Loose Leaf for Engineering Circuit Analysis Format: Loose-leaf
9th Edition
ISBN: 9781259989452
Author: Hayt
Publisher: Mcgraw Hill Publishers
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Question
Chapter 8, Problem 62E
(a)
To determine
Find an expression for
(b)
To determine
Graph your answer over the range of
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Check out a sample textbook solutionStudents have asked these similar questions
The switch in the circuit in Figure 8 changes position from position b to position a at t=0a) Find and plot vc(t)fort≥0.b) Find i1(t)for t>0c) Find i(t)for t>0d) Find v(t)for t>0.
Figure 8 showsa resistor inductor capacitor (RLC) circuit. The input to the system is
the voltage v(t) and the output of the circuit is the current iz (t).
8
R,
i(t)
iz(t)
v(t)
Ve(t)
R2
Figure 8
a)
Determine differential equations containing i, (t), iz (t) and v. (t) for the
appropriate meshes and nodes.
b) Assuming zero initial conditions
i)
derive Laplace transformations of the differential equations found in a)
ii)
determine the transfer function G(s) =
I2(s)
VIs where l2(s) = L{i2 (t}}
and V(s) = L{v(t}.
8.4 Step-Response Series
RLC Circuits (3)
Example 4
Having been in position for a long time, the
switch in the circuit below is moved to position b
at t = 0. Find v(t) and vR(t) for t > 0.
2.5 H
10Ω
a
ww-
12 V
22
10 V
• Please refer to lecture or textbook for more detail elaboration.
Answer: v(t) = {10 + [(-2cos3.464t – 1.1547sin3.464t)e-2t]} V
VR(t)= [2.31sin3.464t]e-2t V
15
-19
ww
Chapter 8 Solutions
Loose Leaf for Engineering Circuit Analysis Format: Loose-leaf
Ch. 8.1 - For the circuit in Fig. 8.2, what value of...Ch. 8.1 - Noting carefully how the circuit changes once the...Ch. 8.2 - In a source-free series RC circuit, find the...Ch. 8.3 - Prob. 4PCh. 8.3 - Prob. 5PCh. 8.4 - Prob. 6PCh. 8.4 - Prob. 7PCh. 8.4 - Prob. 8PCh. 8.5 - Evaluate each of the following at t = 0.8: (a)...Ch. 8.6 - For the circuit of Fig. 8.37, find vc(t) at t...
Ch. 8.7 - Prob. 11PCh. 8.7 - The voltage source 60 40u(t) V is in series with...Ch. 8.7 - Prob. 13PCh. 8.8 - Prob. 14PCh. 8.8 - Prob. 15PCh. 8 - A source-free RC circuit has R = 4 k and C = 22 F,...Ch. 8 - A source-free RC circuit has v(0) = 12 V and R =...Ch. 8 - The resistor in the circuit of Fig. 8.51 has been...Ch. 8 - Prob. 4ECh. 8 - Prob. 5ECh. 8 - Prob. 6ECh. 8 - Prob. 7ECh. 8 - Prob. 8ECh. 8 - Prob. 9ECh. 8 - The switch in Fig. 8.56 has been closed for a long...Ch. 8 - For the circuit in Fig. 8.56, find (a) the total...Ch. 8 - Design a capacitor-based circuit that can achieve...Ch. 8 - (a) Graph the function f (t) = 10e2t over the...Ch. 8 - The current i(t) flowing through a 1 k resistor is...Ch. 8 - Radiocarbon dating has a similar exponential time...Ch. 8 - For the circuit of Fig. 8.4, compute the time...Ch. 8 - Design a circuit which will produce a current of 1...Ch. 8 - Prob. 18ECh. 8 - Prob. 19ECh. 8 - Referring to the circuit shown in Fig. 8.11,...Ch. 8 - Prob. 21ECh. 8 - With the assumption that the switch in the circuit...Ch. 8 - The switch in Fig. 8.57 has been closed since...Ch. 8 - The switch in the circuit of Fig. 8.58 has been...Ch. 8 - Assuming the switch initially has been open for a...Ch. 8 - (a) Obtain an expression for v(t), the voltage...Ch. 8 - For the circuit of Fig. 8.61, determine ix, iL,...Ch. 8 - Prob. 28ECh. 8 - Prob. 29ECh. 8 - Prob. 30ECh. 8 - Prob. 31ECh. 8 - (a) Obtain an expression for vx as labeled in the...Ch. 8 - Prob. 33ECh. 8 - Prob. 34ECh. 8 - Prob. 35ECh. 8 - Prob. 36ECh. 8 - Prob. 37ECh. 8 - The switch in Fig. 8.70 is moved from A to B at t...Ch. 8 - Prob. 39ECh. 8 - Prob. 40ECh. 8 - Evaluate the following functions at t = 1, 0, and...Ch. 8 - Prob. 42ECh. 8 - Prob. 43ECh. 8 - Prob. 44ECh. 8 - You can use MATLAB to represent the unit-step...Ch. 8 - With reference to the circuit depicted in Fig....Ch. 8 - For the circuit given in Fig. 8.75, (a) determine...Ch. 8 - Prob. 48ECh. 8 - Prob. 49ECh. 8 - You build a portable solar charging circuit...Ch. 8 - The switch in the circuit of Fig. 8.78 has been...Ch. 8 - The switch in the circuit of Fig. 8.78 has been...Ch. 8 - Prob. 53ECh. 8 - Prob. 54ECh. 8 - Prob. 55ECh. 8 - For the circuit represented in Fig. 8.82, (a)...Ch. 8 - Prob. 58ECh. 8 - Prob. 59ECh. 8 - For the circuit given in Fig. 8.85, (a) determine...Ch. 8 - The circuit depicted in Fig. 8.86 contains two...Ch. 8 - Prob. 62ECh. 8 - Prob. 63ECh. 8 - A series RL circuit has a voltage that steps from...Ch. 8 - For the two-source circuit of Fig. 8.89, note that...Ch. 8 - (a) Obtain an expression for iL as labeled in Fig....Ch. 8 - Obtain an expression for i(t) as labeled in the...Ch. 8 - Obtain an expression for i1 as indicated in Fig....Ch. 8 - Plot the current i(t) in Fig. 8.93 if (a) R = 10 ;...Ch. 8 - A dc motor can be modeled as a series RL circuit...Ch. 8 - Prob. 71ECh. 8 - Prob. 72ECh. 8 - A series RC sequentially switched circuit has R =...Ch. 8 - Refer to the circuit of Fig. 8.95, which contains...Ch. 8 - In the circuit of Fig. 8.95, a 3 mF capacitor is...Ch. 8 - Prob. 78E
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- In the circuit shown in the figure, the switch is closed for a long time and is opened at t = 0. According to this:(a) Find i(0+) and v(0+).(b) Find (di(0+))/dt(c) Find i(t) for t>0.arrow_forwardConsider the given circuit. The switch has been closed for a very long time before opening at t=0s. Determine the expression for Io(t) for t≥0 (in ms) and the expression for the inductor voltage for t≥0.arrow_forwardThe switch in the circuit has been closed for a long time before opening at t=0. 1. a) Construct the s-domain equivalent circuit for t>0. 2. b) Find Io. 3. c) Find io for t≥0.arrow_forward
- The switch in the circuit has been closed for a long time prior to being thrown open at t=0. (a) Determine the Time Constant, T. (b) Obtain the expression for v(t) which is valid for t> 0. (c) Using simulation (Multisim), show the graph for v(t) and i(t)| 100 Ω ww i 200 Ω 2nF 4 V t=0 150 Ω wwarrow_forward3. The switch in the following circuit has been in position a for a long time and instantaneously moves to position b at t = 0. a. Determine the current, i (t), with the switch in position a (i.e. for t = 0-). b. Determine i (t) just after the switch moves to b and after a long time (i.e. t= 0* and t = ). c. Determine the time constant, t, for the switch in position b. d. Write out the equation for the i (t), for t> 0. e. Plot the current i (t) for t> 0. a 4kQ 2500 5kn t = 0 12V 15ka 20V | 340mHarrow_forwardFor the circuit below, vs(t) is nonzero only between 0 and 20 ms. (a) Find an expression for i(t) that is valid for all values of t. (b) Find the value of i(t) at t=8 [ms], t=15 [ms], and t =25 [ms]. Vs(t) A 10 [V] -5 [V] 10 [ms] 20 [ms] t Vs (t) 392 i(t) ww 6Ω lllll 10 mHarrow_forward
- a). Find V(t) in the circuit for all time t> 0 and t < 0. Assume that the switch has been open for a long time and is closed at t = 0. 1=0 ww 10 V 40= 0.5 F 3 20arrow_forwardThe switch in the circuit in Fig. below has been open for a long time. At t=0 the switch is closed. The current natural response is io (t) = Ae ; with A is: 16 N 12 0 20 V 80 mHarrow_forward3 Ω www 1 mH moo 200 12 V iz(t) + t=0 R592 vc (t)=1mF The switch in the Figure above is opened for a long time. It is closed at t = 0. Find (a) vc(0), i (0+), ic(0*),v₂(0), di(0*)/dt (b) Type of damping (c) For what value of R will the circuit response become critically damped?arrow_forward
- The parameter values for the circuit are as follows: R=1 kΩ, L=12.5 H, C=2 μF, and Idc=30 mA.1. Find vo(t) for t≥0.2. Find io(t) for t≥0.3. Does your solution for io(t) make sense when t=0? Explain.arrow_forward8.5 From the circuit in the figure, if the switch was initially connected with a resistance of 2Ω for a long time and opened as shown at time t = 0, find i0(t) and v0(t) when t > 0arrow_forwardThe switch in the circuit shown below has been in position a for a long time. At t=0, the switch is moved to position b. a) Find the expression for vc(t) and ic(t) for t≥ 0¹; b) Find the time at which vc(t) = 5V. 4 A www 20 92 a www. 5Ω Vc + b 2 Ω www t=0 C= 0.05 F ic www 8Ωarrow_forward
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