Problems 7 through 10 deal with the RC circuit in Fig. 3.7.8, containing a resistor (R ohms), a capacitor (C farads), a switch, a source of emf, but no inductor Substitution of
for the charge
Suppose that in the circuit of Fig. 3.7.8, we have
Want to see the full answer?
Check out a sample textbook solutionChapter 3 Solutions
Differential Equations: Computing and Modeling (5th Edition), Edwards, Penney & Calvis
Additional Engineering Textbook Solutions
Digital Fundamentals (11th Edition)
Starting Out with C++: Early Objects (9th Edition)
Starting Out with Programming Logic and Design (4th Edition)
Objects First with Java: A Practical Introduction Using BlueJ (6th Edition)
Starting Out with Java: From Control Structures through Data Structures (3rd Edition)
Starting Out with Java: From Control Structures through Objects (7th Edition) (What's New in Computer Science)
- 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…arrow_forwardDetermine the transfer function, of the rotational mechanical system shown in T(s) Figure Q2. The variables 6,(t) and 02(t) refer to angular displacement of motion, while T(t) is a torque applied to the system. Given the value of spring, damping coefficient and inertia as; J: 5 kg-m? Di: 5 N-m-s/rad J2: 10 kg-m? K : 6 N-m/rad K2 : 5 N-m/rad D::4 N-m-s/rad D3:2 N-m-s/rad T(t) e,(1) D2 K2 0000 D1 D3 Figure Q2arrow_forward1) Given the sinusoidal voltage v(t) 50 cos(30t + 10°) V, find: (a) the amplitude Vm, (b) the period T, (c) the frequency f, and (d) v(t) at t= 10 ms.arrow_forward
- PROBLEM 24 - 0589: A forced oscillator is a system whose behavior can be described by a second-order linear differential equation of the form: ÿ + Ajý + A2y (t) = (1) where A1, A2 are positive %3D E(t) constants and E(t) is an external forcing input. An automobile suspension system, with the road as a vertical forcing input, is a forced oscillator, for example, as shown in Figure #1. Another example is an RLC circuit connected in series with an electromotive force generator E(t), as shown in Figure #2. Given the initial conditions y(0) = Yo and y(0) = zo , write a %3D FORTRAN program that uses the modified Euler method to simulate this system from t = 0 to t = tf if: Case 1: E(t) = h whereh is %3D constant Case 2: E(t) is a pulse of height h and width (t2 - t1) . Case 3: E(t) is a sinusoid of amplitude A, period 2n/w and phase angle p . E(t) is a pulse train Case 4: with height h, width W, period pW and beginning at time t =arrow_forwardQ1) In the circuit of Fig. (1), if a copper wire of length 5 m and diameter 2 mm is used, find the resistivity of the wire. 20 V P=80mW Rarrow_forwardFind the differential equation from the transfer of the function for the Giving following system and draw the block diagram of the system. 3 H = x(s) u(s) 0.5s + 1arrow_forward
- Logic Function F (x, y, z, w) = ∑ m (0,2,4,6,10,13) + ∑ k (8,12) as sum of minimers are given. (Note: There are terms that are not taken into account.) a. Obtain the Truth Table. b. Simplify with the Karnough Map approach. c. Draw the simplified Logic circuit with two input AND-NOT (NAND) gates. With how many apples you realized, what is your gain? Comment.arrow_forwardProblem (1) For the circuit shown in fig. find the current supplied by the battery by using delta/star transformation 400 www 2002 500 30 V 2002 www 30Ω www 5Ω wwarrow_forwardAns [3.43A , 0.506 , 2.12A , 0.942] Q16/ The star-connected rotor of a 3-phase induction motor has a resistance and standstill reactance 0.4 Q/phase respectively. The e.m.f. induced between the slip rings at standstill is 80V, the stator being connected to a normal supply voltage. Find the rotor current and power factor at starting when the rings are (i) short-circuited (ii) joined to star-connected Ans [18.25A , 0.16,7.76 , 0.91] resistance of 52/phase.arrow_forward
- In the Bohr model of the hydrogen atom, an electron in the 4th excited state moves at a speed of 1.37 x 105 m/s in a circular path of radius 8.46 x 1010 m. What is the effective current associated with this orbiting electron? 4.12373E3 Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. mAarrow_forwardB) Solve the differential equation by using Laplace transform y" - y = -t² y(0)=2 and y'(0)=0arrow_forwardwhere is it demonstrated that the Hamiltonian circuit's tour length is, at most, 4/3 times that of the ideal TSP trip.arrow_forward
- C++ for Engineers and ScientistsComputer ScienceISBN:9781133187844Author:Bronson, Gary J.Publisher:Course Technology Ptr