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Dmitrij [34]
3 years ago
13

Use phasor techniques to determine the impedance seen by the source given that R = 4 Ω, C = 12 μF, L = 6 mH and ω = 2000 rad/sec

. Then determine the current supplied by the source given that V = 12 <0o v. The equivalent impedance seen by the source is Z = ∠ o Ω. (Round the magnitude to three decimal places and the angle to two decimal places.) The current supplied by the source is I = ∠ o A. (Round the magnitude to three decimal places and the angle to two decimal places.)
Engineering
1 answer:
Zielflug [23.3K]3 years ago
7 0

Answer:

Z = 29.938Ω ∠22.04°

I = 2.494A

Explanation:

Impedance Z is defined as the total opposition to the flow of current in an AC circuit. In an R-L-C AC circuit, Impedance is expressed as shown:

Z² = R²+(Xl-Xc)²

Z = √R²+(Xl-Xc)²

R is the resistance = 4Ω

Xl is the inductive reactance = ωL

Xc is the capacitive reactance =

1/ωc

Given C = 12 μF, L = 6 mH and ω = 2000 rad/sec

Xl = 2000×6×10^-3

Xl = 12Ω

Xc = 1/2000×12×10^-6

Xc = 1/24000×10^-6

Xc = 1/0.024

Xc = 41.67Ω

Z = √4²+(12-41.67)²

Z = √16+880.31

Z = √896.31

Z = 29.938Ω (to 3dp)

θ = tan^-1(Xl-Xc)/R

θ = tan^-1(12-41.67)/12

θ = tan^-1(-29.67)/12

θ = tan^-1 -2.47

θ = -67.96°

θ = 90-67.96

θ = 22.04° (to 2dp)

To determine the current, we will use the relationship

V = IZ

I =V/Z

Given V = 12V

I = 29.93/12

I = 2.494A (3dp)

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Explanation:

There are three points in time we need to consider.  At point 0, the mango begins to fall from the tree.  At point 1, the mango reaches the top of the window.  At point 2, the mango reaches the bottom of the window.

We are given the following information:

y₁ = 3 m

y₂ = 3 m − 2.4 m = 0.6 m

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a = -9.8 m/s²

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Use a constant acceleration equation:

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Evaluated at point 2:

0.6 = y₀ + (0) t₂ + ½ (-9.8) t₂²

0.6 = y₀ − 4.9 t₂²

Solve for y₀ in the first equation and substitute into the second:

y₀ = 3 + 4.9 t₁²

0.6 = (3 + 4.9 t₁²) − 4.9 t₂²

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We know t₂ = t₁ + 0.4:

0 = 2.4 + 4.9 (t₁² − (t₁ + 0.4)²)

0 = 2.4 + 4.9 (t₁² − (t₁² + 0.8 t₁ + 0.16))

0 = 2.4 + 4.9 (t₁² − t₁² − 0.8 t₁ − 0.16)

0 = 2.4 + 4.9 (-0.8 t₁ − 0.16)

0 = 2.4 − 3.92 t₁ − 0.784

0 = 1.616 − 3.92 t₁

t₁ = 0.412

Now we can plug this into the original equation and find y₀:

3 = y₀ − 4.9 t₁²

3 = y₀ − 4.9 (0.412)²

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7 0
3 years ago
Steam enters an adiabatic turbine at 10 MPa and 500°C and leaves at 10 kPa with a quality of 90 percent. Neglecting the changes
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Answer:

The mass flow rate of steam m=5.4 Kg/s

Explanation:

Given:

  At the inlet of turbine P=10 MPa  ,T=500 C

 AT the exit of turbine  P=10 KPa   ,x=0.9

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From steam table

<u> At 10 MPa and 500 C:</u>

  h=3374 KJ/Kg  ,s=6.59 KJ/Kg-K  (Super heated steam table)

<u>At 10 KPa:</u>

h_g=2675.1 KJ/Kg, h_f=417.51  KJ/Kg

s_g= 7.3  KJ/Kg-K                ,s_f=1.3   KJ/Kg-K

So enthalpy of steam at the exit of turbine

h= h_f+x(h_g- h_f)

Now by putting the values

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h=2449.34  KJ/Kg

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m=5.4 Kg/s

So the mass flow rate of steam m=5.4 Kg/s

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