An electric circuit with a resistor, a capacitor, an inductor, and a voltage source can be...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
An electric circuit with a resistor, a capacitor, an inductor, and a voltage source can be described by the ODE $$ \begin {equation) L (dl\over dt} + RI+ (Q\over C} = E(t). \tag (76) \end{equation) $$ where \( LdI/dt) is the voltage drop across the inductor, \(I) is the current (measured in amperes, A), (L) is the inductance (measured in henrys, H). (R) is the resistance (measured in ohms, \(\Omega \)), \(Q) is the charge on the capacitor (measured in coulombs, C). (C) is the capacitance (measured in farads, F), (E(t)\) is the time-variable voltage source (measured in volts, V), and (t) is time (measured in seconds, s). There is a relation between \(I) and (Q): SS \begin{equation) {dQ\over dt} = I\tp \tag (77}\end{equation) SS Equations (76)-(77) is a system two ODES. Solve these for \(L=1 \) H₂ \( E(t)=2\sin omega t \) V, \(\omega^2=3.5\hbox { s}^{-2}\). \(C=0.25 ) C₂ (R=0.2\ \Omega \), \(I(0)=1 \) A, and \(Q(0)=1 C). Use the Forward Euler scheme with \( \Delta t = 2\pi/(60\omega) 1). The solution will, after some time, oscillate with the same period as \(E(t)), a period of ( 2\pi/omega \). Simulate 10 periods. Filename: electric_circuit. Remarks It turns out that the Forward Euler scheme overestimates the amplitudes of the oscillations. The more accurate 4th-order Runge-Kutta method is much better for this type of differential equation model. An electric circuit with a resistor, a capacitor, an inductor, and a voltage source can be described by the ODE $$ \begin {equation) L (dl\over dt} + RI+ (Q\over C} = E(t). \tag (76) \end{equation) $$ where \( LdI/dt) is the voltage drop across the inductor, \(I) is the current (measured in amperes, A), (L) is the inductance (measured in henrys, H). (R) is the resistance (measured in ohms, \(\Omega \)), \(Q) is the charge on the capacitor (measured in coulombs, C). (C) is the capacitance (measured in farads, F), (E(t)\) is the time-variable voltage source (measured in volts, V), and (t) is time (measured in seconds, s). There is a relation between \(I) and (Q): SS \begin{equation) {dQ\over dt} = I\tp \tag (77}\end{equation) SS Equations (76)-(77) is a system two ODES. Solve these for \(L=1 \) H₂ \( E(t)=2\sin omega t \) V, \(\omega^2=3.5\hbox { s}^{-2}\). \(C=0.25 ) C₂ (R=0.2\ \Omega \), \(I(0)=1 \) A, and \(Q(0)=1 C). Use the Forward Euler scheme with \( \Delta t = 2\pi/(60\omega) 1). The solution will, after some time, oscillate with the same period as \(E(t)), a period of ( 2\pi/omega \). Simulate 10 periods. Filename: electric_circuit. Remarks It turns out that the Forward Euler scheme overestimates the amplitudes of the oscillations. The more accurate 4th-order Runge-Kutta method is much better for this type of differential equation model.
Expert Answer:
Answer rating: 100% (QA)
python import numpy as np import matplotlibpyplot as plt Constants L 1 inductance H R 02 resistance ... View the full answer
Related Book For
Organic Chemistry A Short Course
ISBN: 978-1111425562
13th edition
Authors: Harold Hart, Christopher M. Hadad, Leslie E. Craine, David J. Hart
Posted Date:
Students also viewed these programming questions
-
Ida Company produces a handcrafted musical instrument called a gamelan that is similar to a xylophone. The gamelans are sold for $874. Selected data for the companys operations last year follow:...
-
TA T Determine the load in members AC and BC shown in Figure 9. 6 m B 8 m FIGURE 9 100 kg 100x11.81 5 6 e-tan e=36.86
-
The following additional information is available for the Dr. Ivan and Irene Incisor family from Chapters 1-5. Ivan's grandfather died and left a portfolio of municipal bonds. In 2012, they pay Ivan...
-
In Problem 12.4 on page 423, you used the percentage of alcohol to predict wine quality. The data are stored in VinhoVerde. From the results of that problem, b 1 = 0.5624 and Sb 1 = 0.1127. a. At the...
-
The stock chart shows the 3-day, 5-day, and 10-day SMA for 16 consecutive trading days of General Electric Co stock. Examine days 6-16. Identify the crossovers and discuss the implications. oHy 50 48...
-
A local hairdresser bought 450 shares of a cosmetics corporation for $33.50 per share. He sold the shares for $39.01 per share. a. What was the percent increase in the price per share? Round to the...
-
There are 4 rooms and 5 suspects. Involve the board game Clue, which involves a deck of 21 cards: 6 suspects, 6 weapons, and 9 rooms. At the beginning of the game, 1 card of each of the 3 types is...
-
The income statement of Boost Plus, Inc. follows: Additional data follow: a. Acquisition of plant assets is $124,000. Of this amount, $108,000 is paid in cash and $16,000 by signing a note payable....
-
You have earned 0 point(s) out of 0 point(s) thus far. Given that y= sin(2x) if x =, dx = 0.25 find the differential. Round your answer to three decimal places. Your answer
-
Recording a Business Combination Petra Corporation paid $ 8 million in cash to acquire the assets and liabilities of Salisbury Company. Petra also agreed to make an additional cash payment in the...
-
A sample of gas occupies a volume of 260 ml when the temperature is 85C and the pressure is 750mm Hg. Both the temperature and pressure were changed causing the volume occupied by the gas to become...
-
Examine this integrated marketing communication: Which one of the goals from the AIDA model is this communication attempting to accomplish? Explain. VITAL PROTEINS VP AMERICA'S #1 COLLAGEN BRAND VIA...
-
The Earring Market in the New Era Currently, the number of men who buy earrings for their personal use is increasing. Although it usually looks like only one, the presence of men in a market that was...
-
In the US , the average per capita power consumption is about 9 kW . Multiply this value to find the power consumption requirements of the entire US . If the entire population of the world is each...
-
Provide four mnemonic devices for recall of material for Microbiology ' Food and industrial microbiology'' ?
-
Scenario 2 The New Dies The Delinos are excited because the lease on their coffee shop expired in January 2022 and they are going to buy the buildine demolish it and rebuild a bieger coffee shop and...
-
From the following, prepare a chart of accounts. View the list of accounts. Prepare a chart of accounts. Start by selecting the balance sheet accounts, and then complete the chart of accounts by...
-
Horse serum containing specific antibody to snake venom has been a successful approach to treating snakebite in humans. How do you think this anti-venom could be generated? What are some advantages...
-
Chloramphenicol is an antibiotic that is particularly effective against typhoid fever. Its structure is What is the configuration (R,S) at each stereogenic center? NO NHCOCHC2 CH,OH
-
Mutations (caused by radiation, cancer-producing agents, or other means) may replace one base with another or may add or delete a base. What would happen to the protein produced if the sequence UUU...
-
What secondary and tertiary structures are characteristic of globular proteins?
-
When is the cost of capital equal to the cost of equity? Can the cost of capital be equal to the cost of debt?
-
How do you explain the fact that rates of return required by investors may be identical for two groups of totally different activities (oil and IT services for example) as long as they have the same .
-
Will liquidity premiums tend to rise or fall during a crash? Why?
Study smarter with the SolutionInn App