Combined Reactances:Consider a circuit containing both capacitive and inductive reactance as shown in figure below:
Figure: A Circuit containing a combination of Reactances
With f = 1 kHz ω = 2πf = 2 x 3.14 x 103 = 6280 rad/sec then:jωL = j 6280 x 100 x 10-3 = j 6.28 x 100 = j 628 Ω-j (1/ωC) = - j [1/(6280 x 0.47 x 10-6)] = - j [(106)/(6.28 x 0.47 x 103)] = -j 339 ΩThen the impedance as observe by the source voltage is as follows:
Current drawn from the source is provided by:i(t) = V(t)/Z = (10∠0o)/(304 ∠21.6o) = 32.9 ∠-21.6o mAVoltage across the resistor in parallel with the inductor is as:VR = VL = i(t) ZR//L = i(t) (283 + j451)By using the above computations. With,|ZR//L| = √2832 + 4512 = 532? ∠ΦR//L = Tan-1 (451/283) = 57.9oVR = VL = i(t) ZR//L = 32.9∠-21.6o x 10-3 x 532∠57.9oVR = VL = 17.5 ∠36.3o VThe currents flowing via each of the individual branches are as:iR = VR/R = (17.5 ∠36.3o )/103 = 17.5∠36.3o mAiL = VL/jωL = (17.5 ∠36.3o)/628∠90o = 27.9 ∠-57.3o mAThe only outstanding quantity that remains unknown is the voltage across capacitor that is given as:VC = V – VL = 10 ∠0o – 17.5 ∠36.3oThe evaluation of VC requires VL expressed in the complex terms from below figure gives:
Figure: Argand Diagram for VL
a = Real(VL) = |VL|cosΦLjb = Imag (VL) = j|VL|sinΦLVL = |VL| cosΦL + j|VL|sinΦLVL = 17.5 cos 36.3 + j 17.5 sin 36.3 Then,VL = 17.5 x 0.8059 + j17.5 x 0.5920VL = 14.1 + j 10.36Then,VC = V – VL = 10 - 14.1 – j10.36 = - 4.1- j10.36And hence finally:|V| = √ (4.1)2 + (10.36)2 = 11.14 V∠ΦC = Tan-1 (-10.36/-4.1) = 68.4o – 180o = -111.6oThe fact that both real and imaginary coefficients of VC are negative should be accounted for which is done by comprising the -180o rotation to place this vector in third quadrant. The whole phasor diagram exhibiting all currents and voltages is given in figure shown below.
Figure: A Complete Phasor Diagram for the Circuit of first figure
Kirchhoff’s Laws:Kirchoff’s laws can be applied to the ac circuits in a similar way to dc circuits. The major difference is that the sources and impedances encompass to be treated as the complex quantities. The values for currents and voltages and can be computed as complex quantities first and transformed into the form of phase and magnitude at the end. Consider the circuit shown in figure below where the frequency and component values have been selected to give round figures for the values of reactance. Such can then be treated as purely imaginary impedances. Such circuit is analysed by using Nodal Analysis by applying the Kirchhoff’s Current Law to node(s) of interest.
Figure: An AC Circuit Requiring Complex Phasor Analysis
jωL = j 2 Π f L = j 6.28 x 50 x 470 x 10-3 = j3K Ω- j (1/ωC) = - j (1/2 Π f C ) = -j [(109)/(2 x 3.14 x 50 x 80)] = -j2K ΩDetermine both the potential at Node A and the current via the inductor, in terms of phase and magnitude.(i) Allocate the currents i1, i2 and i3 at Node A as shown(ii) By applying the Kirchhoff’s Current Law at Node A gives: i1 + i2 = i3(iii) Substituting in terms of potential drops across the components provides:
{(V1 - VA)/R} + {(V2 - VA)/-j(1/ωC)} = VA/jωL
{(V1 - VA)/103} + {(V2 - VA)/(-j2 x 103)} = VA/(j3 x 103)
Replacing and multiplying across by 103[(10 - VA)/1] + [(j5 – VA)/-j2] = (VA/j3)10 – VA + j2 (5/2) – j (VA/2) = -j (VA/3)10 - 2.5 = VA + j 0.5 VA – j 0.33 VA7.5 = VA (1 + j 0.17)VA = 7.5/(1+ j 0.17)Rationalising:VA = [7.5 (1- j 0.17)]/[ (1+ j 0.17) (1- j 0.17)] = [7.5 (1- j 0.17)]/[1 + (0.17)2]VA = (7.5 – j 1.275)/(1.03)VA = 7.28 – j1.24Then, |VA| = √(7.28)2 + (1.24)2 = 7.38∠ΦA = Tan-1 – (1.24/7.28) = -9.7oThe current via the inductor is i3 that can be obtained as:i3 = VA/jωL = (7.28 – j1.24)/(j3 x 103) = - j2.43 – 0.41mA|i3| = √(0.41)2 + (2.43)2 = 2.46 mA∠Φ3 = Tan-1 (-2.43/-0.41) = 80.3o – 180o = -99.7oPhasor diagram:
Latest technology based Electrical Engineering Online Tutoring Assistance
Tutors, at the www.tutorsglobe.com, take pledge to provide full satisfaction and assurance in Electrical Engineering help via online tutoring. Students are getting 100% satisfaction by online tutors across the globe. Here you can get homework help for Electrical Engineering, project ideas and tutorials. We provide email based Electrical Engineering help. You can join us to ask queries 24x7 with live, experienced and qualified online tutors specialized in Electrical Engineering. Through Online Tutoring, you would be able to complete your homework or assignments at your home. Tutors at the TutorsGlobe are committed to provide the best quality online tutoring assistance for Electrical Engineering Homework help and assignment help services. They use their experience, as they have solved thousands of the Electrical Engineering assignments, which may help you to solve your complex issues of Electrical Engineering. TutorsGlobe assure for the best quality compliance to your homework. Compromise with quality is not in our dictionary. If we feel that we are not able to provide the homework help as per the deadline or given instruction by the student, we refund the money of the student without any delay.
tutorsglobe.com orthopedics assignment help-homework help by online bones and joints tutors
Population genetics tutorial all along with the key concepts of History of Population Genetics, study of allele frequency, emergence of modern evolutionary synthesis, Population genetics as a discipline
Let us recognize the main characteristics of computer. These characteristics can be discussed within the headings of speed, versatility, accuracy, diligence and memory.
tutorsglobe.com kingdom plantae assignment help-homework help by online kingdom system of classification tutors
metals-general characteristics tutorial all along with the key concepts of physical properties of metals, chemical properties of metals, occurrence of metals in nature, electrochemical or activity series, extraction of metals
www.tutorsglobe.com offers classification and assembly structures homework help, assignment help, case study, writing homework help, online tutoring assistance by computer science tutors.
Theory and lecture notes of Creating Grouped Frequency Distributions all along with the key concepts of Lists and Statistics, STATS Key, STAT-EDIT, STAT-CALC, LIST Key, LIST-OPS, LIST-MATH. Tutorsglobe offers homework help, assignment help and tutor’s assistance on Creating Grouped Frequency Distributions.
The Cell Cycle tutorial all along with the key concepts of Interphase, Mitosis, Four Phases of Mitosis, Significance of Mitosis, Meiosis, Significance of Meiosis
The radar antenna or dish sends pulses of radio waves or microwaves that bounce off any object in their path.
tutorsglobe.com gene therapy assignment help-homework help by online modern genetics tutors
nucleus and radioactivity tutorial all along with the key concepts of the nucleus, nuclear reactions, radioactivity, nuclear radiations, radioactivity uses and hazards of radioactivity
www.tutorsglobe.com tutorials - assignment help: various elements or components of a system, introduction of a system in programming languages,
www.tutorsglobe.com offers substituted cyclohexane compounds homework help, substituted cyclohexane compounds assignment help, online tutoring assistance, organic chemistry solutions by online qualified tutor's help.
The chairman should attempt to make sure that the board operates like an effectual decision making body and that board meetings are conducted in a business-like manner.
a good insulating material has to possess the following characteristics - extremely high insulation resistance, high dielectric strength, low thermal expansion.
1952865
Questions Asked
3689
Tutors
1486884
Questions Answered
Start Excelling in your courses, Ask an Expert and get answers for your homework and assignments!!