QUESTION 3An application of Kirchhoff's Current Law to the circuit with nodal voltages in Figure 2 givesrise to the following simultaneous equations.(a)(b)(c)V. 10 Ohms5 A↑20 OhmswwwV240 Ohms50 OhmsFigure 2V2 A0.15-0.1V₂ -0.05V = 5-0.1 +0.145V₂ -0.025V = 0-0.05V, -0.02V₂ +0.075V = 2Compute the determinant of the matrix Y.Compute the inverse of the matrix Y.By Matrix Inversion method using YV = I, determine the nodal voltages of V₁, V₂ and

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Answered: An application of Kirchhoff's Current…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A 100-L tank was initially empty, but is to be filled with salt-and-water solution. The way the solution is being poured into the tank is through a device the controls the rate at which it is being poured. The controller ensures the solution is being poured at time t (minutes) with the expression (1 + cos(2t)) in liters per minute. It follows that the amount of salt for every liter of the solution being poured at time t (minutes) is described by the expression 0.2(1 + cos(2t)) in kilograms. This implies the rate the salt- and-water solution being poured into the tank alternately gets faster and slower. Determine which of the following differential equation describing the salt concentration S in the solution at any time t. O A. dS dt OB. dS dt OC. dS dt O D. dS dt = 0.2(1 + cos 21) ² = = = -0.2(1 + cos 21) ² 0.2 (1 + cos 21) ² 0.2 2 (1 + cos 21) ²
Assume that an open economy with a floating exchange rate is described by the equations:C = 0.5(Y-T)T= 1000I= 1500 -250rG= 1500NX= 1000 – 250e(M/P)d = 0.5Y – 500rM= 1000S-I= 500 – 250rP= 2r* = 1 a. Solve for NX and e. b. Using the information from parts a. to be part d. above, graphically illustrate on aclearly labelled diagram, the short-run impact of contractionary fiscal policy on theexchange rate and level of output in this small open economy.c. Assuming that the economy adopted a fixed exchange rate system, illustrate on aclearly labelled diagram, the impact of contractionary fiscal policy.
An RLC circuit, as shown in the figure, withresistance R=10 ohms, capacitance C=0.01 farads and an inductor L=0.5 H, it also has a voltage source E(t) = 12 volts. Assuming that at time t=0 there is no charge on the capacitor and no current in the circuit, determine the charge on the capacitor and the current in the circuit from the moment the switch is closed. In solving this exercise you must calculate and present the following: c) Determine the particular solution of the non-homogeneous differential equation qp, posing the simultaneous equations and their corresponding solution to establish the value of the indeterminate coefficients. d) Determine the general solution for the charge on the capacitor, that is, q(t) = qh + qp
Example 4 (Calculator Active): For 0 ≤s ≤ 5000, the total amount a local college spends on printing is related to the number of students enrolled at the school and is modeled by C(s) = 70-32 cos (2000) where s is the number of students enrolled at the college and C is the total cost of printing, in thousands of dollars. At what rate is the total cost of printing changing, in dollars per student, when 2500 students are enrolled at the college?
A tank contains 460 gallons of water and 45 oz of salt. Water containing a salt concentration of 1/7(1+1/4sint) oz/gal flows into the tank at a rate of 9 gal/min, and the mixture in the tank flows out at the same rate. The long-time behavior of the solution is an oscillation about a certain constant level. What is this level? What is the amplitude of the oscillation? Round the values to two decimal places. Plz correct solution.
Question 1 A tank initially holds 200 gal of brine solution containing 3 lb of salt. At t=0, another brine solution containing 3 lb of salt per gallon is poured into the tank at the rate of 6 gal / min, while the well stirred mixture leaves the tank at the same rate. Find the time at which the mixture in the tank contains 6 lb of salt. (A) 0.216 min B) 0.168 min 2.13 min D) 0.02 min
Set 2: A pork roast was taken out of a hardwood smoker when its internal temperature had reached 180 degrees Fahrenheit and it was allowed to rest in a 75 degrees Fahrenheit house for 20 minutes after which its internal temperature had dropped to 170 degrees Fahrenheit. We will assume the temperature of the roast follows Newton's Law of Cooling, T(t) = Ta +(To-Ta)e-kt, where To is the inital temperature, Ta is the ambient temperature, and k is a decay constant. ("Ambient temperature" means the temperature of the space the object is in.) (a) Find the values of To and Ta for this problem. (b) Find the value of k for this problem. Then write down the function T(t) which gives the temper- ature of the pork roast in degrees Fahrenheit as a function of time t in minutes. (c) Find the time at which the roast dropped to 160 degrees Fahrenheit.
Give the solution to the heat equation.
Suppose an RL circuit with a 11 resistor and a 6H inductor is driven by the voltage E(t) est V. If the initial resistor current is I(0) OA, find the current I, the voltages across the inductor E₁ and the resistor ER in terms of time t. A I(t) = = ER(t) EL(t) = = = V V
An RLC circuit, as shown in the figure, withresistance R=10 ohms, capacitance C=0.01 farads and an inductor L=0.5 H, it also has a voltage source E(t) = 12 volts. Assuming that at time t=0 there is no charge on the capacitor and no current in the circuit, determine the charge on the capacitor and the current in the circuit from the moment the switch is closed. In solving this exercise you must calculate and present the following: e) Determine the particular solution of q(t) by establishing the values of the constants C1 & C2, through the application of the initial values. f) Draw the graph of the final solution q(t) obtained (you can use an application and paste the graph).

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