The circuit in the figure consists of a resistor (R ohms), an inductor (L henrys), a...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
The circuit in the figure consists of a resistor (R ohms), an inductor (L henrys), a capacitor (C farads), and an initial voltage source. Let b = R/(2L), and suppose R, L, and C have been selected so that b also equals 1/LC. (This is done, for instance, when the circuit is used in a voltmeter.) Let v(t) be the voltage (in volts) at time t, measured across the capacitor. It can be shown that v is in the null space H of the linear transformation that maps v(t) into Lv"(t) + Rv'(t) + (1/C)v(t), and H consists of all functions of the form v (t) = e-b! (c1 + c2t). Find a basis for H. R Voltage source The circuit in the figure consists of a resistor (R ohms), an inductor (L henrys), a capacitor (C farads), and an initial voltage source. Let b = R/(2L), and suppose R, L, and C have been selected so that b also equals 1/LC. (This is done, for instance, when the circuit is used in a voltmeter.) Let v(t) be the voltage (in volts) at time t, measured across the capacitor. It can be shown that v is in the null space H of the linear transformation that maps v(t) into Lv"(t) + Rv'(t) + (1/C)v(t), and H consists of all functions of the form v (t) = e-b! (c1 + c2t). Find a basis for H. R Voltage source
Expert Answer:
Related Book For
Physics
ISBN: 9781119539636
11th edition
Authors: John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler
Posted Date:
Students also viewed these electrical engineering questions
-
The circuit shown in the figure consists of a 100-lossless transmission line terminated in a load with ZL = (50 + j100) . If the peak value of the load voltage was measured to be |V L| =12 V,...
-
The device shown in the figure consists of a pointer ABC supported by a spring of stiffness k = 800 N/m. The spring is positioned at distance b = 150 mm from the pinned end A of the pointer. The...
-
The structure shown in the figure consists of a horizontal rigid bar ABCD supported by two steel wires, one of length L and the other of length 3L/4. Both wires have cross-sectional area A and are...
-
The Qantas Group includes a sustainability report in its annual report. What key performance indicators are included in this report? Explain the different stakeholders that would be interested in...
-
Describe the circumstances in which the three major styles of leadership might be used effectively. Which would you use and why?
-
A 0.5-m3 rigid tank containing hydrogen at 20C and 600 kPa is connected by a valve to another 0.5-m3 rigid tank that holds hydrogen at 30C and 150 kPa. Now the valve is opened and the system is...
-
A rectangular wooden column has the cross section shown. If the column is \(6 \mathrm{ft}\) long and subjected to an axial force of \(P=15\) kip, determine the required minimum dimension \(a\) of its...
-
Four economic classifications of mergers are (1) horizontal, (2) vertical, (3) conglomerate, and (4) congeneric. Explain the significance of these terms in merger analysis with regard to (a) the...
-
A solid cylindrical object has a mass-density of rho = 3000kg/m^3 a radius of 0.05 meters, and a height of0.2m. What is the total mass of this cylinder? What is its mass-moment of inertia of this...
-
A gas containing 50 mol% propylene in propane is to be separated with silica gel having the equilibrium properties shown in Figure. The final products are to be 90 mol% propylene and 75 mol% propane....
-
The salesman at the lot of Smiles Pre-Owned Vehicles told the woman buying the car that it was in "mint condition." Is this an express warranty? Why or why not?
-
Suppose that debit cards, ATMs, ACH transactions, and other forms of electronic funds transfers did not exist. How would this change the way you shop and pay bills? How would transactions costs in...
-
What is the appeal of the eurocurrency market?
-
What is the appeal of trade shows and trade missions for small and medium-sized companies?
-
Governments influence the international flow of trade and foreign direct investment in many ways, such as by forming regional economic groups. Select two market entry modes and answer the question:...
-
What is it called when a company grants another the right to use intangible property for a limited period of time?
-
Consider the expression for the consumption of Type A individuals and Type B individuals that was provided in the lecture notes. In class and in the notes we asserted that Type A individuals receive...
-
A consumer magazine is evaluating five brands of trash compactors for their effectiveness in reducing the volume of typical household products that are discarded. In the experiment, each block...
-
You are planning to make a jump with your motorcycle by driving over a ramp that will launch you at an angle of 30.0 with respect to the horizontal. The front edge of the ramp on which you are...
-
A projectile is launched from ground level at an angle of 12.0 above the horizontal. It returns to ground level. To what value should the launch angle be adjusted, without changing the launch speed,...
-
Electron beams are sometimes used to melt and evaporate metals in order to deposit thin metallic films on surfaces (similar to gold plating). One method is to put the material to be evaporated...
-
Show that for a van der Waals gas, C V is a function only of temperature.
-
Justify the statement with mathematical expression: "For all the gases, the positive and negative values of the Joule-Thomson coefficient do not indicate the attainment of cooling effect and heating...
-
Prove that \(C_{P}-C_{V}=R\) for an ideal gas.
Study smarter with the SolutionInn App