A sinusoidal voltage source has a peak voltage of 12 V and a frequency of 50 Hz. What is the voltage at 10 ms?

Answers

Answer 1

Answer:

0

Explanation:

Given that:

The peak of the voltage [tex]V_{peak}[/tex] = 12 V

The frequency f = 50 Hz

At the time t  = 10 ms

[tex]V = V_p \ sin \ \omega t[/tex]

where;

[tex]\omega = 2 \pi f[/tex]

[tex]V = 1 2\ V \times sin \ ( 2 \pi \times 50 \times 10 \ )[/tex]

V = 12V sin (180)

V = 12 V × 0

V = 0


Related Questions

Calculate the LER for the rectangular wing from the previous question if the weight of the glider is 0.0500 Newton’s.

Answers

Answer:

0.2

Explanation:

Since the span and chord of the rectangular wing is missing, due to it being from the other question, permit me to improvise, or assume them. While you go ahead and substitute the ones from your question to it, as it's both basically the same method.

Let the span of the rectangular wing be 0.225 m

Let the chord of the rectangular wing be 0.045 m.

Then, the area of any rectangular chord is

A = chord * span

A = 0.045 * 0.225

A = 0.010 m²

And using the weight of the glider given to us from the question, we can find the LER for the wing.

LER = Area / weight.

LER = 0.010 / 0.05

LER = 0.2.

Therefore, using the values of the rectangular wing I adopted, and the weight of the glider given, we can see that the LER of the glider is 0.2

Please mark brainliest...

Answer: 0.2025

Explanation: I got it correct

Steam enters an adiabatic nozzle at 1 MPa, 250°C, and 30 m/s. At one point in the nozzle the enthalpy dropped 40 kJ/kg from its inlet value. Determine velocity at that point. (A) 31 m/s (B) 110 m/s (C) 250 m/s (D) 280 m/s

Answers

Answer:

284.4 m/s

Explanation:

At the inlet of the nozzle P =1 atm.

Temperature T = 250° C

Velocity of the steam at the inlet V_1 = 30 m/s

Change in enthalpy Δh = 40 KJ/kg

let V_2 be the final velocity

then

[tex]V_2 =\sqrt{2\Delta h+V_1^2} \\=\sqrt{2\times40+30^2}\\= 284.4 m/s[/tex]

4. The instant the ignition switch is turned to the start position,

A. The starter motor starts to rotate before energizing the starter p

O B. Only the pull-in winding is energized.

C. Only the hold-in winding is energized.

D. Both pull-in and hold-in windings are energized.

Answers

Answer:

D. Both pull-in and hold-in windings are energized.

Explanation:

The instant the ignition switch is turned to the start position, "Both pull-in and hold-in windings are energized." This is because the moment the ignition switch is turned to the start position, voltage passes through to the S terminal of the solenoid.

The hold-in winding is attached to the case of the solenoid. Similarly, the pull-in winding is also attached to the starter motor. Thereby, the current will move across both windings by getting energized to generate a strong magnetic field.

Which of these words was first used during the 1970s economic crisis?
influx
stagflation
deficit
programs

Answers

Answer:

stagflation

Explanation:

it was used in the article

A word which was first used during the 1970s economic crisis is stagflation.

The economic crisis of the 1970s.

In the 1970s, an energy crisis took place in the United States of America due to the oil embargo that was imposed on it by OPEC. This oil embargo was imposed on the United States of America by the Organization of Petroleum Exporting Countries (OPEC) in 1973 because of its role in the Arab-Israeli War.

Consequently, the economy of the United States of America experienced stagflation in the following ways:

Slow economic growth.Relatively high unemployment.

Read more on stagflation here: https://brainly.com/question/25505087

Laminar flow normally persists on a smooth flat plate until a critical Reynolds number value is reached. However, the flow can be tripped to a turbulent state by adding roughness to the leading edge of the plate. For a particular situation, experimental results show that the local heat transfer coefficients for laminar and turbulent conditions are

h_lam(x)= 1.74 W/m^1.5. Kx^-0.5
h_turb(x)= 3.98 W/m^1.8 Kx^-0.2

Calculate the average heat transfer coefficients for laminar and turbulent conditions for plates of length L = 0.1 m and 1 m.

Answers

Answer:

At L = 0.1 m

h⁻_lam = 11.004K   W/m^1.5

h⁻_turb = 7.8848K   W/m^1.8

At L = 1 m

h⁻_lam = 3.48K   W/m^1.5

h⁻_turb = 4.975K   W/m^1.8

Explanation:

Given that;

h_lam(x)= 1.74 W/m^1.5. Kx^-0.5

h_turb(x)= 3.98 W/m^1.8 Kx^-0.2

conditions for plates of length L = 0.1 m and 1 m

Now

Average heat transfer coefficient is expressed as;

h⁻ = 1/L ₀∫^L hxdx

so for Laminar flow

h_lam(x)= 1.74 . Kx^-0.5  W/m^1.5

from the expression

h⁻_lam = 1/L ₀∫^L 1.74 . Kx^-0.5   dx

= 1.74k / L { [x^(-0.5+1)] / [-0.5 + 1 ]}₀^L

= 1.74k/L = [ (x^0.5)/0.5)]⁰^L

= 1.74K × L^0.5 / L × 0.5

h⁻_lam= 3.48KL^-0.5

For turbulent flow

h_turb(x)= 3.98. Kx^-0.2 W/m^1.8

form the expression

1/L ₀∫^L 3.98 . Kx^-0.2   dx

= 3.98k / L { [x^(-0.2+1)] / [-0.2 + 1 ]}₀^L

= (3.98K/L) × (L^0.8 / 0.8)

h⁻_turb = 4.975KL^-0.2

Now at L = 0.1 m

h⁻_lam = 3.48KL^-0.5  =  3.48K(0.1)^-0.5  W/m^1.5

h⁻_lam = 11.004K   W/m^1.5

h⁻_turb = 4.975KL^-0.2 = 4.975K(0.1)^-0.2

h⁻_turb = 7.8848K   W/m^1.8

At L = 1 m

h⁻_lam = 3.48KL^-0.5  =  3.48K(1)^-0.5  W/m^1.5

h⁻_lam = 3.48K   W/m^1.5

h⁻_turb = 4.975KL^-0.2 = 4.975K(1)^-0.2

h⁻_turb = 4.975K   W/m^1.8

Therefore

At L = 0.1 m

h⁻_lam = 11.004K   W/m^1.5

h⁻_turb = 7.8848K   W/m^1.8

At L = 1 m

h⁻_lam = 3.48K   W/m^1.5

h⁻_turb = 4.975K   W/m^1.8

Solar energy stored in large bodies of water, called solar ponds, is being used to generate electricity. If such a solar power plant has an efficiency of 4.5 percent and a net power output of 150 kW, determine the average value of the required solar energy collection rate, in Btu/h.

Answers

Answer: 1.137*10^7 Btu/h.

Explanation:

Given data:

Efficiency of the plant = 4.5percent

Net power output of the plant = 150kw

Solution:

The required collection rate

QH = W/n

= 150/0.045 * 0.94782/ 1 /60 */60 Btu/h.

= 3333.333 *3412.152Btu/h.

= 11373840 Btu/h

= 1.137*10^7 Btu/h.

draw afd,sfd and bmd of frame​

Answers

ok hahahhwjwkqowowlkwbwebekekoslslala

Answer:

uh, i dont understand?

Explanation:

It describes the physical and social elements common to this work. Note that common contexts are listed toward the top, and less common contexts are listed toward the bottom. According to O*NET, what are common work contexts for Construction Carpenters? Check all that apply. Spend time sitting wear common protective or safety equipment face-to-face discussions exposed to hazardous equipment spend time using hands to handle, control, or feel objects, tools, or controls public speaking

Answers

Answer:

bcde!!

Explanation:

They also tend to be traditional, which means that they enjoy working in structured environments and are typically organized and detail-oriented. Thus option B,C,D, E is correct.

What are the characteristics of Construction Carpenters?

Carpenters continue to have a bright future in their profession. According to Job Outlook, the carpentry industry is expanding quickly. The advantages of carpentry lead to employment security and a long-term career with this kind of industrial growth.

Carpentry is a physically demanding line of work that calls for endurance. You frequently spend the most of your shift standing, moving slowly, and crouching.

Therefore, As well as using hand tools to shape and cut wood, lifting big objects, moving heavy beams, furniture, or equipment are all possible.

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If the specific surface energy for soda–lime glass is 0.30 J/m2 and its modulus of elasticity is (69 GPa), compute the critical stress required for the propagation of an internal crack of length 0.8 mm.

Answers

Answer: the critical stress for the sodalime glass = 5.7MPa

Explanation:

Ist Step

we Calculate  half length   of internal crack as

2a =0.8 mm

a = 0.8/2 = 0.4 mm

Changing  to meters becomes = 0.4 / 1000 =0.0004m

2nd Step

Now  the critical stress required for the propagation of the internal crack can be calculated using the formulae

Critical Stress (σc) =      (2 E γs/ πa) 1/2

where E= modulus of elasticity

γs= specific surface energy for soda–lime glass

a= Length

= (2 x 69 x 10 ^9 x 0.30/ π x 0.0004)1/2

=[tex]\sqrt{ 32,940,802,036,919}[/tex]

= 5,739,407.8= 5.7 x 10^6 N/m^2

= 5.7MPa

(3 points) One end of a 48 cm long copper rod with a diameter of 2.0 cm is kept at 360 ° C, and the other is immersed in water at 32° C. Calculate the heat conduction rate along the rod. The thermal conductivity for copper is 386 MK​

Answers

Answer:

hi tommoro i have phisics exam i needd help only for 20 min how wants to help messege me instgram  meeraalk99

Explanation:

please

If ice homogeneously nucleates at -44.6°C, calculate the critical radius given values of -3.1 × 10^8 J/m3 and 25 × 10^-3 J/m^2, respectively, for the latent heat of fusion and the surface free energy.

Answers

Answer:the critical radius for the homogeneous nucleating ice is  0.986 nm

Explanation:

Using the formulae below to calculate the  critical radius for homogeneous nucleation,

We Have that

Critical radius ( r *) =  [2γ Tm/ΔHf]{ 1/ Tm- T]

where γ = surface free energy =25 × 10^-3 J/m^2

Tm= solidification temperature at equilibrium =273K

Hf= latent heat of fusion = -3.1 × 10^8 J/m3

Temperature , T = -44.6°C

Critical radius ( r *) = (2 X 25 × 10^-3 J/m^2 x 273)/ (-3.1 × 10^8 J/m3 ) X ( 1/ 273 - ( -44.6 +273)

4.40x 10^-8X ( 1/273-228.4)

4.40x 10^-8  X 1/44.6

4.40x 10^-8  x 0.0224

9.86x 10 ^-10m =0.986 x 10 ^-9m = 0.986nm

How would you expect an increase in the austenite grain size to affect the hardenability of a steel alloy? Why?

Answers

Answer:

The hardenability increases with increasing austenite grain size, because the grain boundary area is decreasing. This means that the sites for the nucleation of ferrite and pearlite are being reduced in number, with the result that these transformations are slowed down, and the hardenability is therefore increased.

For proper function hydraulics systems need a reservoir of which of the following?
A.) Compressible fluid
B.) Non-compressible fluid C.) Non-compressible air

Answers

A. Compressible fluid

Think of brake fluid on a vehicle, compressed as one applies the break= pressure to expand brake cylinders in the wheels which compress the pads on the wheel brake rotors.

Release brake and fluid relaxes back into the reservoir/accumulator.

In a CS amplifier, the resistance of the signal source Rsig = 100 kQ, amplifier input resistance (which is due to the biasing network) Rin = 100kQ, Cgs = 1 pF, Cgd = 0.2 pF, gm = 5 mA/V, ro = 25 kΩ, and RL = 20 kΩ. Determine the expected 3-dB cutoff frequency.

Answers

Answer:

406.140 KHz

Explanation:

Given data:

Rsig = 100 kΩ

Rin = 100kΩ

Cgs = 1 pF,

Cgd = 0.2 pF,  and   etc.

Determine the expected 3-dB cutoff frequency

first find the CM miller capacitance

CM = ( 1 + gm*ro || RL )( Cgd )

     = ( 1 + 5*10^-3 * 25 || 20 ) ( 0.2 )

     = ( 11.311 ) pF

now we apply open time constant method to determine the cutoff frequency

Th = 1 / Fh

hence : Fh = 1 / Th = [tex]\frac{1}{(Rsig +Rin) (Cm + Cgs )}[/tex]

                               = [tex]\frac{1}{( 200*10^3 ) ( 12.311 * 10^{-12} )}[/tex] =  406.140 KHz

A 13.7g sample of a compound exerts a pressure of 2.01atm in a 0.750L flask at 399K. What is the molar mass of the compound?a. 318 g/mol
b. 204 g/mol
c. 175 g/mol
d. 298 g/mol

Answers

Answer: Option D) 298 g/mol  is the correct answer

Explanation:

Given that;

Mass of sample m = 13.7 g

pressure P = 2.01 atm

Volume V = 0.750 L

Temperature T = 399 K

Now taking a look at the ideal gas equation

PV = nRT

we solve for n

n = PV/RT

now we substitute

n = (2.01 atm x 0.750 L) / (0.0821 L-atm/mol-K x 399 K )

= 1.5075 / 32.7579

= 0.04601 mol

we know that

molar mass of the compound = mass / moles

so

Molar Mass = 13.7 g / 0.04601 mol

= 297.7 g/mol  ≈ 298 g/mol

Therefore Option D) 298 g/mol  is the correct answer

The pressure at the bottom of an 18 ft deep storage tank for gasoline is how much greater than at the top? Express your answer in the units of psi.

Answers

5.85 psig

Using a specific gravity of 0.75 as an average for red\automobile gasoline.

Water at standard conditions (60 degF) is 2.31 feet = 1 psig

80/2.31 then multiply x .75 to compensate for specific gravity of water being 1.0

The pressure at the bottom of an 18 ft deep storage tank for gasoline is 5.625 psi.

What is pressure?

Pressure is defined as the force exerted on a surface's unit area. The mass of the air molecules above is what exerts pressure on the atmosphere. The enormous quantities of air molecules that make up the layers of our atmosphere collectively have a tremendous amount of weight, which bears down on whatever is below.

The storage tank's top pressure is 14.7 psi, or p atm, or 2116.8 lb/ft3.

Gasoline has a density of 45 lb/ft3.

Tank depth, h = 18 foot

The storage tank's bottom pressure is 2926.8 pounds per square foot (Pb = 2116.8 + 45 x 18).

As a result, the pressure difference between the tank's bottom and top is as follows: P = Pb - P atm = 20.325 - 14.7 = 5.625 psi

Thus, the pressure at the bottom of an 18 ft deep storage tank for gasoline is 5.625 psi

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Anyone help me please ?

Answers

Answer:

I can help but I need to know what it looking for

You are the project manager assigned to construct a new 10-story office building. You are trying to estimate the costs for this project. You start by assigning the costs associated with each of the project activity. Then you sum up all the individual costs into a final cost estimate. Which type of cost estimation technique did you use?

Answers

Answer:

Bottom-up Estimation

Explanation:

Bottom-up estimation is a type of project cost estimation that considers the cost of individual project activities and finally sums them up or finds the aggregates. The summation gives an idea of what the entire project will cost.

This is an effective way of estimating the cost of a project as it evaluates the costs on a wholistic basis. It also considers the tiniest details during the estimation process. The process moves from the simpler details to the more complicated details.

In which phase and for what purpose does a construction manager work with various consultants? In the [blank] phase, a construction manager works closely with architects, civil engineers, electrical engineers, and other consultants to prepare a [blank].

Choices for first [blank]
A. design and planning
B. Construction
C. Post construction

Choices for second [blank]
A. draft
B. Sketch
C. Blueprint

Answers

Answer:

a and c

Explanation:

An electric circuit is made up of a 100 m long manganin wire with a section of I mm^2; this wire constitutes 4/5 of the total resistance of the circuit itself and the intensity of the current circulating there is 2.5 A. Calculate the voltage applied to the terminals of the manganin wire, the energy dissipated on this wire in 30 minutes and the voltage applied by the generator across the circuit.​

Answers

Answer:

a.dont know e

Explanation:

because d q tlga ammu

Explain the difference between the connection of a cumulative compound and a differential compound motor

Answers

Answer:

Explanation:

A motor is a device that directs current in electrical energy form to mechanical energy, which is known as direct current (DC) motors.

DC motors are of three types: (a) The series motor, (b) The shunt motor, and (c) the compound motor. Our main focus here is the Compound motor, which is further sub-divided into:

i) The cumulative compound motors

ii) The differential compound motors

The difference between these two are:

Cumulative compound motors                  Differential compound motors

In cumulative compound motors,              In differential compound motors,

both the series and shunt windings          both series and shunt are

are connected in a way that,                     connected in a way that the

production of fluxes through them           production of fluxes via them

assist each other i.e. they aid each          always opposes each other i.e.

other in the production of magnetism      they oppose each other in the

                                                                    production of magnetism.

Calculate the Lee for the same wing if we increase the span to 0.245 m. By increasing the span we also increase the glider weight to 0.0523

Answers

Answer:

0.21

Explanation:

This would have been a fairly easy one, except for that the first part of the question is missing, and as such, I'd assume a value.

We need to use chord, so, I'm assuming the length of the chord to be 0.045 m

The Area is given by the formula

Area = span * chord

Area = 0.245 * 0.045

Area = 0.011 m²

This area gotten, is what we then divide the glider weight by to get our answer.

Lee = area / weight

Lee = 0.011 / 0.0523

Lee = 0.21

Therefore, using the values of the chord I'd assumed, the Lee of the same wing is 0.21

Answer: 0.2108

Explanation:got it correct

A magnesium–lead alloy of mass 7.5 kg consists of a solid α phase that has a composition just slightly below the solubility limit at 300°C.
(a) What mass of lead is in the alloy?
(b) If the alloy is heated to 400°C, how much more lead may be dissolved in the αα phase without exceeding the solubility limit of this phase?

Answers

Answer:

(a)This portion of the problem asks that we calculate, for a Pb-Mg alloy, the mass of lead in 7.5 kg of thesolidphase at 300C just below the solubility limit.From Figure 9.20, the solubility limit for thephase at

Explanation:

A MBR treatment plant has a flow of 0.3 mgd with 220 mg/l BOD (the soluble portion is 120 mg/l) and 230 mg/l suspended solids (184 mg/l is volatile). Effluent soluble BOD is 2 mg/l. The design calls for 5000 mg/l MLSS and sludge age of 20 days with a Y = 0.8, kd = 0.4. Calculate the aeration basin volume, detention time, BOD loading, ratio, and waste solids, both VSS and TSS.

Answers

Answer:

attached below is the detailed solution

A) 8288.77 cu.ft

B) 4.96 hours

C) Vss = 131.21 IbVss/day

   Tss = 164 IbTss/day

D) attached below

E ) 0.2

F) 287.23 Ib/day

Explanation:

A) Determine the aeration basin volume

Given

∅c = 20 days

Y = 0.8Ib VSS/Ib BOD

Q = 0.3 mgd

So = 120 mg/l

Se = 2 mg/l

X = 5000 mg/l

Kd = 0.04 per day

attached below is the detailed solution

B) Determine the detention time using this relation

t = ( V / Q )* 24

  = ( 0.062 / 0.3 ) * 24  = 4.96 hours

C ) Determine Vss and Tss

we first calculate the excess biomass Px then assuming Vss ratio to be 80% for sludge age of 20 days

Vss = 131.21 IbVss/day

Tss = 164 IbTss/day

D ) determine BOD loading

  Q = 0.3 mgd , BOD = 220mg/l , V = 8288.77 cu.ft

solution attached below

e) food to microorganism ratio

F/M  = 0.2

solution attached below

f) determine the waste solid

waste solid = Q * SS * % removal of suspended solids

where : Q = 0.3 , SS = 220mgl , % = 50 %

waste solids = 0.3 * 230 * 0.5 * 8.34  = 287.23 Ib/day

the reaction of 4A+3B→2C+D is studied. Unknown masses of the reactants were mixed . After a reaction time of 1 hour the analysis of the mixture showed 2 kmol, 1 kmol of B and 4 kmol of C. product D was present in the mixture but could not be analysed. what is the mole fraction of D in the mixture?

Answers

Answer: the mole fraction of D in the mixture is 0.2222

Explanation:

Given that;

mixture analysis shows 2 kmol A, 1 kmol B, 4 kmol C and some unknown kmol of D was present.

4A+3B→2C+D

As from reaction stoichiometry, for every 2 kmol of C produced, kmol of D produced = 1 kmol

so, for 4 kmol C, kmol of D produced = 4/2 × 1 kmol = 2 kmol

Now our mixture has 2 kmol A, 1 kmol B, 4 kmol C and also 2 kmol of D

so, total moles in mixture, we have (2 + 1 + 4 + 2) kmol = 9 kmol

mole fraction of D in mixture  will be;

( Kmol of D) / (total moles in mixture) = 2 / 9 = 0.2222

Therefore the mole fraction of D in the mixture is 0.2222

A 8-core machine has 4 times the performance of a single-core machine of the same frequency. Performance is proportional to frequency. Voltage decreases proportionally to frequency. To achieve the same performance, how much (in percentage) dynamic power would the 8-core system save?

Answers

Answer: The 8-core machine saves  87.5% of the dynamic power.

Explanation:

Let Fold = f , Vold = V , Cold = Capacitance

so

Old Dynamic power = Cold × (Vold × Vold) × f

therefore for the 8-core machine

 Fnew / Fold = 1/4

Fnew = Fold/4

we were told that Voltage decreases proportional to frequency,

so

Vnew / Vold = 1/4

Vnew = V / 4

So New Capacitance will be;

Cnew = Cold

Thus, New Dynamic power = 8 × Cnew × ( Vnew × Vnew ) ×  Fnew

= 8 × Cold × (Vold × Vold/16) × ( f/4 )

=  8 × ( Cold ) × ( Vold × Vold ) × ( f ) / 64

= (Old Dynamic Power) / 8

therefore

Old Dynamic Power / New Dynamic Power = 8

Thus, Percentage of power saved will be;

Percentage power saved = 100 × ( Old Dynamic Power - New Dynamic Power ) / Old Dynamic Power

=   100 × (8-1) / 8

= 87.5 %

Therefore The 8-core machine saves  87.5% of the dynamic power.

At 800K, a plot of ln[cyclobutane] vs t gives a straight line with a slope of -1.6 s-1. Calculate the time needed for the concentration of cyclobutane to fall to 1/16 of its initial value.

Answers

Answer:

hmmm.........

Explanation:

Indicate similarities between a nucleus and a liquid droplet; why small droplets are stable and very big droplets are not?

Answers

Answer:

There are several similarities between the nucleus and a liquid droplet.

Explanation:

A droplet of liquid simply is is very small or tiny drop of liquid. It is also considered as a tiny column of liquid that is surrounded by surfaces that have zero shear stress.

A nucleus on the other hand is an assembly between protons and neutrons. The latter is electrically charged whilst the former is positively charged. The number of protons present in an element is very crucial to the qualities of an element.

The main similarities between a nucleus and a liquid droplet are:

1. a nucleus consists of a large amount of neutrons and protons in the same volume as would a liquid which contains large numbers of molecules in the same volume;

2. both the nucleus and the droplet are similar for their homogeneity in electric charge and density;

3. the molecules exert the same amount for forces towards one another as would the nuclear forces in the nucleons.

4. both of them cannot be compressed

5. both molecules and nucleus are can be subject to nuclear fission which simply mean the breaking apart into smaller units (in the case of the nucleus) or the breaking apart into smaller droplets in the case of the liquid molecule.

6. There are two types of phenomena which occurs in both the liquid droplet and the nucleus which are similar to one another. They are:

Evaporation (in the case of the liquid molecule) and reaction emission (in the case of the nucleus). In evaporation, particles are lost, in Atomic transmutation, particles are lost as well.

B)  the forces which determine the stability of droplets are surface tension and gravitation. The smaller the area, the stronger the surface tension available to keep the drops from going out of shape.

Cheers

For a 3-Phase, Wye connected system the Line to Line Voltage measures 12,470 Volts, the Phase current measures 120 Amps.

Required:
a. What will the Line-to-Neutral/Phase voltage be?
b. What will the Line current be?

Answers

Answer:

A. 7199.55 volts

B. 120A

Explanation:

In this question we have the

line voltage = VLL = 12470volts

Phase current = Iph = 120 amps

A.)

We are to calculate the line-to-neutral/phase voltage here

VLL = √3VL-N

VL-N = VLL/√3

VL-N = 12470/√3

This gives a line to neutral phase/voltage of 7199.55 volts.

B.

We are to calculate the line current here:

In this connection, the line current and the phase current are equal

ILL = Iph = 120A

A laboratory furnace wall is constructed of 0.2 m thick fireclay brick having a thermal conductivity of 1.82 W/m-K. The wall is covered on the outer surface with insulation of thermal conductivity of 0.095 W/m-K. The furnace inner brick surface is at 950 K and the outer surface of the insulation material is at 300 K. The maximum allowable heat transfer rate through the wall of the furnace is 830 W/m^2. Determine how thick in cm the insulation material must be.

Answers

Answer:

The appropriate solution will be "6.4 cm".

Explanation:

The given values are:

Length,

l = 0.2 m

Thermal conductivity,

K₁ = 1.82 W/m-K

K₂ = 0.095 W/m-K

Temperature,

T = 950 K

T = 300 K

Heat transfer rate,

Q = 830 W/m²

Now,

⇒  [tex]Q = \frac{\Delta T}{\frac{L_1}{K_1 A} +\frac{L_2}{K_2 A} }=\frac{A \Delta T}{\frac{L_1}{K_1 } +\frac{L_2}{K_2 } }[/tex]

⇒ [tex]\frac{Q}{A} =\frac{\Delta T}{\frac{L_1}{K_1} +\frac{L_2}{K_2} }[/tex]

On substituting the above given values in the equation, we get

⇒ [tex]830=\frac{(980-300)}{\frac{0.2}{1.82} +\frac{x}{0.095} }[/tex]

On applying cross-multiplication, we get

⇒ [tex]\frac{0.2}{1.82} +\frac{x}{0.095} =\frac{950-300}{830}[/tex]

⇒ [tex]\frac{0.2}{1.82} +\frac{x}{0.095} =\frac{650}{830}[/tex]

⇒                [tex]x =0.639 \ m[/tex]

⇒                [tex]x=6.345 \ i.e., 6.4 \ m[/tex]  

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