Consider the following circuit , where the voltage v(t) is imposed for t 2 0, R 4 Ω, L-1H and C 1/4F. The initial in...
2. Consider the circuit below, where the value of the capacitor is C 1 F, the initial condition is tr (0)--1 volts. Assume the input is the current source i,(t) and the voltage in the capacitor is ve(t) the output. Let the current source be ilt)-ult)- 1F (a) Find the outputv(t) analytically and plot it. (b) Suppose we double the input current, ie. i.(t) = 2(a(t)-u(t-1)), but keep the same initial condition (0). Find the new (t). (c) Can you...
subject: signals and systems 2. Consider the electric circuit shown in Fig. ??, L = 1H, C = 1F. • Determine the differential equation that relates the input (t) to output y(t). Recall that ic(t) = C2C and vy(t) = • Find the characteristic equation for this circuit. • Determine the zero-input response given an initial capacitor voltage of one volt and an initial inductor current of zero ampere. That is, find yo(t) given uc(0) = 2V and iL(0) =...
use R=1Ω, L=1H and C= 1/5 F Instead (c) In the circuit shown in Figure P2.61(c), x(t) is the input voltage. The voltage y(t) across the capacitor is considered to be the system output wwww L 1H R=20 + y(t) x(t) C (c) Figure P2.61c (i) Determine the differential equation relating x(t) and y(t) (ii) Show that the homogeneous solution of the differential equation from part (i) has the forme "{K\ej2 + K2e"j2r}, and specify the value of a (iii...
of linear and time-invariant components with -3(2, C-1/4F, and L-1 H. vs is the input, and vc is the output. a. Calculate the impulse response h(t) b. Calculate the complete response for us (t) = u (t), and initial conditions vc(V, and i(0) 2A. Calculate the sinusoidal steady state response (the response after the circuit has settled for a long time) for the input v(t) = 5cos2t, and same initial conditions as part b. c. R1
12. A series RC circuit is driven by a periodic square wave voltage V(t) with a period T=0.3 sec. V(t) 0 for t<0. After t=0, the voltage alternates between 15 V and 0 V. Assume that R-40 , C 150 HF. We will call the voltage across the capacitor and the resistor Ve(t) and Vr(t) respectively (c) The capacitor above is now replaced by an inductor whose inductance is 0.24 H. We call the voltage across the inductor VL(t) Calculate...
3. Natural response, for ? > 0 of a series R-L-C circuit has R = 1 Ω , L = 1 H and C = 1 F. The initial capacitor voltage is 4 V, and initial inductor current is zero. The series current is i. (i) Draw the time domain circuit. (ii) Draw the Laplace transform domain circuit. (iii) From (ii), determine Io =Io (s) (iv) From (iii), determine ?? = ??(?) for t > 0
Please do the problem if you can do ALL parts. t-0 a SW1 SW2 0.5 Ω 2 1Ω V. R3 20 A T v(t) 0.5 F 0.5 H 0 Find the initial current i(0) through the inductor and the initial voltage v(0) across the capacitor at t 0. b. Write a node equation at node a fort2 0. c. Represent v(t) as a function of i(t) on the series connection of R2 and L. Find dv(t)/dt. Derive a second-order differential...
Problem 1 (Problem Solving Workshop 1) For a parallel RL circuit R-10, L 1H Determine 1) 21 3) 4) The transfer function H(s) = (s), the pole-zero map, and the step response. Let L(0) - OA The state and output equations. Let Lt) be the state variable The block diagram of this system. Let (O) = -1 The response (t) due to a step input (t) = (t) A) using a known software. Problem #2 (Problem Solving Workshop 1) For...
2. In the circuit shown in Figure 2, let C=0.5 F L=1H, R-312. Find the voltage vo(t) for t>0 L volt) Figure 2 2. In the circuit shown in Figure 2, let C=0.5 F L=1H, R-312. Find the voltage vo(t) for t>0 L volt) Figure 2
Problem 4 RI İL(t) For the above circuit C 1F, L 0.25H, R1R2 1.3092 Find: 1) Initial inductor current iu(0') and initial capacitor voltage Vc(0*) 2) The total solution for the voltage vo(t) for> 0. Answer: Vo(t) = 0.5-e-2t + 0.5 e-4t V