If the integral is
[tex]\displaystyle \int \frac{\ln(3x^2)}{x^5}\,\mathrm dx[/tex]
substitute u = ln(3x ²) and du = 6x/(3x ²) dx = 2/x dx.
Then x ² = exp(u)/3 and x ⁴ = exp(2u)/9.
The integral is transformed to
[tex]\displaystyle \int \frac{\ln(3x^2)}{x^5}\,\mathrm dx = \int \frac{\ln(3x^2)}{2x^4} \times \dfrac2x \,\mathrm dx \\\\ = \int \frac{u}{2\times\dfrac{e^{2u}}9}\,\mathrm du \\\\ = \frac92 \int ue^{-2u}\,\mathrm du[/tex]
Integrate by parts:
[tex]f = u \implies \mathrm df = \mathrm du \\\\ \mathrm dg = e^{-2u}\,\mathrm du \implies g = -\dfrac12 e^{-2u}[/tex]
[tex]\displaystyle \int ue^{-2u}\,\mathrm du = fg - \int g\,\mathrm df \\\\ = -\dfrac12 ue^{-2u} + \displaystyle \frac12 \int e^{-2u}\,\mathrm du \\\\ = -\frac12 ue^{-2u} - \frac14 e^{-2u} + C[/tex]
Then
[tex]\displaystyle \frac92 \int ue^{-2u}\,\mathrm du = -\frac94 ue^{-2u} - \frac98 e^{-2u} + C[/tex]
which in terms of x would be
[tex]\displaystyle \int \frac{\ln(3x^2)}{x^5}\,\mathrm dx = -\frac94\times\frac{\ln(3x^2)}{9x^4} - \frac98 \times \frac1{9x^4} + C \\\\ = \boxed{-\frac{\ln(3x^2)}{4x^4}-\frac1{8x^4}+C}[/tex]
A piece of coaxial cable has 75ohms Characteristics impedance and a nominal capacitance of 69pF/m. what is its inductance per meter ? If the diameter of the inner conductor is 0.584mm, and the dielectric constant of the insulation is 2.23, what is the outer diameter of the conductor ?
Answer:
A) L = 0.388 μm
B) D = 3.78 mm
Explanation:
We are given;
Characteristics impedance; Z_o = 75 ohms
Nominal capacitance; C = 69pF/m = 69 × 10^(-12) F/m
dielectric constant; k = 2.23
Inner diameter of conductor; d = 0.584 mm
A) Now formula for Characteristics impedance is given as;
Z_o = √(L/C)
Where L is the inductance per metre.
Making L the subject, we have;
L = (Z_o)²C
L = 75² × 69 × 10^(-12)
L = 0.388 × 10^(-6) m
L = 0.388 μm
B) To get the outer diameter, we will use the formula;
Z_o = (138/√k) log(D/d)
Where;
D is outer diameter.
Thus, Plugging in the relevant values;
75 = (138/√2.23) × log (D/0.584)
log (D/0.584) = 0.81158611538
(D/0.584) = 10^(0.81158611538)
D/0.584 = 6.48016576435
D = 6.48016576435 × 0.584
D = 3.78 mm
Karl and Susan have agreed to come to our party, _______ has made Maria very happy. that which what who
Answer:
that
I am not sure that this is the answer
but i hopethis will help you
Karl and Susan agreed to come to our party, which made Maria very happy. The correct option is b.
What are relative pronouns?Relative pronouns are words that are used to show the relation between two statements. Who/whom, whoever/whomever, whose, that, and which are the most common relative pronouns. "what," "when," and "where" might operate as relative pronouns.
Relative pronouns introduce dependent sentences called relative clauses. Happy is an emotion that is non-living things and with non-living things, which is used.
The relative pronouns "which" and "that" begin adjective clauses. Both provide additional information about the noun they follow.
Therefore, the correct option is b, which. Karl and Susan agreed to come to our party, which made Maria very happy.
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On the inner surface of the cylinder, the third principal stress is not zero. The third principal stress acts in the radial direction. Determine the third principal stress. Include the proper sign for your value.
Answer:
σ1, σ2 and σ3.
Explanation:
The three principal stresses are labelled or written as σ1, σ2 and σ3. The σ1 is the maximum principal stress or most tensile stress, σ2 is the intermediate principal stress and σ3 is the minimum or most compressive principal stress. Principal stresses are the maximum and minimum extensional stresses present in an object. The principal directions have no shear stresses connected with them.
Two engineers are to solve an actual heat transfer problem in a manufacturing facility. Engineer A makes the necessary simplifying assumptions and solves the problem analytically, while engineer B solves it numerically using a powerful software package. Engineer A claims he solved the problem exactly and, thus, his results are better, while engineer B claims that he used a more realistic model and, thus, his results are better. Will the experiments prove engineer B right
Answer:
Engineer A results will be more accurate
Explanation:
Analytical method is better than numerical method. Engineer A has used analytical method and therefore his results will be more accurate because he used simplified method. Engineer B has used software to solve the problem related to heat transfer his results will be approximate.
Wave flow of an incompressible fluid into a solid surface follows a sinusoidal pattern. Flow is two-dimensional with the x-axis normal to the surface and y axis along the wall. The x component of the flow follows the pattern
u = Ax sin (2πt/T)
Determine the y-component of flow (v) and the convective and local components of the acceleration vector.
Answer:
sorry , for my point
Explanation:
Apart from the type of emergency, what factors affect the decision on weather to evacuate or shelter in place?
Answer:
. 1. Type of building
2. Location of emergency
3. Extent of emergency
Explanation:
1. The kind of building in which people find themselves could be a factor that can be used to make this decision. a lot of buildings can be easily affected by disasters such as explosions or tornadoes the extent of the effect is dependent on how the building is constructed. in some situations it is better to shelter in, while in others it is best to evacuate.
2. Another factor to be considered is the location or area where this is happening it is good to consider this so that people can be safely moved given that help can be easily accessed or if best to stay in.
3. The last is the extent of what is happening. The risk involved is one way of making the choice to evacuate or to stay.
The factors that affect the decision on whether to evacuate or shelter in place include:
Type of building.Location of emergency.Extent of emergencyIt should be noted that the building where an individual lives play a vital role during emergencies. Buildings that have poor foundations can easily be affected during emergencies.
Another factor that should be considered is the location where the emergency is taking place. Lastly, the extent of the emergency can determine if the person should stay or not.
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Doubling the diameter of a solid, cylindrical wire doubles its strength in tension.
True
False
Answer:
True ❤️
-Solid by solid can make Cylindrical wire doubles Strengths in tension
A gas tank is known to have a thickness of 0.5 inches and an internal pressure of 2.2 ksi. Assuming that the maximum allowable shear stress in the tank wall is 12 ksi, determine the necessary outer diameter for the tank. Assume that the tank is made of a cold drawn steel whose elastic modulus is 35000 ksi and whose Poisson ratio is 0.292. If y
Answer:
[tex]D_o=11.9inch[/tex]
Explanation:
From the question we are told that:
Thickness [tex]T=0.5[/tex]
Internal Pressure[tex]P=2.2Ksi[/tex]
Shear stress [tex]\sigma=12ksi[/tex]
Elastic modulus [tex]\gamma= 35000[/tex]
Generally the equation for shear stress is mathematically given by
[tex]\sigma=\frac{P*r_1}{2*t}[/tex]
Where
r_i=internal Radius
Therefore
[tex]12=\frac{2.2*r_1}{2*0.5}[/tex]
[tex]r_i=5.45[/tex]
Generally
[tex]r_o=r_1+t[/tex]
[tex]r_o=5.45+0.5[/tex]
[tex]r_o=5.95[/tex]
Generally the equation for outer diameter is mathematically given by
[tex]D_o=2r_o[/tex]
[tex]D_o=11.9inch[/tex]
Therefore
Assuming that the thin cylinder is subjected to integral Pressure
Outer Diameter is
[tex]D_o=11.9inch[/tex]
A rod that was originally 100-cm-long experiences a strain of 82%. What is the new length of the rod?
122 cm
182 cm
82 cm
22 cm
108.2 cm
Answer:
The new length of the rod is 182 cm.
Explanation:
Given that a rod that was originally 100-cm-long experiences a strain of 82%, to determine what is the new length of the rod, the following calculation must be performed:
100 x 1.82 = X
182 = X
Therefore, the new length of the rod is 182 cm.
EnQueue(X): Thêm phần tử X vào Queue
DeQueue() : Lấy 1 phần tử ra khỏi Queue
Hãy cho biết phần tử ở đầu của Queue có giá trị bằng bao nhiêu sau khi thực hiện lần lượt các phép toán sau:
EnQueue(1); EnQueue(2); DeQueue(); EnQueue(3);
EnQueue(4); DeQueue(); DeQueue();
Calculate the minimum area moment of inertia for a rectangular cross-section with side lengths 6 cm and 4 cm.
Answer:
Minimum area of rectangle = 24 cm²
Explanation:
Given:
Length of rectangle = 6 cm
Width of rectangle = 4 cm
Find:
Minimum area of rectangle
Computation:
Area of rectangle = Length of rectangle x Width of rectangle
Minimum area of rectangle = Length of rectangle x Width of rectangle
Minimum area of rectangle = 6 x 4
Minimum area of rectangle = 24 cm²
How would you describe what would happen to methane if the primary bonds were to break?
Answer:
All the bonds in methane (CH4CH4) are equivalent, and all have the same dissociation energy.
The product of the dissociation is methyl radical (CH3CH3). All the bonds in methyl radical are equivalent, and all have the same dissociation energy.
The product of that dissociation is methylene (CH2CH2). All the bonds in methylene are equivalent, and all have the same dissociation energy.
The product of that dissociation is methyne (CHCH) .
The C-H bonds in methane do not have the same dissociation energy as C-H bonds in methyl radical, which in turn do not have the same dissociation energy as the C-H bonds in methylene, which are again different from the C-H bond in methyne.
If (by some miracle) you were able to get all four bonds in methane to dissociate absolutely simultaneously, they would all show the same dissociation energy… but that energy, per bond broken, would be different than the energy required to break just one C-H bond in methane, because the products are different.
(In this case, it’s CH4→C+4HCH4→C+4H versus CH4→CH3+HCH4→CH3+H.)
To alter hydrocarbons you add enough energy to break a C-H bond. Why does only one bond break? What concentrates the energy on one C-H bond?
the weakest CH bond is the one that breaks. in plain alkanes it has to do with the molecular orbital interactions between neighboring carbon atoms. look at propane for example. the middle carbon has two C-C bonds, and each of those C-C bonds is strengthened by slight electron delocalization from the C-H bonds overlapping with the antibonding orbitals of the adjacent carbons.
since the C-H bonds on the middle carbon donate electron density to both of its neighbors, those two are weakest.
one of them will break preferentially.
which one actually breaks depends on the reaction conditions (kinetics). frankly it's whichever one ramdomly approaches a nucleophile first. when the nucleophile pulls of one of the H's, the other C-H bonds start to share (delocalize) the negative charge across the whole molecule. so while the middle C feels the majority of the negative charge character, the other two C's take on a fair amount as well...
by the way, alkanes don't really like to break and form anions like that.
a better example would be something like isopropyl iodide, where the C-I bond breaks and the I carries away the electron pair, forming a carbocation (also not particularly stable, but more so than the carbanion).
A investor will invest in mutual fundwith a probability of 0.6, will invest in government fundwith a probability of 0.3, and will invest in both fundswith a probability of 0.15. Find the probability that the investor will invest in either mutual fundor government fund.
Answer:
0.75
Explanation:
From this question above we have the following information
A = probability of investment in mutual fund= 0.6
B = probability of investment in government fund = 0.3
C = probability of investing in both the mutual fund and the government= 0.15
Where to find the probability of this investor investing in either of these two
= Prob(a) + prob(b) - prob(c)
= 0.6 + 0.3 - 0.15
= 0.9 - 0.15
= 0.75
If a cylindrical part with a length of 20 mm and a diameter of 20 mm is to be machined to a cylindrical part with 18 mm in diameter with the same length. The machine has a mechanical efficiency of 50% and a power of 80 kW. If the cutting rake angle is 0 degrees and the cutting tool is made of uncoated carbides and the cutting speed is 10 m/s. What material can we choose for the cylinder
Answer:
Titanium Alloy
Explanation:
Length ( L ) = 20 mm
D1 = 20 mm
d2 = 18 mm
l = 20 mm
Mechanical efficiency = 50%
power = 80 kW
cutting rake angle = 0°
cutting speed ( v ) = 10 m/s
Determine the material to be for the cylinder
In order to choose a material for the cylinder we have to calculate the cutting force
P = Fc * V
80 = Fc * 10 m/s
therefore Fc = 80 / 10 = 8 N
Hence the material we can use is Titanium Alloy due to low cutting force value
Which of the following would make a column more likely to buckle?
Increase its ultimate compressive strength
Increase its length
Increase its Young’s modulus
Increase its cross-sectional area
Increase its area moment of inertia
True or false: Increasing a material’s ultimate compressive strength makes it less likely to crush under its own weight (assuming all other things equal).
True
False
True or false: The area moment of inertia of an object only depends on its shape, not its size.
True
False
Answer:
1) B: Increase its length
2) True
3) True
Explanation:
1) Columns are compressive members and are subjected to primarily compressive stresses.
Now, there is what we call slender Ness ratio in columns which is basically used to check the ability of a column to resist buckling.
The formula is;
Slenderness ratio = Effective length of column/radius of gyration
Thus, the longer the column the more the Slenderness ratio and the more likely it is to buckle.
Thus, increasing the length is what makes columns likely buckle.
2) Compressive strength is the ability of a material to withstand loads that may reduce size or make the material crush under load.
Now, increasing the compressive strength simply means more ability to withstand loads that may lead to crushing under load.
Ultimate compressive strength is the maximum amount of compressive stress that a material can take before it crushes under load. Thus, increasing the ultimate compressive strength means it is less likely to crush under its own weight.
3) There are different factors that affect moment of inertia and they are;
- the mass of the body
- axis of rotation of the body
- shape and size of the body.
However, for area moment of inertia, what is most relevant to us is the shape of the body in question since we are dealing with area and not how big it is.
in plumbing what is a video snake used for
Answer:
How to stop toilets
Explanation:
I think
Hope this helps
zener shunt regulator employs a 9.1-V zener diode for which VZ = 9.1 V at IZ = 9 mA, with rz = 40 and IZK= 0.5 mA. The available supply voltage of 15 V can varyas much as ±10%. For this diode, what is the value of VZ0?For a nominal load resistance RL of 1 k and a nominal zenercurrent of 10 mA,what current must flow in the supply resistorR? For the nominal value of supply voltage, select a valuefor resistor R, specified to one significant digit, to provideat least that current. What nominal output voltage results?For a ±10% change in the supply voltage, what variationin output voltage results? If the load current is reduced by50%, what increase in VO results? What is the smallest valueof load resistance that can be tolerated while maintainingregulation when the supply voltage is low? What is the lowestpossible output voltage that results? Calculate values for theline regulation and for the load regulation for this circuit usingthe numerical results obtained in this problem.
Answer:
[tex]V_z=9.1v[/tex]
[tex]V_{zo}=8.74V[/tex]
[tex]I=10mA[/tex]
[tex]R=589 ohms[/tex]
Explanation:
From the question we are told that:
Zener diode Voltage [tex]V_z=9.1-V[/tex]
Zener diode Current [tex]I_z=9 .A[/tex]
Note
[tex]rz = 40\\\\IZK= 0.5 mA[/tex]
Supply Voltage [tex]V_s=15[/tex]
Reduction Percentage [tex]P_r= 50 \%[/tex]
Generally the equation for Kirchhoff's Voltage Law is mathematically given by
[tex]V_z=V_{zo}+I_zr_z[/tex]
[tex]9.1=V_{z0}+9*10^{-3}(40)[/tex]
[tex]V_{zo}=8.74V[/tex]
Therefore
[tex]At I_z-10mA[/tex]
[tex]V_z=V_{z0}+I_zr_z[/tex]
[tex]V_z=8.74+(10*10^{-3}) (40)[/tex]
[tex]V_z=9.1v[/tex]
Generally the equation for Kirchhoff's Current Law is mathematically given by
[tex]-I+I_z+I_l=0[/tex]
[tex]I=10mA+\frac{V_z}{R_l}[/tex]
[tex]I=10mA+\frac{9.1}{0}[/tex]
[tex]I=10mA[/tex]
Therefore
[tex]R=\frac{15V-V_z}{I}[/tex]
[tex]R=\frac{15-9.1}{10*10^{-3}}[/tex]
[tex]R=589 ohms[/tex]
Air enters a diffuser operating at steady state at 540°R, 15 lbf/in.2, with a velocity of 600 ft/s, and exits with a velocity of 60 ft/s. The ratio of the exit area to the inlet area is 8. Assume that The air is the ideal gas model for the air and ignoring heat transfer, determine
Answer: Hello the question is incomplete below is the missing part
Question: determine the temperature, in °R, at the exit
answer:
T2= 569.62°R
Explanation:
T1 = 540°R
V2 = 600 ft/s
V1 = 60 ft/s
h1 = 129.0613 ( value gotten from Ideal gas property-air table )
first step : calculate the value of h2 using the equation below
assuming no work is done ( potential energy is ignored )
h2 = [ h1 + ( V2^2 - V1^2 ) / 2 ] * 1 / 32.2 * 1 / 778
∴ h2 = 136.17 Btu/Ibm
From Table A-17
we will apply interpolation
attached below is the remaining part of the solution
Please help me:
Use the Node analysis to find the power of all resistors
c. Assuming a fixed-priority scheduling. Consider two tasks to be executed periodically on a single processor, where task 1 has period p= 4 and task 2 has period p= 6.
If execution time of task I be e;=1
Find the maximum value for the execution time e2 of task 2 such that the Rate Monotonic (RM) schedule is feasible.
Answer:
hi hello tata byebye nice
As per the given data, the maximum value of e2 such that the RM schedule is feasible is 0.985.
What is fixed-priority scheduling?Fixed-priority scheduling is a scheduling algorithm used in real-time operating systems to assign priorities to tasks based on their relative importance or urgency.
In a fixed-priority scheduling algorithm, tasks with higher priority are assigned shorter periods.
Since task 1 has a period of 4 and task 2 has a period of 6, we can assume that task 1 has a higher priority than task 2. Therefore, we can apply the Rate Monotonic (RM) scheduling algorithm.
The RM scheduling algorithm states that a feasible schedule exists if the following condition is satisfied:
Σ (ei / pi) ≤ n(2^(1/n)-1)
Where Σ (ei / pi) is the sum of the ratio of execution time to period for all tasks, n is the total number of tasks, and the base of the exponential function is 2.
In this case, we have two tasks, so n = 2. We know that e1 = 1 and p1 = 4. For task 2, we need to find the maximum value of e2 such that the schedule is feasible. Therefore, we can set e2 = x and p2 = 6.
Substituting the values into the RM scheduling formula, we get
(e1/p1) + (e2/p2) ≤ 2^(1/2) - 1
(1/4) + (x/6) ≤ 0.4142
Multiplying both sides by 12, we get:
3 + 2x ≤ 4.97
2x ≤ 1.97
x ≤ 0.985
Therefore, the maximum value of e2 such that the RM schedule is feasible is 0.985.
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A force measuring instrument comes with a certificate of calibration that identifies two instrument errors and assigns each an uncertainty at 95% confidence over its range. Provide an estimate of the instrument design-stage uncertainty.
Resolution: 0.25 N
Range: 0 to 100 N
Linearity error: within 0.20 N over range
Hysteresis error: within 0.30 N over range
Answer:
[tex]U=\pm 0.382N[/tex]
Explanation:
From the question we are told that:
Resolution: 0.25 N
Range: 0 to 100 N
Linearity error: within 0.20 N over range
Hysteresis error: within 0.30 N over range
Generally the equation for Stage Uncertainty is mathematically given by
[tex]U=\sqrt{u_0^2+u_T^2}[/tex]
Where
[tex]u_0=Zero\ order\ uncertainty[/tex]
[tex]u_0=\pm 0.5*0.25[/tex]
[tex]u_0=\pm=0.125[/tex]
And
u_T=Total instrumental Uncertainty
[tex]u_T=\sqrt{l_e^2+h_e^2}[/tex]
Where
l_e=Error of linearity
h_e=Error due to hysteresis
Hence
[tex]u_T=\sqrt{0.20^2+0.30^2}[/tex]
[tex]u_T=\pm 0.36[/tex]
Therefore
[tex]U=\sqrt{(0.125)^2+0.36^2}[/tex]
[tex]U=\pm 0.382N[/tex]
If an elevator repairer observes that cables begin to fray after 15 years, what process might he or she use to create a maintenance schedule for their replacement? fallacious reasoning reductive reasoning inductive reasoning deductive reasoning
Answer:
inductive reasoning
Explanation:
Inductive reasoning is one of the type of reasoning method in which generalized consequences are derived from limited observations. By observing few data, general conclusions are drawn. The conclusions drawn are false in inductive reasoning. In the given situation, the conclusion drawn by the elevator repairer has been drawn by inductive reasoning. His observation of some cables led him to draw the conclusion about all the cables. The result of the reasoning is false.
Block A hangs by a cord from spring balance D and is submerged in a liquid C contained in beaker B. The mass of the beaker is 1.20 kg; the mass of the liquid is 1.85 kg. Balance D reads 3.10 kg and balance E reads 7.50 kg. The volume of block A is 4.15 × 10−3 m3.
a) What is the density of the liquid?
b) What will the balance D read if block A is pulled up out of the liquid?
c) What will the balance E read if block A is pulled up out of the liquid?
Answer:
a) [tex]m_e= 3.05 Kg[/tex]
b) [tex]\rho=1072.3kg/m^3[/tex]
c) [tex]m_e= 3.05 Kg[/tex]
Explanation:
From the question we are told that:
Beaker Mass [tex]m_b=1.20[/tex]
Liquid Mass [tex]m_l=1.85[/tex]
Balance D:
Mass [tex]m_d=3.10[/tex]
Balance E:
Mass [tex]m_e=7.50[/tex]
Volume [tex]v=4.15*10^{-3}m^3[/tex]
a)
Generally the equation for Liquid's density is mathematically given by
[tex]m_e=m_b+m_l+(\rho*v)[/tex]
[tex]\rho=\frac{7.50-(1.2+1.85)}{4.15*10^{-3}}[/tex]
[tex]\rho=1072.3kg/m^3[/tex]
b)
Generally the equation for D's Reading at A pulled is mathematically given by
m_d = mass of block - mass of liquid displaced
[tex]m_d=m- (\rho *v )[/tex]
[tex]m=3.10+ (1072.30 *4.15*10^{-3}m^3 )[/tex]
[tex]m=18.10kg[/tex]
c)
Generally the equation for E's Reading at A pulled is mathematically given by
[tex]m_e=m_b+m_l[/tex]
[tex]m_e = 1.20 + 1.85[/tex]
[tex]m_e= 3.05 Kg[/tex]
In heavy traffic areas you should wave pedestrians across the street if there is no crosswalk
In heavy traffic areas, you should wave pedestrians across the street if there is no crosswalk: False.
What is a crosswalk?A crosswalk can be defined as the marked or specially paved part of a road that is characterized by heavy traffic, so as to enable pedestrians have right of way to cross the street because drivers are required by traffic law to stop for them.
However, a driver or other road users in heavy traffic areas shouldn't wave pedestrians across the street if there is no crosswalk
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For an applied transformer with a primary winding of 220, a secondary winding of 113 turns, a core of 45 cm2 cross-section and a rated supply voltage of 220 V, frequency f = 50 Hz, number system Core style K = 1,2.
one. Calculated from the sensor in the core transformer.
NS. Calculate the rated capacity of the transformer application.
C. Calculating no-load voltage and current levels.
NS. If the power point is reduced by 7% from the voltage level; voltage scortation feature.
e. If use the core machine variable on random form; powerpress same as the host variable on; compare the capacity of the random transformer with the capacity of the transformer application.
Explanation:
https://www.chegg.com/homework-help/questions-and-answers/iron-core-wish-design-transformer-part-dc-power-supply-moderately-high-current-rating-volt-q53186459?trackid=83dbc34cec2e&strackid=3efc9f324415
Make a sketch of a simple mechanically expanded brake and indicate the forces acting on the leading shoe when the brake is applied.
a system is linear if it has
A system is a linear system if all equations inside the system can be simplified into the form,
[tex]y=mx+n[/tex]
aka linear form of a linear equation.
So to sum up, a system is linear if all equations are linear equations.
Hope this helps :)
Alternating current lesson 4 exam
An unconstrained 10mm thick plate of steel 100mm on a side with a 25mm diameter hole in the center is heated from 20 degrees C to 120 degrees C. The linear CTE is 12x10-6/⁰C. What is the final diameter of the hole
Answer:
The correct answer is "25.03 mm".
Explanation:
Given:
Thickness of plate,
= 10 mm
On a side,
= 100 mm
Diameter hole,
= 25 mm
Coefficient of thermal expansion,
CTE = [tex]12\times 10^{-6} /^{\circ} C[/tex]
Now,
⇒ [tex]D_i\times (12\times 10^{-6}) \Delta \theta = \Delta D[/tex]
= [tex]25\times 12\times 10^{-6} \Delta \theta[/tex]
= [tex]3\times 10^{-4} \Delta \theta[/tex]
= [tex]3\times 10^{-2}[/tex]
hence,
The final diameter of hole will be:
[tex]D_f=25.03 \ mm[/tex]
A moving-coil instrument, which gives full-scale deflection with 0.015 A has a copper coil having resistance of 1.5 Ohm at 15°C and a temperature coefficient of 1/234.5 at 0 degree C in series with a swamp resistance 3.5 Ohm having a negligible temperature coefficient. Determine the resistance of shunt required for a full-scale deflection of 20 A and the resistant required for a full-scale deflection of 250 V. If the instrument reads correctly at 15°C, determine the percentage error in each case when the temperature is 25°C.
Answer: check answers in pictures (2 p)
The resistance of the shunt required for a full-scale deflection of 20 A is 2.528 Ohm.
What is resistance?Resistance is a measure of an electrical circuit's resistance to current flow. Resistance is measured in ohms, which is represented by the Greek letter omega.
Full-scale deflection current = 0.015 A
Full-scale deflection current for 20 A = 20/0.015 = 1333.33 times full-scale deflection current
The current through the meter coil is given by:
Ic = Im * (Rm / (Rm + Rs))
At full scale, Ic = 1333.33 * 0.015 A = 20 A, Rm = 1.5 Ohm, and Rs = 3.5 Ohm.
Therefore:
20 A = Im * (1.5 Ohm / (1.5 Ohm + 3.5 Ohm))
Im = 20 A * (3.5 Ohm / 5 Ohm)
Im = 14 A
The current through the shunt resistor is therefore:
Ish = Im - Ic
Ish = 14 A - 20 A
Ish = -6 A
Since the shunt resistor is in parallel with the meter, its resistance can be calculated using the following formula:
Rs = Rm * (Im / Ish - 1)
Substituting the values, we get:
3.5 Ohm = 1.5 Ohm * (14 A / (-6 A) - 1)
3.5 Ohm = 1.5 Ohm * (-1.333 - 1)
3.5 Ohm = 1.5 Ohm * (-2.333)
Rs = 1.5 Ohm * (14 A / (-6 A) - 1) / (-2.333)
Rs = 2.528 Ohm
Therefore, the resistance of the shunt required for a full-scale deflection of 20 A is 2.528 Ohm.
Now, let's find the resistance required for a full-scale deflection of 250 V:
Full-scale deflection current = 0.015 A
Resistance required for full-scale deflection of 250 V = 250 V / 0.015 A
Resistance required for full-scale deflection of 250 V = 16666.67 Ohm
This resistance is in parallel with the meter coil, so the total resistance in the circuit will be:
Rtotal = Rm || Rext
Rtotal = (Rm * Rext) / (Rm + Rext)
Substituting the values, we get:
Rtotal = (1.5 Ohm * 16666.67 Ohm) / (1.5 Ohm + 16666.67 Ohm)
Rtotal = 1.43 Ohm
This resistance is in series with the meter coil, so the total resistance in the circuit will be:
Rtotal = Rm + Rext + Rs
Substituting the values we get:
1.43 Ohm = 1.5 Ohm + 16666.67 Ohm + Rs
Rs = 1.43 Ohm - 1.5 Ohm - 16666.67 Ohm
Rs = -16666.74 Ohm
Thus, the calculated value of Rs is negative, it means that the shunt resistor must be used instead of a series resistor to achieve a full-scale deflection of 250 V.
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