(5) Consider the application of Ohm's law and Kirchhoff's law to a given electrical net-work. The potential applied between two of the nodes in the network is V volts. We wishto find the potentials at several nodes within the network. Denoting these potentials byU1, U2, U6, we obtain the following set of equations for the v; values:11v1 - 5v2v6 = 5V, -20v₁ + 41v2 - 15v3 - 6v5 = 0, -3v2+7v3 - 4v4 = 0,--V3 +2v4v5 = 0, -3v2-10v4 + 28v5 - 1506(a) Write this linear system in matrix-vector form.=--0, 2v1 15v5 + 47v6= 0.(b) Set V50 and use the software for solving linear systems that was introduced in therecitation to solve this system.

Step 1: Step 2:MATLAB code% Define the coefficient matrix A A = [11, -5, 0, 0, 0, -1; -20, 41,…

Answered: (5) Consider the application of Ohm's…

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter11: Nonlinear Programming

Section11.10: Quadratic Programming

Problem 7P

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3. You have seen how Kirchhoff's laws were used in your lectures to obtain a 2nd order differential equation where we solved for the current. This time we will use an even simpler concept: principle of conservation of energy to derive the 2nd order differential equation where we will solve for the charge. Take a look at the circuit below. IHE 2F In the circuit above, we have a capacitor with capacitance 2 F, an inductor of inductance 5 H and a resistor of 32 (a) The total energy that is supplied to the resistor is LI? E = 2 Q? 20 where L is the inductance, I is the current, C is the capacitance and Q is the charge. Write down the total energy supplied E in terms of Q and t only. OP Remember that I = dt (b) Now you know that the power dissipation through a resistor is -1R. Use the conservation of energy (energy gain rate = energy loss rate) to derive the differential equation in terms Q and t only. (c) Solve the differential equation for initial charge to be Qo with a initial current of…
Electromagnetic Pulse propagating at oblique angle to a dielectric interface Consider a gaussian wave pulse propagating along the z-axis from region 1 with refractive index n1 and onto a dielectric interface y = m z (for all x). To the left of this dielectric interface, the refractive index is n2. Devise an initial value computer algorithm to determine the time evolution of the reflected and transmitted electromagnetic fields for this pulse. e.g., n1 = 1 , n2 = 2 initial profile (t = 0, with z0 < 0) Ex = E0 exp[-a (z-z0)^2] By = n1 * Ex Choose parameters so that the pulse width is at least a fact of 8 less than the z- domain of integration ( -L < z < L). For the slope of the interface, one could choose m = 1.
2. calculates the trajectory r(t) and stores the coordinates for time steps At as a nested list trajectory that contains [[xe, ye, ze], [x1, y1, z1], [x2, y2, z2], ...]. Start from time t = 0 and use a time step At = 0.01; the last data point in the trajectory should be the time when the oscillator "hits the ground", i.e., when z(t) ≤ 0; 3. stores the time for hitting the ground (i.e., the first time t when z(t) ≤ 0) in the variable t_contact and the corresponding positions in the variables x_contact, y_contact, and z_contact. Print t_contact = 1.430 X_contact = 0.755 y contact = -0.380 z_contact = (Output floating point numbers with 3 decimals using format (), e.g., "t_contact = {:.3f}" .format(t_contact).) The partial example output above is for ze = 10. 4. calculates the average x- and y-coordinates 1 y = Yi N where the x, y, are the x(t), y(t) in the trajectory and N is the number of data points that you calculated. Store the result as a list in the variable center = [x_avg, y_avg]…
An aluminum wire having a cross-sectional area equal to 4.60 x 10-6 m? carries a current of 7.50 A. The density of aluminum is 2.70 g/cm³. Assume each aluminum atom supplies one conduction electron per atom. Find the drift speed of the electrons in the wire. 1.95E-4 The equation for the drift velocity includes the number of charge carriers per volume, which in this case is equal to the number of atoms per volume. How do you calculate that if you know the density and the atomic weight of aluminum? mm/s
Suppose we have an 80-lb lead-acid battery. 10% of the weight of the battery is active material on the plates, i.e., we have a total of 8 lb of active Pb and PbO, on the plates that can be used to make electric power. Use the Gibbs free energy method to estimate the total stored energy in the battery. Assume that the open circuit voltage for a lead-acid cell is 2.1 V. [The answer should be a little less than 1 kilowatt-hour of energy.]
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Find the solution.
Questions 1. Special electrical circuits called LC circuits are critical to the operation of the tuning dial on a car radio. The charge Q(t) (measured in units of Coulombs C) in an LC circuit at any given time t (measured in seconds s) subject to a given voltage V(t) (given in Joules per Coulomb, J/C) obeys the expression LQ" (t) + + =—= Q(t) = = V(t) where L, c are given constants depending on the particular design of the circuit. What are the units of L and c? ⚫L and care unit-less. ⚫ The units of L are Js2/C2 and the units of c are J/C². • The units of L are Js2/C2 and the units of c are C²/J. ⚫ The units of L are J/C2 and the units of c are C²/J. ⚫ The units of L are J/C² and the units of c are J/C². 1 of 7 2. Matt collects vinyl records, but he doesn't always keep every record he buys. Let K(t) be the total number of vinyl records Matt has kept from the moment he started collecting up to week t, where t is the number of weeks since January 1, 2024. Which of the statements below is…

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