1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
blagie [28]
3 years ago
13

A series R-L circuit is given. Circuit is connected to an AC voltage generator. a) Derive equations for magnitude and phase of c

urrent and voltages on resistor and inductor in the phasor domain. Assume that the resistance of the resistor is R, inductance of the inductor is L, magnitude of the source voltage is Vm and phase of the source voltage is θ. Note that you don’t have numbers in this step, so to find the magnitude and phase for current I and voltages VR and VL you must first derive both numerator and denominator in polar form using variables R, omega, L, Vm, Vphase (do not use numbers). The solutions should look like equations in slide 24/27! b) In this step, assume that R
Engineering
1 answer:
igomit [66]3 years ago
6 0

Answer:

The equations for magnitude and phase of current and voltages on resistor and inductor are:

I=\frac{V_m}{\sqrt{R^2+(\omega L)^2}}\angle \theta - tan^{-1}(\omega L / R)

V_R=I\cdot Z_R=\frac{V_m \cdot R}{\sqrt{R^2+(\omega L)^2}}\angle \theta - tan^{-1}(\omega L / R)

V_L=I\cdot Z_L=\frac{V_m \cdot (\omega L)}{\sqrt{R^2+(\omega L)^2}}\angle \theta - tan^{-1}(\omega L / R)+90^{\circ}

Explanation:

The first step is to find the impedances of the resistance (R) and the inductor (L).

The impedance of the resistor is:

  • Rectangular form: Z_R=R
  • Polar form: Z_R=R\angle 0^{\circ}

The impedance of the inductor is:

  • Rectangular form: Z_L=j\omega L
  • Polar form: Z_L=\omega L \angle 90^{\circ}

Where \omega is the angular frequency of the source, and the angle is 90^{\circ} because a pure imaginary number is on the imaginary axis (y-axis).

The next step is to find the current expression. It is the same for the resistor and inductor because they are in series. The total impedance equals the sum of each one.

I=\frac{V}{Z_R+Z_L}

It is said that V=V_m\angle \theta, so, the current would be:

I=\frac{V_m\angle \theta }{R+j\omega L}

The numerator must be converted to polar form by calculating the magnitude and the angle:

  • The magnitude is \sqrt{R^2+(\omega L)^2}
  • The angle is tan^{-1}(\omega L / R)

The current expression would be as follows:

I=\frac{V_m\angle \theta }{\sqrt{R^2+(\omega L)^2}\, \angle tan^{-1}(\omega L / R)}

When dividing, the angles are subtracted from each other.

The final current expression is:

I=\frac{V_m}{\sqrt{R^2+(\omega L)^2}}\angle \theta - tan^{-1}(\omega L / R)

The last step is calculating the voltage on the resistor V_R and the voltage on the inductor V_L. In this step the polar form of the impedances could be used. Remember that V=I\cdot Z.

(Also remember that when multiplying, the angles are added from each other)

Voltage on the resistor V_R

V_R=I\cdot Z_R=\bigg( \frac{V_m}{\sqrt{R^2+(\omega L)^2}}\angle \theta - tan^{-1}(\omega L / R)\bigg) \cdot (R\angle 0^{\circ})

The final resistor voltage expression is:

V_R=I\cdot Z_R=\frac{V_m \cdot R}{\sqrt{R^2+(\omega L)^2}}\angle \theta - tan^{-1}(\omega L / R)

Voltage on the inductor V_L

V_L=I\cdot Z_L=\bigg( \frac{V_m}{\sqrt{R^2+(\omega L)^2}}\angle \theta - tan^{-1}(\omega L / R)\bigg) \cdot (\omega L \angle 90^{\circ})

The final inductor voltage expression is:

V_L=I\cdot Z_L=\frac{V_m \cdot (\omega L)}{\sqrt{R^2+(\omega L)^2}}\angle \theta - tan^{-1}(\omega L / R)+90^{\circ}

Summary: the final equations for magnitude and phase of current and voltages on resistor and inductor are:

I=\frac{V_m}{\sqrt{R^2+(\omega L)^2}}\angle \theta - tan^{-1}(\omega L / R)

V_R=I\cdot Z_R=\frac{V_m \cdot R}{\sqrt{R^2+(\omega L)^2}}\angle \theta - tan^{-1}(\omega L / R)

V_L=I\cdot Z_L=\frac{V_m \cdot (\omega L)}{\sqrt{R^2+(\omega L)^2}}\angle \theta - tan^{-1}(\omega L / R)+90^{\circ}

You might be interested in
For the SR-latch below high levels of Set and Reset result in Q= 1 and 0, respectively. The next state is unknown when both inpu
dusya [7]

Answer:

hello your question lacks the required image attached to this answer is the image required

answer :  NOR1(q_) wave is complementary to NOR2(q)

Explanation:

Note ; NOR 2 will be addressed as q in the course of this solution while NOR 1 will be addressed as q_

Initial state is unknown i.e q = 0 and q_= 1

from the diagram the waveform reset and set

= from 0ns to 20ns reset=1 and set=0.from the truth table considering this given condition q=0 and q_bar=1 while  

from 30ns to 50ns reset=0 and set=1.from the truth table considering this condition q=1 and q_bar=1.so from 35ns also note there is a delay of 5 ns for the NOR gate hence the NOR 2 will be higher ( 1 )

From 50ns to 65ns both set and reset is 0.so NOR2(q)=0.

From 65 to 75 set=1 and reset=0,so our NOR 2(q)=1 checking from the truth table

also  from 75 to 90 set=1 and reset=1 , NOR2(q) is undefined "?" and is mentioned up to 95ns.

since q_ is a complement of q, then NOR1(q_) wave is complementary to NOR2(q)

3 0
2 years ago
The temperature of an electric welding arc is about?
N76 [4]

Answer:

The heat of the arc melts the surface of the base metal and the end of the electrode. The electric arc has a temperature that ranges from 3,000 to 20,000 °C

Explanation:

Welding fumes are complex mixtures of particles and ionized gases.

7 0
3 years ago
For the unity negative feedback system G(s) = K(s+6)/ (s + 1)(s + 2)(s + 5) It's known that the system is operating with a domin
Ad libitum [116K]

Answer:The awnser is 5

Explanation:Just divide all of it

4 0
2 years ago
Give me an A please!!!¡!!!!¡
Andrei [34K]

Answer:

I am in 6th grade why am i in high school things.

Explanation:

8 0
3 years ago
The human eye, as well as the light-sensitive chemicals on color photographic film, respond differently to light sources with di
jeka57 [31]

Answer:

a) at T = 5800 k  

  band emission = 0.2261

at T = 2900 k

  band emission = 0.0442

b) daylight (d) = 0.50 μm

    Incandescent ( i ) =  1 μm

Explanation:

To Calculate the band emission fractions we will apply the Wien's displacement Law

The ban emission fraction in spectral range λ1 to λ2 at a blackbody temperature T can be expressed as

F ( λ1 - λ2, T ) = F( 0 ----> λ2,T) - F( 0 ----> λ1,T )

<em>Values are gotten from the table named: blackbody radiati</em>on functions

<u>a) Calculate the band emission fractions for the visible region</u>

at T = 5800 k  

  band emission = 0.2261

at T = 2900 k

  band emission = 0.0442

attached below is a detailed solution to the problem

<u>b)calculate wavelength corresponding to the maximum spectral intensity</u>

For daylight ( d ) = 2898 μm *k / 5800 k  = 0.50 μm

For Incandescent ( i ) = 2898 μm *k / 2900 k = 1 μm

3 0
2 years ago
Other questions:
  • Steam flows at steady state through a converging, insulated nozzle, 25 cm long and with an inlet diameter of 5 cm. At the nozzle
    11·1 answer
  • Write a program to control the operation of the RED/GREEN/BLUE LED (LED2) as follows: 1. If no button is pressed, the LED should
    15·1 answer
  • CNG is a readily available alternative to
    5·1 answer
  • Block A has a weight of 8 lb. and block B has a weight of 6 lb. They rest on a surface for which the coefficient of kinetic fric
    8·1 answer
  • B1) 20 pts. The thickness of each of the two sheets to be resistance spot welded is 3.5 mm. It is desired to form a weld nugget
    12·1 answer
  • The elastic settlement of an isolated single pile under a working load similar to that of piles in the group it represents, is p
    8·1 answer
  • The primary energy source for the controller in a typical control system is either brainlythe primary energy source for the cont
    10·1 answer
  • Two ball bearings from different manufacturers are being considered for a certain application. Bearing A has a catalog rating of
    10·1 answer
  • A heating element for a cooking appliance is stretched too far during installation. What action can be performed? A. Dispose of
    7·1 answer
  • Which level of acceleration should you use when accelerating on a short highway entry ramp?
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!