7 ots) 4. (a) The switch in the circuit below closes at t-o. Write the differential...
VO P. 2; The switch in the circuit shown closes at t=o. . (@) First, derive the m to integro-differential equation og that governs the behavior T of the voltage utt), for t>o. (6) Secoed, denive V (s) = Voc IRC s'+l'ac)s+('/20)
7. Given the circuit below. The switch has been opened for a very long time. At t = 0, we close the switch. M 2007 M 100 av ile & 5mH a. What will be the initial current of the inductor at I.(t = 0)? (before switch is closed)? Why? b. What will be the final current of the inductor 1, (t +00)? (after switch has been closed for a long time) Why? C. Find the first order linear differential...
Problem 4 In the circuit shown below, the switch has been opened for a very long time prior to t= 0 and closes at t = 0 and remains closed for a long time. Please find: a) i (0), vc(ot), b) the steady-state voltage across the capacitor in terms of Us, Rı, and R2 c) the steady state current through the inductor in terms of Us, Ry, and R2 d) Write the differential equation for it) in terms of Vs,...
(3) The RL circuit shown in Figure 3 has a switch that is closed att 0. Assume that the circuit has reached steady state prior to the switch closing. You are given R1 1 kQ, R2-10 kQ, R3-R4-100 k2, L 10 mH, Vs-5 V. (a) [15 pts] Calculate the steady-state inductor current before the switch is closed (b) [16 pts] Give the differential equation as an expression of the inductor current fort>0 (i.e. write the differential equation) (c) 13 pts]...
In the circuit shown below in Figure #2, Switch U2 is normally closed and Switch U1 is normally open. At t= 0 seconds switch U1 closes. After 100 milli-seconds have passed, switch U2 opens. Assume the inductor has zero current at t=0 - (before switch U1 closes). Determine the following: a) Rth and τ when switch U1 closes. b) Rth and τ when switch U2 opens. c) the equation for the current through the inductor during the charge cycle. d)...
do not use s domain method ,use only differential equation 3. In the circuit shown, switch 1 has been closed for a long time before it is opened at t 0, and switch 2 has been opened for a long time before it is closed at t = 0. SW2 sw, 0.5Ω R2 1(2 A, 20 A i(t) 0.5 H a. Find the initial voltage v(O)- Vo across the capacitor and initial current through the inductor (0) lo at t...
(4) (10 points) For the circuit shown below, find i(t) after the switch closes at t=0. 140 Ω 18 Ω 60 Ω * 7 0.2 Η 60 Ω 120 ΩΣ
- Switch S Switch S2 42 х. 42 t 0 t-0 100u(t 1F + 4H 20) 40) LOOP 2 LOOP1 Figure 1 0. Before switch St closes, no energy is Switch S2 stays open while switch St closes at t stored in the inductor or capacitor. Namely-i (0- ) = uc ( 0) = 0. (a.) (10 points) Find i(t) when switch S, closes but switch S2 stays open. (b.) (10 points) After a long time or after an appropriate...
i(t) 2e 40,000mA Note this may or may not be the correct solution to the above circuit. Find: Using this value for i,(t), deterrmine Vi(t) 40KO L(t) 400mH <20k it) 40k The initial current through the inductor is 2 mA. Find: Determine the governing differential equation for i(t). You do NOT have to solve the equation. [7 pts] Assume you determined in(t) to be in (t) = 2e- 40,000t mA Note this may or may not be the correct solution...
7. a For the circuit shown below: (a) Determine the time constant. 20K (b) Write the mathematical equation for the current is after the switch is closed. Also, sketch the waveform. (c) Determine the current through the inductor 1.8 us after the switch is closed (d) Find the time it will take the current through the inductor to reach 800 μA.