii) If the transformer is used for 3.5 hours, how much energy is wasted during that time?"A transformer is an electric device used to transfer electrical energy from one circuit to another. The input power is given as 28,000 W, and the output power is 23,000 W. The efficiency of the transformer can be calculated as follows:Efficiency
= output power / input power × 100%Efficiency
= 23,000 W / 28,000 W × 100%Efficiency
= 82.14% (2 significant figures)Therefore, the efficiency of the transformer is 82.14%. (a)The power dissipated due to the heating effect is the difference between the input power and the output power.Power dissipated
= input power - output power Power dissipated
= 28,000 W - 23,000 W Power dissipated
= 5,000 W (i)Therefore, the power dissipated due to the heating effect is 5,000 W. (b)The energy wasted by the transformer during 3.5 hours can be calculated by using the formula:E
= P × t where, E is the energy wasted, P is the power dissipated, and t is the time used.Energy wasted
= power dissipated × time used Energy wasted
= 5,000 W × 3.5 hours Energy wasted
= 17,500 Wh or 17.5 kWh (4 significant figures)Therefore, the energy wasted by the transformer during 3.5 hours is 17.5 kWh.
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Q.EL15-3) Please help me with the solution to this
electromagnetism problem.
Q3】 As shown in Fig. 3(a), there is a toroidal core with permeability \( \mu \). The mean radius of the toroidal core is \( a \), and the cross sectional area of the core is \( A=\pi b^{2} \), where
A toroidal core's inductance is provided by the inductance formula, which is given by[tex]\[L_{S}=N^{2}\mu \pi \left( \frac{b^{2}}{a}[/tex] \right) \]where N is the number of turns of wire around the toroidal core, a is the mean radius of the toroidal core, b is the radius of the wire used to wrap the toroidal core, and μ is the core's permeability. (b) The self-inductance of the toroidal core is \( L_{S}=N^{2}\mu \pi \left( \frac{b^{2}}{a} \right) \). (c) Mutual inductance.
The mutual inductance between two toroidal cores is given by the equation\[tex][M_{21}=\frac{N_{2}N_{1}\mu \pi b_{2}^{2}b_{1}^{2}}{a_{2}+a_{1}}\ln \frac{a_{2}}{a_{1}}\][/tex]where N1 is the number of turns of wire around the first toroidal core, N2 is the number of turns of wire around the second toroidal core, a1 and a2 are the mean radii of the first and second toroidal cores, and b1 and b2 are the radii of the wire used to wrap the first and second toroidal cores,
respectively. (d) The coefficient of coupling. The coefficient of coupling is given by the equation\[k=\frac{M}{\sqrt{L_{1}L_{2}}}\]where M is the mutual inductance between two toroidal cores, and L1 and L2 are the self-inductances of the two toroidal cores, respectively. (e) The equivalent inductance when two coils are wound on the toroidal core. When two coils are wound on a toroidal core, the equivalent inductance is given by\[L_{eq}=\frac{L_{1}L_{2}}{L_{1}+L_{2}+2M}\]
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A single phase 220/6 Volt, 50 Hz transformer has a rated primary current = 0.5 A. its maximum efficiency is at load current = 15 A and equal to 94% at unity p.f. Its efficiency at rated load, 0.65 p.f. lagging is:
a) 87.8%.
b) 92.3%.
c) 90.9%.
d) None.
None of the given options (a, b, c) accurately represents the efficiency of the transformer at rated load and a power factor of 0.65 lagging. We can use the given information about the transformer's maximum efficiency and rated primary current. The correct option is D.
To calculate the efficiency of the transformer at a rated load and a power factor of 0.65 lagging, we can use the given information about the transformer's maximum efficiency and rated primary current.
Given:
Rated primary current = 0.5 A
Maximum efficiency = 94% at a unity power factor
Load current at maximum efficiency = 15 A
Efficiency is calculated using the formula:
Efficiency = (Output power / Input power) * 100
At maximum efficiency, the output power is equal to the input power. Therefore, we can write:
Output power at maximum efficiency = Input power at maximum efficiency
Let's denote the input power at maximum efficiency as Pin_max and the output power at rated load and a power factor of 0.65 lagging as Pout_rated.
Now, we can set up the equation:
Pin_max = Pout_rated
Since the efficiency at maximum load and unity power factor is given as 94%, we can write:
0.94 = (Pout_rated / Pin_max) * 100
Solving for Pout_rated / Pin_max:
Pout_rated / Pin_max = 0.94 / 100
Pout_rated / Pin_max = 0.0094
Now, we can calculate the efficiency at the rated load and a power factor of 0.65 lagging:
Efficiency = (Output power / Input power) * 100
Efficiency = (Pout_rated / Pin_rated) * 100
Where Pin_rated is the input power at rated load and a power factor of 0.65 lagging.
We know that:
Pin_max = Pin_rated * Power factor
Substituting the given power factor of 0.65 lagging:
Pin_max = Pin_rated * 0.65
Solving for Pin_rated:
Pin_rated = Pin_max / 0.65
Substituting the value of Pout_rated / Pin_max:
Efficiency = (Pout_rated / (Pin_max / 0.65)) * 100
Efficiency = (Pout_rated / Pin_max) * (100 / 0.65)
Efficiency = (0.0094) * (100 / 0.65)
Efficiency ≈ 1.446 %
Therefore, none of the given options (a, b, c) accurately represents the efficiency of the transformer at rated load and a power factor of 0.65 lagging.
The correct option is D.
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You connect a battery, resistor, and capacitor as in (Figure 1), where R=17.0Ω and C=5.00×10 −6
F. The switch S is closed at t=0. When the current in the circuit has magnitude 3.00 A, the charge on the capacitor is 40.0×10 −6
C. What is the emf of the battery? Express your answer with the appropriate units. is Incorrect; Try Again; 5 attempts remaining Part B At what time t after the switch is closed is the charge on the capacitor equal to 40.0×10 −6
C ? Express your answer with the appropriate units. When the current has magnitude 3.00 A, at what rate is energy being stored in the capacitor? Express your answer with the appropriate units. Part D When the current has magnitude 3.00 A, at what rate is energy being supplied by the battery? Express your answer with the appropriate units.
The emf of the battery is 51.0 volts, the time when the charge on the capacitor is 40.0×10⁻⁶ C is approximately 0.157 s, the rate at which energy is being stored in the capacitor when the current is 3.00 A is 153 watts, and the rate at which energy is being supplied by the battery when the current is 3.00 A is also 153 watts.
To find the emf of the battery, we can use Ohm's Law. Ohm's Law states that the voltage across a resistor (V) is equal to the current through the resistor (I) multiplied by the resistance (R). In this case, the resistor has a resistance of 17.0 Ω and the current is 3.00 A. Therefore, the voltage across the resistor is:
V = I * R
V = 3.00 A * 17.0 Ω
V = 51.0 V
So, the emf of the battery is 51.0 volts.
To find the time (t) when the charge on the capacitor is equal to 40.0×10⁻⁶ C, we need to use the equation that relates the charge on a capacitor (Q) to the capacitance (C) and the voltage across the capacitor (V). The equation is:
Q = C * V
Rearranging the equation to solve for time (t):
t = Q / (C * V)
t = 40.0×10^(-6) C / (5.00×10⁻⁶ F * 51.0 V)
t = 0.156862745 s
Therefore, when the charge on the capacitor is 40.0×10⁻⁶ C, the time is approximately 0.157 s.
To find the rate at which energy is being stored in the capacitor when the current has magnitude 3.00 A, we can use the formula for the power (P) in a circuit:
P = IV
where I is the current and V is the voltage across the capacitor.
Since the current is 3.00 A and we know the voltage across the capacitor is 51.0 V (calculated earlier), we can calculate the power:
P = 3.00 A * 51.0 V
P = 153 W
Therefore, when the current has magnitude 3.00 A, the rate at which energy is being stored in the capacitor is 153 watts.
Finally, to find the rate at which energy is being supplied by the battery when the current has magnitude 3.00 A, we can use the same formula for power:
P = IV
Since the current is 3.00 A and we know the emf of the battery is 51.0 V (calculated earlier), we can calculate the power:
P = 3.00 A * 51.0 V
P = 153 W
Therefore, when the current has magnitude 3.00 A, the rate at which energy is being supplied by the battery is 153 watts.
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Explain the rate of change of voltage of a thyristor in relation to reverse-biased.
The rate of change of voltage of a thyristor in relation to reverse-biased operation is typically high.
When a thyristor is reverse-biased, it is designed to block the flow of current in the opposite direction, acting like an open switch. In this state, the thyristor maintains a high impedance, preventing significant current from flowing through it.
If the reverse voltage across the thyristor exceeds its breakdown voltage, it enters a state called the reverse breakdown region. In this region, the thyristor starts conducting current in the reverse direction, allowing a high current to flow through it. During this transition, the voltage across the thyristor drops rapidly, causing a high rate of change of voltage.
It's important to note that the reverse breakdown region is an undesirable operating condition for a thyristor, as it can lead to damage or failure. Thyristors are typically designed to operate in forward-biased mode, where they exhibit lower voltage drop and better control of current flow.
In summary, when a thyristor is reverse-biased and enters the reverse breakdown region, the rate of change of voltage is high as the thyristor transitions from a high-impedance state to conducting current in the reverse direction.
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Question 1 In Compton scattering, calculate the maximum kinetic energy given to the recoil electron for a given photon energy
Compton scattering is a physical phenomenon that refers to the interaction between a high-energy photon and a target, typically an electron. It's named after Arthur Holly Compton, who discovered it in 1922.The Compton effect is used in various fields of science, including nuclear physics and astronomy, among others.
Compton scattering is a physical phenomenon that refers to the interaction between a high-energy photon and a target, typically an electron. It's named after Arthur Holly Compton, who discovered it in 1922.The Compton effect is used in various fields of science, including nuclear physics and astronomy, among others. In this phenomenon, the photon loses energy while the electron gains energy and recoils. Compton scattering is an inelastic scattering phenomenon. The formula for calculating the maximum kinetic energy given to the recoil electron for a given photon energy is as follows: KE = Eγ - Eγ' + (Eγ - Eγ')2/mec2
where KE is the kinetic energy of the recoil electron, Eγ is the energy of the incident photon, Eγ' is the energy of the scattered photon, me is the rest mass of the electron, and c is the speed of light. The formula can be rearranged to solve for the maximum kinetic energy of the recoil electron:
KEmax = Eγ/(1 + Eγ/me*c2) - Eγ'/(1 - cosθ)
where θ is the angle between the incident photon and the scattered photon. The maximum kinetic energy given to the recoil electron for a given photon energy can be calculated using the Compton scattering formula. Compton scattering is a physical phenomenon that occurs when a high-energy photon interacts with a target, typically an electron. When this interaction occurs, the photon loses energy while the electron gains energy and recoils. This phenomenon is known as Compton scattering. Compton scattering is an inelastic scattering process.
The formula for calculating the maximum kinetic energy given to the recoil electron for a given photon energy is KE = Eγ - Eγ' + (Eγ - Eγ')2/mec2. The formula can be rearranged to solve for the maximum kinetic energy of the recoil electron, which is KEmax = Eγ/(1 + Eγ/me*c2) - Eγ'/(1 - cosθ).
In this formula, KE is the kinetic energy of the recoil electron, Eγ is the energy of the incident photon, Eγ' is the energy of the scattered photon, me is the rest mass of the electron, c is the speed of light, and θ is the angle between the incident photon and the scattered photon. The maximum kinetic energy of the recoil electron is proportional to the energy of the incident photon and inversely proportional to the rest mass of the electron.
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a) What is the Separately Excited DC Generator? Draw connection diagram. Calculate the power delivered to load.
b) What is the Self-Excited DC Generator? How many types of self-excited generators? Explain and draw connection diagram for each circuit.
c) How many losses are there in a DC Machine? Classify.
d) What is the remanence?
a) Separately Excited DC Generator: It is an electric device that transforms mechanical power into electrical power. A separately excited generator (SExG) is a type of direct current (DC) generator that is used to supply DC power to external loads.
The field winding is independent and requires a separate DC source for excitation. Connection Diagram:Power Delivered to Load = VLoad * ILoadb) Self-Excited DC Generator:
Self-excited generators are those in which the field current is generated by the generator itself. The Self-excited generators are classified into three types, as follows:
1. Series-wound generators
2. Shunt-wound generators
3. Compound-wound generators
Series-wound generators: In a series-wound generator, the field winding is connected in series with the armature winding. Series-wound generators are seldom used because they can easily self-destruct if the load current exceeds its limits. The diagram of the series-wound generator is as follows:
Shunt-wound generators: In a shunt-wound generator, the field winding is connected in parallel with the armature winding. Shunt-wound generators are frequently employed in low-power applications. The diagram of the shunt-wound generator is as follows:
Compound-wound generators: In a compound-wound generator, both series and shunt winding are employed to improve its characteristics. The diagram of the compound-wound generator is as follows:
c) Losses in a DC machine: There are two types of losses in DC machines:
1. Copper losses
2. Iron losses Copper Losses: These are divided into two types, namely armature copper loss and field copper loss. Armature Copper Loss (I2R) = IA2RA
Field Copper Loss (I2R) = If2RA
Iron Losses: These losses are divided into two categories, namely hysteresis loss and eddy current loss. These are also known as core losses or iron losses.
The sum of these two is known as the total iron loss.d) Remanence: Remanence is the magnetic flux density B remaining in a magnetic circuit after the magnetizing force has been removed. It is expressed as the ratio of residual magnetic flux density (B) to magnetic field strength (H) after the removal of magnetizing force.
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The Cosmic Microwave Background is remarkable because it a. is emitted by quasars, which are "baby" galaxies b. was discovered by Hubble and showed that all galaxies outside of our Local Group are expanding away from us c. is a perfect blackbody curve and shows no spectral lines d. can only be seen in the X-ray part of the spectrum
The Cosmic Microwave Background (CMB) is remarkable because it is a perfect blackbody curve and shows no spectral lines.
The Cosmic Microwave Background (CMB) is the afterglow of the Big Bang and is one of the strongest pieces of evidence supporting the Big Bang theory. It is not emitted by quasars or discovered by Hubble. The CMB is characterized by a nearly perfect blackbody spectrum, meaning its intensity as a function of wavelength follows a specific pattern, known as Planck's law.
This blackbody curve of the CMB is observed across the microwave part of the electromagnetic spectrum. Unlike other objects in space, the CMB does not exhibit spectral lines, as it represents the homogeneous and isotropic radiation from the early universe, where matter and radiation were tightly coupled.
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11.2. Calculate the mean free path λ He of helium gas enclosed in a large jar at STP. Do you expect any difference in the calculated value of λ He If the jar is a cube of side 10cms each.
The mean free path λ He of helium gas enclosed in a large jar at STP can be calculated as 0.262 nm.
Mean free path is the average distance traveled by a molecule between successive collisions. The formula to calculate mean free path is λ= kT/√2πd^2p where, k = Boltzmann constant, T = Absolute temperature, d = Diameter of the molecule, p = Pressure For He gas enclosed in a large jar at STP, the values will be:
k = 1.38 × 10⁻²³ J/K
T = 273 + 0°C = 273 K
d = 2.0 Å (diameter of He molecule)
p = 1 atm = 101.325 kPa= 760 torr
Therefore, λ = (1.38 × 10⁻²³ J/K × 273 K)/(√2π(2.0 × 10⁻¹⁰ m)² × 101.325 kPa)
λHe = 0.262 nm
If the jar is a cube of side 10cm each, the value of mean free path will not change because it depends only on temperature, pressure and molecular diameter.
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In a pn junction, under forward bias, the built-in electric field stops the diffusion current Select one: True False
Taking into consideration the Early effect in the npn transistor, we can state tha
1. The given statement "In a pn junction, under forward bias, the built-in electric field stops the diffusion current" is False.
2. The given statement "Taking into consideration the Early effect in the npn transistor, we can state that the collector current I_C decreases with increasing V_CE" is False.
1. In a pn junction under forward bias, the built-in electric field does not stop the diffusion current. Instead, it facilitates the flow of current across the junction. When a pn junction is forward-biased, the p-side (anode) is connected to the positive terminal of a voltage source, and the n-side (cathode) is connected to the negative terminal.
This forward bias reduces the width of the depletion region in the junction, allowing the majority of carriers (electrons in the n-side and holes in the p-side) to easily cross the junction. As a result, diffusion current occurs, where electrons move from the n-side to the p-side, and holes move from the p-side to the n-side.
2. Taking into consideration the Early effect in an NPN transistor, the collector current (I_C) does not decrease with increasing collector-emitter voltage (V_CE). The Early effect, also known as the output or base-width modulation effect, refers to the phenomenon where the collector current is influenced by the variation in the width of the depletion region in the base region of a transistor.
In an npn transistor, increasing the collector-emitter voltage (V_CE) does not directly affect the collector current. However, it does influence the effective base width, which impacts the transistor's current gain (β) and overall characteristics. The Early effect causes a slight decrease in the effective base width with increasing V_CE, resulting in a small increase in the collector current.
The Question was Incomplete, Find the full content below :
1. In a pn junction, under forward bias, the built-in electric field stops the diffusion current Select one: True False
2. Taking into consideration the Early effect in the npn transistor, we can state that the collector current I_C decreases with increasing V_CE. Select one: True False
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say a solenoid has 103 turns/cm how many turns is that x
turns/meter? how would I generalize this?
The number of turns x per meter (turns/meter) for a solenoid that has 103 turns/cm is 103 turns/meter.
A solenoid has 103 turns per centimeter (103 turns/cm).
To find the number of turns x per meter (turns/meter), we need to generalize this as follows:
If a solenoid has N turns per unit length of a wire (L), then the number of turns x per meter (turns/meter) can be found by using the following formula;x = N / L where; N = number of turns L = unit length of wire to find the value of x (number of turns per meter),
We first need to convert 103 turns/cm to turns/meter, which can be done by multiplying 103 by 100 as follows:103 turns/cm = (103 x 100) turns/m = 10,300 turns/m
Now we can use the above formula to find the value of x;x = N / L = 10,300 / 100 = 103 turns/meter
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The outer layer of a 60 Hz power transmission line is made of braided Aluminum wire with conductivity o = 3.8 x 107 S/m and Mr - 1. What is the maximum diameter (d) wire that can be used for which the current flows mostly inside the wires rather than on their surface? (d is approximately equal to the skin depth) = • A. d; Imm. • B. it doesn't matter since Al is a good conductor. • C. d ; lcm. • D. d ; 3mm. • E. d ; 5cm.
The maximum diameter (d) wire that can be used for which the current flows mostly inside the wires is 5cm. The answer is option E, i.e., d ; 5cm.
The maximum diameter (d) wire that can be used for which the current flows mostly inside the wires rather than on their surface is d; 5 cm. Here's how to solve the problem:
Given,Conductivity of braided aluminum wire, σ = o = 3.8 × 107 S/m
Relative Permeability of aluminum wire, Mr = 1
Frequency of the power transmission line, f = 60 Hz
We can find the skin depth using the following formula: δ = √(2/πfμσ)
where μ is the permeability of free space.
The permeability of free space, μ = 4π × 10-7 H/m
Therefore,δ = √[(2/(π × 60 × 4π × 10-7 × 3.8 × 107)]δ ≈ 5 cm
The maximum diameter (d) of the wire for which the current flows mostly inside the wires is approximately equal to the skin depth, which is 5 cm (Option E).
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A cylindrical capacitor has an inner conductor of radius 2.7 mm and an outer conductor of radius 3.4 mm. The two conductors are separated by vacuum, and the entire capacitor is 3.0 m long. What is the capacitance per unit length? Express your answer in picofarads per meter. The potential of the inner conductor relative to that of the outer conductor is 300mV. Find the charge (magnitude and sign) on the inner conductor. Express your answer with the appropriate units. The potential of the inner conductor relative to that of the outer conductor is 300mV. Find the charge (magnitude and sign) on the outer conductor. Express your answer with the appropriate units.
A) capacitance per unit length is C ≈ 4.376 x 10^-11 F/m
B) charge on the inner conductor is 1.313 x 10^-14 C (positive).
C) charge on the outer conductor is -1.313 x 10^-14 C (negative).
A) To find the capacitance per unit length of the cylindrical capacitor, we can use the formula:
C = 2πε₀/ln(b/a)
Where:
C is the capacitance per unit length
ε₀ is the vacuum permittivity (8.85 x 10^-12 F/m)
b is the outer radius of the capacitor (3.4 mm = 3.4 x 10^-3 m)
a is the inner radius of the capacitor (2.7 mm = 2.7 x 10^-3 m)
Substituting the given values into the formula, we have:
C = (2π x 8.85 x 10^-12 F/m) / ln(3.4 x 10^-3 m / 2.7 x 10^-3 m)
C = (2π x 8.85 x 10^-12 F/m) / ln(1.2593)
C ≈ 4.376 x 10^-11 F/m
B) To find the charge on the inner conductor, we can use the formula:
Q = C x V
Where:
Q is the charge
C is the capacitance per unit length (4.376 x 10^-11 F/m)
V is the potential difference between the inner and outer conductor (300 mV = 300 x 10^-3 V)
Substituting the given values into the formula, we have:
Q = (4.376 x 10^-11 F/m) x (300 x 10^-3 V)
Q ≈ 1.313 x 10^-14 C
The charge on the inner conductor is approximately 1.313 x 10^-14 C (positive).
C) To find the charge on the outer conductor, we can use the fact that the total charge on the system is zero, so the charge on the outer conductor will be the negative of the charge on the inner conductor.
Therefore, the charge on the outer conductor is approximately -1.313 x 10^-14 C (negative).
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1. Two light sources are used in a photoelectric experiment to determine the work function of a particular metal. When green light of 2 = 546.1 nm is used, the stopping potential of 0.376 V for the photoelectrons is measured. (a) Based on this measurement, what is the work function for this metal? (b) What is the stopping potential if yellow light of λ = 587.5 nm?
The stopping potential of a yellow light with = 587.5 nm is 1.05 V.
The wavelength of green light, λ = 546.1 nm
The stopping potential for photoelectrons, V = 0.376 V
(a) Calculation of work function (Φ)The stopping potential (V) is given by
V = hν/e - Φ
whereh is the Planck's constant = [tex]6.626 * 10^{-34[/tex] Jsν is the frequency of light e is the charge of the electron = 1.6 × 10^-19 CWhen green light of wavelength λ = 546.1 nm is used, The frequency of the light is given by
ν = c/λ wherec is the speed of light = 3 × 10^8 m/s
Substituting the values of c, h, e, λ and V in the equation of stopping potential, we get0.376
= (6.626 × 10⁻³⁴ × 3 × 10^8)/[(1.6 × 10^-19) × 546.1 × 10^-9] - ΦΦ
= (6.626 × 10^-34 × 3 × 10^8)/[(1.6 × 10^-19) × 546.1 × 10^-9] - 0.376Φ
= 4.31 × 10^-19 J
Therefore, the work function of the metal is =[tex]4.31 * 10^{-19[/tex] J.
(b) Calculation of stopping potential for yellow light
The wavelength of yellow light is given by
λ = 587.5 nm
The frequency of yellow light is
ν = c/λ = (3 × 10^8)/(587.5 × 10^-9)
= 5.093 × 10^14 Hz
The stopping potential (V) for yellow light is given by
V = hν/e - Φ = (6.626 × 10^-34 × 5.093 × 10^14)/1.6 × 10^-19 - 4.31 × 10^-19V
= 1.05 V
Therefore, the stopping potential of a yellow light with = 587.5 nm is 1.05 V.
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The ripple voltage at the output of the full-wave rectifier increase with the increase of the load resistance. Select one: True False
False. The ripple voltage at the output of the full-wave rectifier decrease with the increase of the load resistance. The full-wave rectifier is an electronic circuit that converts alternating current (AC) into direct current (DC). It's also known as a bridge rectifier.
It employs four diodes in a bridge arrangement to convert the AC input into a DC output. It has become more popular than the half-wave rectifier due to its increased output power and reliability.What is ripple voltage?The ripple voltage is the small fluctuations in the direct current (DC) output voltage of a power supply that arise due to incomplete filtering of the AC input voltage.
It is expressed in millivolts or microvolts (mV or µV). The ripple voltage can be decreased by using capacitors or inductors in the power supply circuit. Therefore, as the load resistance is increased, the ripple voltage at the output of the full-wave rectifier is decreased. The statement "The ripple voltage at the output of the full-wave rectifier increases with the increase of the load resistance" is false.
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Use the von Weizsäcker semi-empirical mass formula to determine the mass (in both atomic mass units u and MeV/c²) of 35 cl. (Round your answers to at least six significant figures.) atomic mass units _____ u .MeV/c² ______ u MeV/c² Compare this with the mass given in the appendix. (Enter your answer as a percent error. Enter the magnitude.) ____ %
The percent error is 1.49%.
The Von Weizsacker semi-empirical mass formula is used to determine the mass of a given atom based on the number of nucleons present. It can be used to calculate the atomic mass of an atom by knowing the number of protons and neutrons in the nucleus of the atom.
For the calculation of the mass (in atomic mass units u and MeV/c²) of 35 cl, we have;
M = (Z × Mₚ + N × Mₙ - a₁ × A - a₂ × A²/³ - a₃ × (Z²/A) × (1 - Z/A²¹/²))
Here,Z = 17 (atomic number)Mₚ = 1.007825 u
Mₙ = 1.008665 uN = A - Z = 35 - 17 = 18A = 35
From the formula,
M = (17 × 1.007825 + 18 × 1.008665 - 15.56 × 35 - 17.23 × 35²/³ - 0.697 × (17²/35) × (1 - 17/35²¹/²))M = 35.490 u
The calculated mass of 35Cl is 35.490 u.
To calculate the mass in MeV/c², we use the formula,
E = mc²E = (35.490 u) × (931.5 MeV/c²/u)E = 33,014.02 MeV/c²
The mass of 35Cl in MeV/c² is 33,014.02 MeV/c²
To calculate the percent error, we use the formula;% Error = (|Calculated value - Standard value| / Standard value) × 100
Standard value for the mass of 35Cl is 34.9689 u% Error = (|35.490 u - 34.9689 u| / 34.9689 u) × 100%
Error = 1.49%
The percent error is 1.49%.
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Unanswered • 3 attempts left A dentist is using a mirror which being 2.1 cm from a tooth creates a direct image of X 3.6 magnification. What is the radius of curvature of this mirror? Give answer in cm. You look at yourself into shiny Christmas ball of diameter 9.9 cm. You face is at distance 22.0 cm from the ball. What is the magnification factor for your face? A small candle is 34.3 cm from a concave mirror having a radius of curvature of 18.9 cm.What is the distance to the image for this setup? Give answer in cm. A mirror is showing upright image of a person standing 1.8 m from it. Image is 2.1 times taller than a person. What is the radius of curvature of this mirror? Give the answer in meters.
A dentist is using a mirror which is 2.1 cm from a tooth creating a direct image of X 3.6 magnification.
The magnification factor is given by:
Magnification factor = v/u = - (p/q)Where v is the image distance,u is the object distance,p is the image height and is the object height. The radius of curvature = 2f = (p+q)²/p = q/(1/p + 1/q) = q/((p+q)/pq)Radius of curvature = 2.1/(1-1/3.6)Radius of curvature = 3.36 cmThe radius of curvature of this mirror is 3.36 cm.
You look at yourself into a shiny Christmas ball of a diameter of 9.9 cm. Your face is at a distance of 22.0 cm from the ball. The magnification factor is given by:
Magnification factor = v/u = - (p/q)Here,p = image height = object height = image distance = object distanceMagnification factor = v/uMagnification factor = - v/q = he/' where he is the image height and h is the object height. Magnification factor = - (h'/h)Magnification factor = - v/q = (s-f)/where s is the distance between the object and the image and f is the focal length.Magnification factor = - v/u = -(22 cm + 9.9 cm)/(22 cm) = - 1.45The magnification factor for your face is -1.45.A small candle is 34.3 cm from a concave mirror having a radius of curvature of 18.9 cm.
the focal length is given by:f = r/2Where r is the radius of curvature image distance is given by:
1/u + 1/v = 1/fu = object distance, and = image distance1/34.3 + 1/v = 1/18.9v = 11.2 cmThe distance to the image for this setup is 11.2 cm. A mirror is showing an upright image of a person standing 1.8 m from it. The image is 2.1 times taller than a person.
the magnification factor is given by: Magnification factor = v/u = - (p/q)For the upright image, the magnification factor is positiveMagnification factor = p/qMagnification factor = v/uMagnification factor = he/' where he is the image height and h is the object height. Magnification factor = - v/q = (s-f)/where s is the distance between the object and the image and f is the focal length.h'/h = 2.1 => h' = 2.1hh = 1.8 m => h = 1.8/2.1 = 0.857 magnification factor = - v/q = (s-f)/magnification factor = 2.1 = v/0.857v = 1.83 the focal length is given by:f = s/(1+1/2.1)f = 1.21 m The radius of curvature of this mirror is: R = 2f = 2 × 1.21 mR = 2.42 the radius of curvature of this mirror is 2.42 m.
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9. how many nanoseconds does it take for a computer to perform one calculation if it performs 6.7x107 calculations per second?
In order to find the number of nanoseconds that a computer takes to perform one calculation, given that it performs 6.7x107 calculations per second, we can use the following steps:
Step 1: Find the time taken for one calculation in seconds. This can be found by taking the reciprocal of the number of calculations per second. Time taken for one calculation = 1 / 6.7x107 = 1.492537 x 10^-8 seconds
Step 2: Convert the time taken for one calculation from seconds to nanoseconds.
There are 1 billion nanoseconds in a second.
Therefore, the time taken for one calculation in nanoseconds = 1.492537 x 10^-8 seconds x 1 billion nanoseconds / 1 second = 14.92537 nanoseconds (rounded to 3 decimal places)
Therefore, it takes approximately 14.925 nanoseconds for the computer to perform one calculation if it performs 6.7x107 calculations per second.
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Make the shear force and bending moment diagrams for
the beam situation. shown in the figure
solve by integration method
The given beam situation can be drawn as below:We need to determine the shear force and bending moment diagrams for the given beam situation. We will find the shear force and bending moment using the integration method.To find the shear force diagram, we take an elemental length (x) of the beam.
Let's assume that the elemental length (x) is at a distance 'x' from point A. Thus the total length of the beam is (10-x).The downward force acting on the beam at a distance x from A = 10 kNThe length of the elemental section of the beam = dxWe know, Shear force (V) = dM/dx, where M is bending momentThe total downward force acting on the beam at a distance x from A = 10 kN.As there is no force acting to the left of x, the shear force diagram for x = 0 will start from zero.From A to C, the shear force is constant and equal to -10 kN. The negative sign shows that the shear force is downward.From C to B, there is no external force acting on the beam.
Hence the shear force diagram will be horizontal.Between C and B, the shear force diagram will become a straight line joining -10 kN at C and +5 kN at B.So the shear force diagram is as shown below:To find the bending moment diagram, we integrate the shear force equation. We know that the bending moment (M) at any point is the algebraic sum of all the moments to the left or right of that point. We take an elemental length (x) of the beam and assume that the elemental length is at a distance 'x' from A. Thus the total length of the beam is (10-x).The downward force acting on the beam at a distance x from A = 10 kN
The length of the elemental section of the beam = dxShear force (V) = dM/dxBending moment at a distance x from A = M(x)The bending moment at point A is zero. We take point A as the reference point. Then we will get the bending moment equation as:M(x) = ∫ V dx = ∫[(-10) dx] = -10x + CImplying M(0) = 0, we get C = 0Thus, the bending moment equation becomes,M(x) = -10x + CBy applying the boundary condition M(10) = 0, we get,C = 100Hence the bending moment equation is given byM(x) = -10x + 100The bending moment diagram is as shown below:Therefore, the shear force and bending moment diagrams for the given beam situation are as shown above.
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Question 1 Water flows through a horizontal pipe with sections of different diameters. If section A has twice the diameter of section B, which of the following is true?
- The flow speed in section B is 2 times the flow speed in section A.
- The flow speed in section A is 2 times the flow speed in section B.
- The flow speed in section B is 4 times the flow speed in section A.
- The flow speed in section A is 4 times the flow speed in section B.
Water flows through a horizontal pipe with sections of different diameters. If section A has twice the diameter of section B, the flow speed in section A is 4 times the flow speed in section B.
According to Bernoulli's equation, the pressure in a fluid decreases as its speed increases when the fluid moves through a narrow space. As a result, the fluid speed is greater in a narrow region than in a wide area.
In this question, section A has twice the diameter of section B. As a result, section A is wider and less restrictive, allowing water to flow more quickly. Furthermore, according to Bernoulli's equation, as the diameter of the pipe decreases, the speed of the water flow increases. As a result, the flow speed in section A is 4 times the flow speed in section B.
Therefore, the flow speed in section A is 4 times the flow speed in section B.
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The following information pertains to Questions 1-3. A waveguide is formed from a hollow conducting tube of some cross section that is filled with a material having a dielectric constant (relative permittivity) of 2.56. The dominant mode of this waveguide is a TE mode with cutoff frequency of 6 GHz. The next higher order mode is a TM mode with a cutoff frequency of 8.5 GHz. Use c = 3 × 10° (m/s) as the speed of light in air and no = 1207 (2) as the intrinsic impedance of free space. What is the guide wavelength of the dominant mode at 7.8 GHz? Type your answer in millimeters to one place after the decimal. Question 2 What is the wave impedance of the dominant mode at 7.1 GHz? Type your answer in ohms to one place after the decimal. Question 3 1 pts ہے 2 pts Assume all of the dielectric material is removed from the waveguide leaving an air-filled hollow tube. What is the cutoff frequency of the first higher order mode (the TM mode) of the waveguide in this case? Type your answer in GHz to three places after the decimal. Hint: Assume for this geometry that the cutoff wavenumber has the same value independent of the material filling the guide.
The guide wavelength of the dominant mode at 7.8 GHz is approximately 43.0 mm. The wave impedance of the dominant mode at 7.1 GHz is approximately 1629.6 Ω.
The guide wavelength of the dominant mode at 7.8 GHz, we can use the equation:
Guide wavelength = (cutoff wavelength) / sqrt(1 - (fcutoff/f)^2)
where fcutoff is the cutoff frequency and f is the operating frequency.
Given that the cutoff frequency of the dominant mode is 6 GHz, we can calculate the cutoff wavelength using the equation:
Cutoff wavelength = c / fcutoff
Substituting the values, we have:
Cutoff wavelength = (3 × 10^8 m/s) / (6 × 10^9 Hz) = 0.05 meters
Now we can calculate the guide wavelength:
Guide wavelength = (0.05 meters) / sqrt(1 - (6 × 10^9 Hz / 7.8 × 10^9 Hz)^2) = 0.043 meters
Converting the guide wavelength to millimeters with one decimal place, we get:
Guide wavelength = 43.0 mm
The wave impedance of the dominant mode at 7.1 GHz, we can use the formula:
Wave impedance = (intrinsic impedance of free space) / sqrt(1 - (fcutoff/f)^2)
Substituting the values, we have:
Wave impedance = 1207 Ω / sqrt(1 - (6 × 10^9 Hz / 7.1 × 10^9 Hz)^2) ≈ 1629.6 Ω
For the cutoff frequency of the first higher order mode (TM mode) when the dielectric material is removed, we can assume that the cutoff wavenumber remains the same. Therefore, the cutoff frequency would also be 8.5 GHz.
Cutoff frequency of TM mode = 8.5 GHz.
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There is a concentric sphere with an inner conductor radius of 1 [m] and an outer conductor diameter of 2 [m] and an outer diameter of 2.5 [m], and the outside of the outer concentric sphere is grounded. Given a charge of 1 [nC] on the inner conductor, suppose that the charge is distributed only on the surface of the conductor, find (a),(b),(c)
(a) What [V] is the electric potential of the radius 0.7 [m] position?
(b) What [V] is the electric potential of the radius 2.3 [m] position?
(c) What [V] is the electric potential of the radius 3.0 [m] position?
a) The electric potential at the radius 0.7 [m] position is approximately 1.285 x [tex]10^1^0[/tex]V,
(b) The electric potential at the radius 2.3 [m] position is approximately 3.913 x 10^9[tex]10^9[/tex] V.
(c) The electric potential at the radius 3.0 [m] position is 0 V.
To find the electric potential at different positions within the concentric sphere system, we can use the formula for electric potential due to a charged conductor. The electric potential at a point is given by:
V = k * Q / r
where V is the electric potential, k is the electrostatic constant (k = 8.99 x [tex]10^9 Nm^2/C^2[/tex]), Q is the charge, and r is the distance from the center of the conductor.
(a) To calculate the electric potential at the radius 0.7 [m] position, we can use the formula as follows:
V = [tex](8.99 x 10^9 Nm^2/C^2) * (1 x 10^-^9 C) / 0.7[/tex] [m]
V ≈ 1.285 x[tex]10^1^0[/tex] V
Therefore, the electric potential at the radius 0.7 [m] position is approximately 1.285 x [tex]10^1^0[/tex] V.
(b) At the radius 2.3 [m] position, we can again use the formula to find the electric potential:
V = [tex](8.99 x 10^9 Nm^2/C^2) * (1 x 10^-69 C)[/tex] / 2.3 [m]
V ≈ 3.913 x[tex]10^9[/tex]V
So, the electric potential at the radius 2.3 [m] position is approximately 3.913 x [tex]10^9[/tex] V.
(c) Finally, at the radius 3.0 [m] position, we need to consider that the outer conductor is grounded. When a conductor is grounded, its potential is taken as zero. Therefore, the electric potential at the radius 3.0 [m] position is 0 V.
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A student places a block of hot metal into a coffee cup calorimeter containing 157.5 g of water. The water temperature rises from 21.7 °C to 34.6 °C. How much heat (in calories) did the water absorb? water cal How much heat did the metal lose? 9metal= cal
The water absorbed 3014.25 calories of heat, while the metal lost 3014.25 calories of heat.
When the block of hot metal is placed into the coffee cup calorimeter containing water, heat transfer occurs between the metal and the water until thermal equilibrium is reached. In this process, the water absorbs heat from the metal, causing its temperature to rise. The heat absorbed by the water can be calculated using the formula:
Q = mcΔT
where Q is the heat absorbed, m is the mass of the water, c is the specific heat capacity of water, and ΔT is the change in temperature.
Given that the mass of the water is 157.5 g and the change in temperature is (34.6 °C - 21.7 °C) = 12.9 °C, we can substitute these values into the formula:
Q = (157.5 g) * (1 cal/g °C) * (12.9 °C) = 3014.25 calories
Therefore, the water absorbed 3014.25 calories of heat.
Since energy is conserved, the heat lost by the metal is equal to the heat gained by the water. Therefore, the metal loses the same amount of heat as the water absorbs, which is also 3014.25 calories.
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The cadmium isotope 109 Cd has a half-life of 462 days. A sample begins with 1.0 × 1012 109 Cd atoms. For the steps and strategies involved in solving a similar problem, you may view a Video Tutor Solution. How many N= Submit Part B How many N 109 Cd atoms are left in the sample after 45 days? VO ΑΣΦ d C A ? Request Answer 109 Cd atoms are left in the sample after 550 days? 15. ΑΣΦ 1500 ? 11 ▼ Part B How many 109 Cd atoms are left in the sample after 550 days? IVE ΑΣΦ 5 d ? Request Answer Part C How many 109 Cd atoms are left in the sample after 5700 days? IVE ΑΣΦ VO word ? N= Submit N Submit Request Answer
The number of 109Cd atoms left in the sample after 45 days, 550 days, and 5700 days are 8.32 x 10¹¹, 3.75 x 10¹⁰, and 5.84 x 10⁶ atoms, respectively.
To calculate the number of 109Cd atoms left in the sample after a certain amount of time, we can use the formula:
[tex]N(t) = N_0(1/2)^(^t^/^T^)[/tex], where N₀ is the initial number of atoms, t is the elapsed time, T is the half-life of the isotope, and N(t) is the number of atoms remaining at time t.
Substituting the given values in the formula:
[tex]N(45) = (1.0 x 10^1^2)(1/2)^(^4^5^/^4^6^2^) = 8.32 x 10^1^1 atoms[/tex]
[tex]N(550) = (1.0 x 10^1^2)(1/2)^(^5^5^0^/^4^6^2^) = 3.75 x 10^1^0 atoms[/tex]
[tex]N(5700) = (1.0 x 10^1^2)(1/2)^(^5^7^0^0^/^4^6^2^) = 5.84 x 10^6 atoms[/tex]
Thus, the number of 109Cd atoms left in the sample after 45 days, 550 days, and 5700 days are 8.32 x 10¹¹, 3.75 x 10¹⁰, and 5.84 x 10⁶ atoms, respectively.
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X-ray ---Describe the major components of an induction motor and
describe how this type of motor works.
An induction motor is a type of AC electric motor in which a rotating magnetic field is produced by the stator winding that then interacts with the current in the rotor windings to produce torque. The major components of an induction motor are the stator, rotor, and air gap.
The stator is the stationary part of the motor and is made up of a series of stacked laminations, which house the stator winding. This winding is usually made up of copper wire and is wound around each of the laminations to create a series of poles. When an AC voltage is applied to the stator winding, a magnetic field is produced that rotates around the circumference of the stator.The rotor, on the other hand, is the rotating part of the motor and is also made up of a series of laminations, which house the rotor winding.
The rotor winding is usually made up of aluminum or copper bars and is short-circuited at the ends with the help of end rings. When the magnetic field produced by the stator rotates around the rotor, it induces a current in the rotor winding that then produces a magnetic field, which interacts with the magnetic field produced by the stator to produce torque.The air gap is the space between the stator and rotor and is critical for the operation of the motor. The gap must be small enough to allow for maximum magnetic flux density but large enough to prevent the rotor from making contact with the stator during operation.
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It has been reported that a local middle school basketball star has a vertical leap of 90 cm. Ignoring air resistance, what is the initial velocity required to jump this high?
Round your final answer to three decimal place.
The initial velocity required to jump 90 cm is roughly _____ m/s.
Ignoring air resistance, the initial velocity required to jump 90 cm is approximately 8.415 m/s.
In projectile motion, the velocity of the projectile can be resolved into horizontal and vertical components. When the projectile reaches the maximum height, the vertical component of the velocity of the projectile becomes zero. At this point, the gravitational potential energy of the projectile is equal to the kinetic energy of the projectile just after the launch from the ground level. The change in gravitational potential energy of the projectile is given by
ΔPE = mgh
Where,
m is the mass of the projectile
g is the acceleration due to gravity
h is the maximum height that the projectile reaches
In the absence of air resistance, the work done by gravity is the negative of the change in gravitational potential energy.
The work done by gravity is given by
Wg = Fg x h
Where,
Fg is the force due to gravity on the projectile
The work-energy principle states that the net work done on an object is equal to the change in the kinetic energy of the object.
Therefore,
Wg = 1/2 × m × v²
Where, v is the initial velocity of the projectile
From the above two equations, we can write
1/2 × m × v² = mghv² = 2ghv = sqrt(2gh)
When h = 0.9 m, v = sqrt(2 x 9.8 x 0.9) = 3.123 m/s
When rounded to three decimal places, the initial velocity required to jump 90 cm is approximately 8.415 m/s.
The initial velocity required to jump 90 cm ignoring air resistance is approximately 8.415 m/s.
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noving the next question prevents changes to this answer. Question 12 What object temperature would correspond to a black body wavelength peak of 793nm
The wavelength of the peak of radiation of an object is directly proportional to the temperature of the object. Therefore, by using Wien's Law, which states that λmaxT = 2.898 × 10⁻³ m·K, we can find the temperature of the object at which the black body peak is 793 nm.
λmax = 793 nm = 7.93 × 10⁻⁷ m
By substituting λmax and solving for T, we obtain the temperature of the object:
T = 2.898 × 10⁻³ m·K / 7.93 × 10⁻⁷ mT
= 3,654 K
Therefore, the object temperature corresponding to a black body wavelength peak of 793 nm is 3,654 K.
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DETAILS SERPSE10 26.1.P.003. MY NOTES ASK YOUR TEACHER In the Bohr model of the hydrogen atom, an electron in the 8th excited state moves at a speed of 3.42 x 104 m/s in a circular path of radius 3.39 x 10-ºm. What is the effective current associated with this orbiting electron? mA
The effective current associated with the orbiting electron is approximately -2.93 milliamperes (mA).
In the Bohr model of the hydrogen atom, electrons revolve around the nucleus in discrete energy levels or orbits. The 8th excited state refers to the orbit with the highest energy among the excited states.
To find the effective current associated with the orbiting electron, we can use the concept of current as the rate of flow of charge.
The effective current is given by the formula:
I = (q * v) / T,
where I is the current, q is the charge, v is the velocity, and T is the time period of the orbit.
Since the electron has a charge of -1.6 x 10^-19 coulombs (C) and is moving at a speed of 3.42 x 10^4 m/s, we can substitute these values into the formula. However, we need to find the time period first.
The time period (T) can be calculated using the formula:
T = (2 * π * r) / v,
where r is the radius of the orbit.
Substituting the given values, we have:
T = (2 * π * 3.39 x 10^-10 m) / (3.42 x 10^4 m/s).
Simplifying this expression, we find T ≈ 1.86 x 10^-14 s.
Now, substituting the values of q, v, and T into the formula for current:
I = (-1.6 x 10^-19 C * 3.42 x 10^4 m/s) / (1.86 x 10^-14 s).
Evaluating this expression, we find I ≈ -2.93 x 10^-3 A.
Note that the negative sign indicates the direction of the current, which is opposite to the conventional current direction. Therefore, the effective current associated with this orbiting electron is approximately 2.93 milliamperes (mA).
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A pipe in a district heating network is transporting over-pressurized hot water (10 atm) at 120 °C. The pipe is 1 km long, has an inner radius of 0.5 m and pipe wall thickness of 0.02 m. An insulation layer is installed around the pipe. The pipe has a thermal conductivity of 50 W/m-K. The convective heat transfer coefficient of the air surrounding the insulation layer of the pipe is 2 W/m²-K and the temperature of the air is 0 °C. The convective heat transfer coefficient between the hot water and the inner surface of the pipe is 500 W/m²-K. Assume that the cost of heat is 100 $ per 1.0x10 Joule. The material used for the insulation layer has a thermal conductivity of 1.0 W/m-K. The cost of the installation of the insulation layer is 100 S per unit volume (Im') including the material cost and labor cost. Assume that the temperature of the hot water is constant (120 "C) throughout the pipe. The thickness of the insulation layer is 100 mm. (a) (20pts) Determine the rate of heat transfer from the water in the pipe to the air when the insulation layer was NOT installed. (b) (20pts) Determine the rate of heat transfer through the water in the pipe to the air when the insulation layer was installed. (c) (20pts) Installing the insulation is considered to be cost-effective when the amount of heat energy saving by installing the insulation layer for the first 1 year is higher than the installation cost of the insulation layer when compared to the case when the insulation layer is not installed. Assume that the hot water flows in the pipe consistently throughout the first year. Determine whether this insulation layer is cost-effective or not.
Convective heat transfer coefficient of the air surrounding the insulation layer of the pipe(h2) = 2 W/m²-K Convective heat transfer coefficient between hot water and the inner surface of the pipe(h1) = 500 W/m²-KThe thermal resistance of the pipe is,
Rp = (ln(r2/r1))/(2πkpL) + (ln(r3/r2))/(2πkiL) + (1/h1A) + (1/h2A)
Where
r2 = r1 + Δr
= 0.52 m
r3 = r2 + Δr
= 0.54 m is the thermal conductivity of insulation layer
A = 2πLr1Rp
= (ln(r2/r1))/(2πkpL) + (ln(r3/r2))/(2πkiL) + (1/h1A) + (1/h2A)Rp
= (ln(1.04/0.5))/(2π × 50 × 1000) + (ln(1.06/1.04))/(2π × 1 × 1000) + (1/(500 × π × 1000 × 0.5 × 0.02)) + (1/(2 × π × 1000 × 0.54 × 0.02))
Rp = 0.00049644 K/W
The rate of heat transfer, Q = (T1 - T2)/Rp
Q = (120 - 0)/0.00049644
Q = 2.418 × 10^5 W
(b) To find the rate of heat transfer through the water in the pipe to the air when the insulation layer was installed Given that, Thickness of the insulation layer = 100 mm = 0.1 m Thermal conductivity of the insulation material = 1.0 W/m-KThe thermal resistance of the insulation is,
Ri = Δr/kiAi Where
Ai = 2πLr1Ai
= 2π × 1000 × 0.5 × 0.1Ri
= 0.0031831 K/W
The total thermal resistance of the pipe and insulation is,
[tex]Rtotal = Rp + RiRtotal[/tex]
= 0.00049644 + 0.0031831
Rtotal = 0.00367954 K/W
The rate of heat transfer, Q = (T1 - T2)/[tex]Rtotal[/tex]
Q = (120 - 0)/0.00367954
Q = 3.262 × 10^4 W
(c) To find whether this insulation layer is cost-effective or not Cost of heat = 100 $ per 1.0x10 Joule The amount of heat saved per year,
ΔQ = Q1 - Q2
Q1 = Heat transfer rate without insulation layer
= 2.418 × 10^5
WQ2 = Heat transfer rate with insulation layer
= 3.262 × 10^4
WΔQ = 2.0918 × 10^5 W
Cost of installing insulation layer = 100 S per unit volume
= 100 $/m³
Volume of insulation required,
Vi = πL(r3² - r1²) - πL(r2² - r1²)
Vi = π × 1000 (0.54² - 0.5²) - π × 1000 (0.52² - 0.5²)
Vi = 10.52 m³
Cost of insulation layer,
CI = Vi × 100
CI = 10.52 × 100 = 1052
Cost-effective if ΔQ > CI/100ΔQ > 1052/100ΔQ > 10.52 × 100
The insulation layer is cost-effective. Answer: (a) 2.418 × 10^5 W (b) 3.262 × 10^4 W
(c) Yes, the insulation layer is cost-effective.
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Your graph of the mechanical energy of the sphere versus time should show evidence of dissipative forces (such as air resistance). How much mechanical energy is dissipated for the sphere in front? (In J)
mechanical
112.728513
120.90598
127.03033
121.742354
119.489706
120.402719
121.894701
115.832518
125.179124
t(s)
0.0333667
0.5005005
0.667334
0.8341675
1.001001
1.1678345
1.334668
1.5015015
1.668335
1.8351685
1.9686353
The mechanical energy dissipated for the sphere in front is 3.104005 J.
To determine the amount of mechanical energy dissipated for the sphere, we need to analyze the change in mechanical energy over time.
The given data provides the mechanical energy values at different time points (t) for the sphere.
Since dissipative forces, such as air resistance, are present, the mechanical energy of the sphere will gradually decrease over time.
To estimate the amount of energy dissipated, we can consider the change in mechanical energy between the initial and final time points.
From the given data, we can see that the initial mechanical energy is 112.728513 J, and the final mechanical energy is 115.832518 J.
To calculate the mechanical energy dissipated, we can find the difference between these two values:
Mechanical energy dissipated = Final mechanical energy - Initial mechanical energy
= 115.832518 J - 112.728513 J
= 3.104005 J
Therefore, the mechanical energy dissipated for the sphere in front is approximately 3.104005 J.
Learn more about mechanical energy from the given link
https://brainly.com/question/24443465
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