2. The switch in the circuit shown in Figure below has been open for a long time. At t = 0 the switch is closed. Find the expression for a) Calculate the initial and final values of i. b) Calculate the initial and final energy stored in the inductor. c) i(t) when t>0 d) v(t) when t >0+. e) At what time t, the i(t) will be 10A. Answer: (a) 5 A, 20A; (b) 1000 mJ, 16000 mJ ; (c) 20- 15e12.51 A ; (d) 15e12.5t V, t>0+; (e) 32.44 ms. t%3D0 i(i) 20 V v(t) 80 mH

2. The switch in the circuit shown in Figure below has been open for a long time. At t = 0 the switch is closed. Find the expression for a) Calculate the initial and final values of i. b) Calculate the initial and final energy stored in the inductor. c) i(t) when t>0 d) v(t) when t >0+. e) At what time t, the i(t) will be 10A. Answer: (a) 5 A, 20A; (b) 1000 mJ, 16000 mJ ; (c) 20- 15e12.51 A ; (d) 15e12.5t V, t>0+; (e) 32.44 ms. t%3D0 i(i) 20 V v(t) 80 mH

Power System Analysis and Design (MindTap Course List)

6th Edition

ISBN:9781305632134

Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Publisher:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Chapter11: Transient Stability

Section: Chapter Questions

Problem 11.18P

See similar textbooks

Similar questions

Consider the circuit. The switch has been closed for a long time before opening at t=0s. Give the expression for the capacitor current for t≥0 and the total dissipated energy (in μJ) in the 10KΩ resistor 5ms after the switch has been opened.
Let the first order circuit be shown in the following figure:The switch shown is known to change itsstate from open to closed at time t = 0 and that,once this change has occurred, the circuit reaches thesteady state at approximately 4.5 μs.a) Find the expression for the voltage v (t), for all t> 0, and graph, soapproximate, its behavior as a function of time.b) Find the value of the inductance L.
The switch in the circuit has been in position a fora long time. At t=0, the switch moves instantaneously to position band stays there. Find the initial and final values of the capacitorvoltage, the time constant for t≥0, and the expression for thecapacitor voltage for t≥0.
The current in and the voltage across a 5 H inductor are known to be zero for t≤0. The voltage across the inductor is given by the graph shown for t≥0. 1. Derive the expression for the current as a function of time in the intervals 0≤t≤1 s, 1 s≤t≤3 s, 3 s≤t≤5 s, 5 s≤t≤6 s, and 6 s≤t<∞. 2. For t>0, what is the current in the inductor when the voltage is zero? 3. Sketch i versus t for 0≤t<∞.
Now suppose the switch in the circuit in has been inposition b for a long time. At t=0, the switch moves instantaneouslyto position a and stays there. Find the initial and final values of thecapacitor voltage, the time constant for t≥0, and the expression forthe capacitor voltage for t≥0
The switch in the circuit shown has been closed for a long ttme and is opened at t=0. Find: a) v at time t = 0^(-)b) v at time t = 0^(+)c) the time constant (RC)d) the numerical expression for v(t) after the switch has been openede) the initial energy stored in the capacitor f) the length of ttme required to dissipate 50% of the initially stored energy.
1) The circuit shown below is initially, for t < 0, with capacitor C connected to a battery (Vbat = 12 V).The key is switched at t = 0, disconnecting the battery and turning on the capacitor to the rest of the circuit.a)Calculate the circuit current in the time domain, i(t).b) In practice, after how long can the energy stored in the circuit be considered to be irrelevant (close to zero)?
The switch in the circuit shown in FIGURE Q2 has been closed for a long time. At t = 0 the switch is opened. i. With the switch closed, determine the inductor's initial current, i(0) and with the switch opened, determine the inductor's final current, i(∞) and the time constant. ii. Evaluate whether the circuit is a source - free or step response circuit. Hence, determine the inductor's current, i(t) for t > 0 iii. Discuss how the values of the voltage source and resistors in the circuit, affect the inductor's current, i(t).
For the electric circuit shown, the switch has been closedfor a long time before it opens at t = 0. Find the mathematicalexpression for the capacitor voltage vC(t) for t > 0
From the given circuit. Switch S1 is in position A switch S2 is open. Both switches are in these states for a very long time. At t=0, switch S1 moves from position A to B while switch S2 remains open. 10ms after switch S1 moves to position B, switch S2 is closed and remains closed for 20ms only. ANSWER THE FOLLOWING: a.) Expression for the inductor current for 0 ≤ ? < 10??b.) Expression for the inductor current for 10?? ≤ ? < 30?? and 30?? ≤ ? < ∞c.) What is the time (in ms) after switch S1 moves to position B is the current in the inductor equivalent to 30% of the initial value (at ?=0).
Consider the circuit below with V = 20 V, R1 = 100 ohms, R2 = 60 ohms, and L1 = 900 mH. Assume the initial energy stored in the inductor is zero. a. Find the differential equation for the current through the inductor for t greater than zero. (Hint: Find the Thevenin equivalent with respect to the inductor.) b. Find the current through the inductor i(t) based on the solution to the differential equation. c. Find the voltage across the inductor v(t) using the current you found in b. d. Using Laplace transforms, find the voltage across the inductor.
Let be the first-order electric circuit shown in the figure below. It is known that the switch T changes state, from open to closed, at instant t=0 and that, once said switch is activated, the network reaches the stable state after 500 ms a) Find the expression for the voltage v(t), for all t>0b) Find the value of the capacitance Cc) Represent graphically, and approximately, the behavior as a function of time of the voltage found in part a)